From 3d3a98e69795ae83007c1ec4cf20a87ee34cf8d3 Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 16 Jan 2014 14:32:45 +0800 Subject: [PATCH 01/19] remove useless file --- bluez/SConstruct | 6 -- bluez/simplescan.c | 49 ------------ fs/SConstruct | 3 - fs/about_stat.cpp | 28 ------- stack/SConstruct | 4 - stack/cstack.c | 180 --------------------------------------------- stack/stack.cpp | 133 --------------------------------- 7 files changed, 403 deletions(-) delete mode 100644 bluez/SConstruct delete mode 100644 bluez/simplescan.c delete mode 100644 fs/SConstruct delete mode 100644 fs/about_stat.cpp delete mode 100644 stack/SConstruct delete mode 100644 stack/cstack.c delete mode 100644 stack/stack.cpp diff --git a/bluez/SConstruct b/bluez/SConstruct deleted file mode 100644 index 9cb6406..0000000 --- a/bluez/SConstruct +++ /dev/null @@ -1,6 +0,0 @@ -print "sudo apt-get install libbluetooth-dev" - -env = Environment(CCFLAGS='-g') -env.ParseConfig('pkg-config --cflags --libs bluez') - -env.Program('simplescan.c') diff --git a/bluez/simplescan.c b/bluez/simplescan.c deleted file mode 100644 index 1a634da..0000000 --- a/bluez/simplescan.c +++ /dev/null @@ -1,49 +0,0 @@ -#include -#include -#include -#include -#include -#include -#include - -int main(int argc, char *argv[]) -{ - inquiry_info *ii = NULL; - int max_rsp, num_rsp; - int dev_id, sock, len, flags; - int i; - char addr[19] = {0}; - char name[248] = {0}; - - dev_id = hci_get_route(NULL); - sock = hci_open_dev(dev_id); - if (dev_id < 0 || sock < 0) { - perror("opening socket"); - exit(1); - } - - len = 8; - max_rsp = 255; - flags = IREQ_CACHE_FLUSH; - ii = (inquiry_info*)malloc(max_rsp * sizeof(inquiry_info)); - - num_rsp = hci_inquiry(dev_id, len, max_rsp, NULL, &ii, flags); - if (num_rsp < 0) - perror("hci_inquiry"); - - for (i = 0; i < num_rsp; i++) { - ba2str(&(ii+i)->bdaddr, addr); - memset(name, 0, sizeof(name)); - if (hci_read_remote_name(sock, &(ii+i)->bdaddr, sizeof(name), - name, 0) < 0) - strcpy(name, "[unknown]"); - printf("%s %s\n", addr, name); - } - - free(ii); - ii = NULL; - close(sock); - sock = -1; - - return 0; -} diff --git a/fs/SConstruct b/fs/SConstruct deleted file mode 100644 index bef207e..0000000 --- a/fs/SConstruct +++ /dev/null @@ -1,3 +0,0 @@ -env = Environment(CCFLAGS='-g') - -env.Program('about_stat.cpp') diff --git a/fs/about_stat.cpp b/fs/about_stat.cpp deleted file mode 100644 index 89d3107..0000000 --- a/fs/about_stat.cpp +++ /dev/null @@ -1,28 +0,0 @@ -#include -#include -#include -#include -#include -#include - -void AboutStat(const char* FilePath) -{ - struct stat Buf; - - if (stat(FilePath, &Buf) != 0) - { - std::cout << "fail to stat " << FilePath << std::endl; - std::cout << strerror(errno) << std::endl; - return; - } - - std::cout << "file: " << FilePath << std::endl; - std::cout << "inode: " << Buf.st_ino << std::endl; -} - -int main(int argc, char* argv[]) -{ - AboutStat(argv[1] ? argv[1] : __FILE__); - - return 0; -} diff --git a/stack/SConstruct b/stack/SConstruct deleted file mode 100644 index c663f7e..0000000 --- a/stack/SConstruct +++ /dev/null @@ -1,4 +0,0 @@ -env = Environment(CCFLAGS='-g') - -env.Program('cstack.c') -env.Program('stack.cpp') diff --git a/stack/cstack.c b/stack/cstack.c deleted file mode 100644 index 368f2f7..0000000 --- a/stack/cstack.c +++ /dev/null @@ -1,180 +0,0 @@ -#include -#include - -typedef struct stack_element { - int data; - struct stack_element *next; -} stack_element_t; - -typedef struct { - /* Return size */ - int (*size)(); - /* Access next element */ - stack_element_t *(*top)(); - /* Insert element */ - void (*push)(); - /* Remove top element */ - void (*pop)(); - void (*travel)(); -} stack_t; - -/* Construct */ -stack_t *stack_init(); -/* Destruct */ -void stack_cleanup(stack_t *stack); - -static int m_count = 0; -/* Begin && Current element */ -static stack_element_t *m_begin_element = NULL; -static stack_element_t *m_current_element = NULL; -static stack_element_t *m_top_element = NULL; - -static int m_size(); -static stack_element_t *m_top(); -static void m_push(int data); -static void m_pop(); -static void m_travel(); -static void m_cleanup(); - -stack_t *stack_init() -{ - stack_t *stack = malloc(sizeof(stack_t)); - - if (stack == NULL) - { - printf("%s fail to malloc\n", __PRETTY_FUNCTION__); - return NULL; - } - stack->size = m_size; - stack->top = m_top; - stack->push = m_push; - stack->pop = m_pop; - stack->travel = m_travel; - - return stack; -} - -static int m_size() -{ - return m_count; -} - -static stack_element_t *m_top() -{ - if (m_top_element == NULL) - m_top_element = m_begin_element; - else - m_top_element = m_top_element->next; - - return m_top_element; -} - -static void m_push(int data) -{ - stack_element_t *tmp = malloc(sizeof(stack_element_t)); - - if (tmp == NULL) - return; - - tmp->data = data; - tmp->next = NULL; - - if (m_begin_element == NULL) - m_begin_element = tmp; - else - m_current_element->next = tmp; - - m_current_element = tmp; - m_count++; -} - -static void m_pop() -{ - stack_element_t *tmp = NULL; - - if (m_begin_element == NULL || m_current_element == NULL) - return; - - tmp = m_begin_element; - while (tmp) - { - if (tmp->next == m_current_element) - { - free(tmp->next); - tmp->next = NULL; - m_current_element = tmp; - m_count--; - break; - } - tmp = tmp->next; - } -} - -static void m_travel() -{ - stack_element_t *tmp = m_begin_element; - - while (tmp) - { - printf("%d\t", tmp->data); - tmp = tmp->next; - } - printf("\n"); -} - -static void m_cleanup() -{ - stack_element_t *tmp = m_begin_element; - - while (tmp) - { - free(tmp); - tmp = tmp->next; - } - m_begin_element = NULL; - m_current_element = NULL; - m_top_element = NULL; -} - -void stack_cleanup(stack_t *stack) -{ - if (stack == NULL) - return; - - m_cleanup(); - stack->size = NULL; - stack->top = NULL; - stack->push = NULL; - stack->pop = NULL; - stack->travel = NULL; - free(stack); - stack = NULL; -} - -int main(int argc, char *argv[]) -{ - stack_t *stack = stack_init(); - int i; - - for (i = 0; i < 10; i++) - { - stack->push(i); - } - printf("DEBUG: top %d\n", stack->top()->data); - printf("DEBUG: top %d\n", stack->top()->data); - printf("DEBUG: top %d\n", stack->top()->data); - printf("DEBUG: size %d\n", stack->size()); - printf("DEBUG: travel\n"); - stack->travel(); - printf("DEBUG: pop\n"); - stack->pop(); - printf("DEBUG: travel\n"); - stack->travel(); - printf("DEBUG: push 66\n"); - stack->push(66); - printf("DEBUG: travel\n"); - stack->travel(); - stack_cleanup(stack); - - return 0; -} diff --git a/stack/stack.cpp b/stack/stack.cpp deleted file mode 100644 index 030634e..0000000 --- a/stack/stack.cpp +++ /dev/null @@ -1,133 +0,0 @@ -#include - -template -class stack_element -{ -public: - stack_element() :next(NULL) {} - T data; - stack_element* next; -}; - -template -class stack -{ -public: - stack() :m_size(0), m_begin_element(NULL), m_current_element(NULL), - m_top_element(NULL) {} - - ~stack() - { - stack_element* tmp = m_begin_element; - - while (tmp) - { - delete tmp; - tmp = tmp->next; - } - - m_begin_element = NULL; - m_current_element = NULL; - m_top_element = NULL; - } - - int size() - { - return m_size; - } - - stack_element* top() - { - if (m_top_element == NULL) - m_top_element = m_begin_element; - else - m_top_element = m_top_element->next; - - return m_top_element; - } - - void push(T data) - { - stack_element* tmp = new stack_element(); - - if (tmp == NULL) - return; - - tmp->data = data; - tmp->next = NULL; - - if (m_begin_element == NULL) - m_begin_element = tmp; - else - m_current_element->next = tmp; - - m_current_element = tmp; - m_size++; - } - - void pop() - { - stack_element* tmp = NULL; - - if (m_begin_element == NULL || m_current_element == NULL) - return; - - tmp = m_begin_element; - while (tmp) - { - if (tmp->next == m_current_element) - { - delete tmp->next; - tmp->next = NULL; - m_current_element = tmp; - m_size--; - break; - } - tmp = tmp->next; - } - } - - void travel() - { - stack_element* tmp = m_begin_element; - - while (tmp) - { - std::cout << tmp->data << '\t'; - tmp = tmp->next; - } - std::cout << std::endl; - } - -private: - int m_size; - stack_element* m_begin_element; - stack_element* m_current_element; - stack_element* m_top_element; -}; - -int main(int argc, char* argv[]) -{ - stack stack_obj; - int i; - - for (i = 0; i < 10; i++) - { - stack_obj.push(i); - } - std::cout << "DEBUG: top " << stack_obj.top()->data << std::endl; - std::cout << "DEBUG: top " << stack_obj.top()->data << std::endl; - std::cout << "DEBUG: top " << stack_obj.top()->data << std::endl; - std::cout << "DEBUG: travel" << std::endl; - stack_obj.travel(); - std::cout << "DEBUG: pop" << std::endl; - stack_obj.pop(); - std::cout << "DEBUG: travel" << std::endl; - stack_obj.travel(); - std::cout << "DEBUG: push 66" << std::endl; - stack_obj.push(66); - std::cout << "DEBUG: travel" << std::endl; - stack_obj.travel(); - - return 0; -} From 2179d92570a6d138e7ef61b928080b74f92c06b0 Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 16 Jan 2014 17:15:06 +0800 Subject: [PATCH 02/19] added Longest Palindromic Substring Part II question directly use github md --- .../longest-palindromic-substring-part-ii.md | 176 ++++++++++++++++++ 1 file changed, 176 insertions(+) create mode 100644 questions/longest-palindromic-substring-part-ii.md diff --git a/questions/longest-palindromic-substring-part-ii.md b/questions/longest-palindromic-substring-part-ii.md new file mode 100644 index 0000000..0f80194 --- /dev/null +++ b/questions/longest-palindromic-substring-part-ii.md @@ -0,0 +1,176 @@ +最长回文子字符串 第二部 +======================= + +给定一个字符串S，找出S中最长的回文子字符串。 + +Note: +This is Part II of the article: Longest Palindromic Substring. Here, we describe an algorithm (Manacher’s algorithm) which finds the longest palindromic substring in linear time. Please read Part I for more background information. +注意： +这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。 + +In my previous post we discussed a total of four different methods, among them there’s a pretty simple algorithm with O(N2) run time and constant space complexity. Here, we discuss an algorithm that runs in O(N) time and O(N) space, also known as Manacher’s algorithm. + +Hint: +Think how you would improve over the simpler O(N2) approach. Consider the worst case scenarios. The worst case scenarios are the inputs with multiple palindromes overlapping each other. For example, the inputs: “aaaaaaaaa” and “cabcbabcbabcba”. In fact, we could take advantage of the palindrome’s symmetric property and avoid some of the unnecessary computations. + +An O(N) Solution (Manacher’s Algorithm): +First, we transform the input string, S, to another string T by inserting a special character ‘#’ in between letters. The reason for doing so will be immediately clear to you soon. + +For example: S = “abaaba”, T = “#a#b#a#a#b#a#”. + +To find the longest palindromic substring, we need to expand around each Ti such that Ti-d … Ti+d forms a palindrome. You should immediately see that d is the length of the palindrome itself centered at Ti. + +We store intermediate result in an array P, where P[ i ] equals to the length of the palindrome centers at Ti. The longest palindromic substring would then be the maximum element in P. + +Using the above example, we populate P as below (from left to right): + +T = # a # b # a # a # b # a # +P = 0 1 0 3 0 1 6 1 0 3 0 1 0 +Looking at P, we immediately see that the longest palindrome is “abaaba”, as indicated by P6 = 6. + +Did you notice by inserting special characters (#) in between letters, both palindromes of odd and even lengths are handled graciously? (Please note: This is to demonstrate the idea more easily and is not necessarily needed to code the algorithm.) + +Now, imagine that you draw an imaginary vertical line at the center of the palindrome “abaaba”. Did you notice the numbers in P are symmetric around this center? That’s not only it, try another palindrome “aba”, the numbers also reflect similar symmetric property. Is this a coincidence? The answer is yes and no. This is only true subjected to a condition, but anyway, we have great progress, since we can eliminate recomputing part of P[ i ]‘s. + +Let us move on to a slightly more sophisticated example with more some overlapping palindromes, where S = “babcbabcbaccba”. + + +Above image shows T transformed from S = “babcbabcbaccba”. Assumed that you reached a state where table P is partially completed. The solid vertical line indicates the center (C) of the palindrome “abcbabcba”. The two dotted vertical line indicate its left (L) and right (R) edges respectively. You are at index i and its mirrored index around C is i’. How would you calculate P[ i ] efficiently? +Assume that we have arrived at index i = 13, and we need to calculate P[ 13 ] (indicated by the question mark ?). We first look at its mirrored index i’ around the palindrome’s center C, which is index i’ = 9. + + +The two green solid lines above indicate the covered region by the two palindromes centered at i and i’. We look at the mirrored index of i around C, which is index i’. P[ i' ] = P[ 9 ] = 1. It is clear that P[ i ] must also be 1, due to the symmetric property of a palindrome around its center. +As you can see above, it is very obvious that P[ i ] = P[ i' ] = 1, which must be true due to the symmetric property around a palindrome’s center. In fact, all three elements after C follow the symmetric property (that is, P[ 12 ] = P[ 10 ] = 0, P[ 13 ] = P[ 9 ] = 1, P[ 14 ] = P[ 8 ] = 0). + + +Now we are at index i = 15, and its mirrored index around C is i’ = 7. Is P[ 15 ] = P[ 7 ] = 7? +Now we are at index i = 15. What’s the value of P[ i ]? If we follow the symmetric property, the value of P[ i ] should be the same as P[ i' ] = 7. But this is wrong. If we expand around the center at T15, it forms the palindrome “a#b#c#b#a”, which is actually shorter than what is indicated by its symmetric counterpart. Why? + + +Colored lines are overlaid around the center at index i and i’. Solid green lines show the region that must match for both sides due to symmetric property around C. Solid red lines show the region that might not match for both sides. Dotted green lines show the region that crosses over the center. +It is clear that the two substrings in the region indicated by the two solid green lines must match exactly. Areas across the center (indicated by dotted green lines) must also be symmetric. Notice carefully that P[ i ' ] is 7 and it expands all the way across the left edge (L) of the palindrome (indicated by the solid red lines), which does not fall under the symmetric property of the palindrome anymore. All we know is P[ i ] ≥ 5, and to find the real value of P[ i ] we have to do character matching by expanding past the right edge (R). In this case, since P[ 21 ] ≠ P[ 1 ], we conclude that P[ i ] = 5. + +Let’s summarize the key part of this algorithm as below: + +if P[ i' ] ≤ R – i, +then P[ i ] ← P[ i' ] +else P[ i ] ≥ P[ i' ]. (Which we have to expand past the right edge (R) to find P[ i ]. +See how elegant it is? If you are able to grasp the above summary fully, you already obtained the essence of this algorithm, which is also the hardest part. + +The final part is to determine when should we move the position of C together with R to the right, which is easy: + +If the palindrome centered at i does expand past R, we update C to i, (the center of this new palindrome), and extend R to the new palindrome’s right edge. +In each step, there are two possibilities. If P[ i ] ≤ R – i, we set P[ i ] to P[ i' ] which takes exactly one step. Otherwise we attempt to change the palindrome’s center to i by expanding it starting at the right edge, R. Extending R (the inner while loop) takes at most a total of N steps, and positioning and testing each centers take a total of N steps too. Therefore, this algorithm guarantees to finish in at most 2*N steps, giving a linear time solution. + + +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 +14 +15 +16 +17 +18 +19 +20 +21 +22 +23 +24 +25 +26 +27 +28 +29 +30 +31 +32 +33 +34 +35 +36 +37 +38 +39 +40 +41 +42 +43 +44 +45 +46 +47 +48 +49 +// Transform S into T. +// For example, S = "abba", T = "^#a#b#b#a#$". +// ^ and $ signs are sentinels appended to each end to avoid bounds checking +string preProcess(string s) { + int n = s.length(); + if (n == 0) return "^$"; + string ret = "^"; + for (int i = 0; i < n; i++) + ret += "#" + s.substr(i, 1); + + ret += "#$"; + return ret; +} + +string longestPalindrome(string s) { + string T = preProcess(s); + int n = T.length(); + int *P = new int[n]; + int C = 0, R = 0; + for (int i = 1; i < n-1; i++) { + int i_mirror = 2*C-i; // equals to i' = C - (i-C) + + P[i] = (R > i) ? min(R-i, P[i_mirror]) : 0; + + // Attempt to expand palindrome centered at i + while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) + P[i]++; + + // If palindrome centered at i expand past R, + // adjust center based on expanded palindrome. + if (i + P[i] > R) { + C = i; + R = i + P[i]; + } + } + + // Find the maximum element in P. + int maxLen = 0; + int centerIndex = 0; + for (int i = 1; i < n-1; i++) { + if (P[i] > maxLen) { + maxLen = P[i]; + centerIndex = i; + } + } + delete[] P; + + return s.substr((centerIndex - 1 - maxLen)/2, maxLen); +} +Note: +This algorithm is definitely non-trivial and you won’t be expected to come up with such algorithm during an interview setting. However, I do hope that you enjoy reading this article and hopefully it helps you in understanding this interesting algorithm. You deserve a pat if you have gone this far! :) + +Further Thoughts: + +In fact, there exists a sixth solution to this problem — Using suffix trees. However, it is not as efficient as this one (run time O(N log N) and more overhead for building suffix trees) and is more complicated to implement. If you are interested, read Wikipedia’s article about Longest Palindromic Substring. +What if you are required to find the longest palindromic subsequence? (Do you know the difference between substring and subsequence?) +Useful Links: +» Manacher’s Algorithm O(N) 时间求字符串的最长回文子串 (Best explanation if you can read Chinese) +» A simple linear time algorithm for finding longest palindrome sub-string +» Finding Palindromes +» Finding the Longest Palindromic Substring in Linear Time +» Wikipedia: Longest Palindromic Substring From 01ed356917b69acb76c96be716ccf172939b2225 Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 16 Jan 2014 17:39:36 +0800 Subject: [PATCH 03/19] to see md effect --- .../longest-palindromic-substring-part-ii.md | 61 +++---------------- {clonegraph => src/clonegraph}/SConstruct | 0 {clonegraph => src/clonegraph}/clonegraph.cpp | 0 {palindrome => src/palindrome}/SConstruct | 0 {palindrome => src/palindrome}/dict.txt | 0 {palindrome => src/palindrome}/find_word.cpp | 0 {palindrome => src/palindrome}/gettysburg.txt | 0 {palindrome => src/palindrome}/helper.cpp | 0 {palindrome => src/palindrome}/palin_num.cpp | 0 {palindrome => src/palindrome}/palin_str.cpp | 0 10 files changed, 7 insertions(+), 54 deletions(-) rename {questions => question}/longest-palindromic-substring-part-ii.md (92%) rename {clonegraph => src/clonegraph}/SConstruct (100%) rename {clonegraph => src/clonegraph}/clonegraph.cpp (100%) rename {palindrome => src/palindrome}/SConstruct (100%) rename {palindrome => src/palindrome}/dict.txt (100%) rename {palindrome => src/palindrome}/find_word.cpp (100%) rename {palindrome => src/palindrome}/gettysburg.txt (100%) rename {palindrome => src/palindrome}/helper.cpp (100%) rename {palindrome => src/palindrome}/palin_num.cpp (100%) rename {palindrome => src/palindrome}/palin_str.cpp (100%) diff --git a/questions/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md similarity index 92% rename from questions/longest-palindromic-substring-part-ii.md rename to question/longest-palindromic-substring-part-ii.md index 0f80194..63fe684 100644 --- a/questions/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -3,12 +3,12 @@ 给定一个字符串S，找出S中最长的回文子字符串。 -Note: -This is Part II of the article: Longest Palindromic Substring. Here, we describe an algorithm (Manacher’s algorithm) which finds the longest palindromic substring in linear time. Please read Part I for more background information. 注意： -这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。 +这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述一个算法（Manacher算法），可以在线性时间内找出最长回文子字符串。请阅读第一部 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多的内幕（傲骄了）。 + +Manacher +![ScreenShot](https://raw.github.com/xiangzhai/goaxel/master/image/ManG490.jpg) -In my previous post we discussed a total of four different methods, among them there’s a pretty simple algorithm with O(N2) run time and constant space complexity. Here, we discuss an algorithm that runs in O(N) time and O(N) space, also known as Manacher’s algorithm. Hint: Think how you would improve over the simpler O(N2) approach. Consider the worst case scenarios. The worst case scenarios are the inputs with multiple palindromes overlapping each other. For example, the inputs: “aaaaaaaaa” and “cabcbabcbabcba”. In fact, we could take advantage of the palindrome’s symmetric property and avoid some of the unnecessary computations. @@ -62,56 +62,7 @@ The final part is to determine when should we move the position of C together wi If the palindrome centered at i does expand past R, we update C to i, (the center of this new palindrome), and extend R to the new palindrome’s right edge. In each step, there are two possibilities. If P[ i ] ≤ R – i, we set P[ i ] to P[ i' ] which takes exactly one step. Otherwise we attempt to change the palindrome’s center to i by expanding it starting at the right edge, R. Extending R (the inner while loop) takes at most a total of N steps, and positioning and testing each centers take a total of N steps too. Therefore, this algorithm guarantees to finish in at most 2*N steps, giving a linear time solution. - -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20 -21 -22 -23 -24 -25 -26 -27 -28 -29 -30 -31 -32 -33 -34 -35 -36 -37 -38 -39 -40 -41 -42 -43 -44 -45 -46 -47 -48 -49 +``` // Transform S into T. // For example, S = "abba", T = "^#a#b#b#a#$". // ^ and $ signs are sentinels appended to each end to avoid bounds checking @@ -161,6 +112,8 @@ string longestPalindrome(string s) { return s.substr((centerIndex - 1 - maxLen)/2, maxLen); } +``` + Note: This algorithm is definitely non-trivial and you won’t be expected to come up with such algorithm during an interview setting. However, I do hope that you enjoy reading this article and hopefully it helps you in understanding this interesting algorithm. You deserve a pat if you have gone this far! :) diff --git a/clonegraph/SConstruct b/src/clonegraph/SConstruct similarity index 100% rename from clonegraph/SConstruct rename to src/clonegraph/SConstruct diff --git a/clonegraph/clonegraph.cpp b/src/clonegraph/clonegraph.cpp similarity index 100% rename from clonegraph/clonegraph.cpp rename to src/clonegraph/clonegraph.cpp diff --git a/palindrome/SConstruct b/src/palindrome/SConstruct similarity index 100% rename from palindrome/SConstruct rename to src/palindrome/SConstruct diff --git a/palindrome/dict.txt b/src/palindrome/dict.txt similarity index 100% rename from palindrome/dict.txt rename to src/palindrome/dict.txt diff --git a/palindrome/find_word.cpp b/src/palindrome/find_word.cpp similarity index 100% rename from palindrome/find_word.cpp rename to src/palindrome/find_word.cpp diff --git a/palindrome/gettysburg.txt b/src/palindrome/gettysburg.txt similarity index 100% rename from palindrome/gettysburg.txt rename to src/palindrome/gettysburg.txt diff --git a/palindrome/helper.cpp b/src/palindrome/helper.cpp similarity index 100% rename from palindrome/helper.cpp rename to src/palindrome/helper.cpp diff --git a/palindrome/palin_num.cpp b/src/palindrome/palin_num.cpp similarity index 100% rename from palindrome/palin_num.cpp rename to src/palindrome/palin_num.cpp diff --git a/palindrome/palin_str.cpp b/src/palindrome/palin_str.cpp similarity index 100% rename from palindrome/palin_str.cpp rename to src/palindrome/palin_str.cpp From fc3f47d335af50ee1216564df08df2cd6996ebdd Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 16 Jan 2014 18:10:58 +0800 Subject: [PATCH 04/19] gotta home to take dinner --- image/ManG490.jpg | Bin 0 -> 29550 bytes .../longest-palindromic-substring-part-ii.md | 23 +++++++++--------- 2 files changed, 11 insertions(+), 12 deletions(-) create mode 100644 image/ManG490.jpg diff --git a/image/ManG490.jpg b/image/ManG490.jpg new file mode 100644 index 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zdPjzpFJpVjRC$>(pzMkX7$00@{{Z!r%ld z7y}p?6j4JO+_LMn*UUTif^*WLmf@QSN6U=h9CyYjqNQ#Y(6tU+x-$}_9=z2bIIjRM O2OR|zQ2r(hWB=J5^A-vK literal 0 HcmV?d00001 diff --git a/question/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md index 63fe684..670822c 100644 --- a/question/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -3,30 +3,29 @@ 给定一个字符串S，找出S中最长的回文子字符串。 -注意： +# 注意 这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述一个算法（Manacher算法），可以在线性时间内找出最长回文子字符串。请阅读第一部 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多的内幕（傲骄了）。 -Manacher +Manacher http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 ![ScreenShot](https://raw.github.com/xiangzhai/goaxel/master/image/ManG490.jpg) +# 提示 +思考你会如何改进比O(N^2)更简单的方法。考虑最坏情况。最坏的情况是输入了多个盘根错节的回文。举个栗子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 -Hint: -Think how you would improve over the simpler O(N2) approach. Consider the worst case scenarios. The worst case scenarios are the inputs with multiple palindromes overlapping each other. For example, the inputs: “aaaaaaaaa” and “cabcbabcbabcba”. In fact, we could take advantage of the palindrome’s symmetric property and avoid some of the unnecessary computations. +# 一个O(N)答案（Manacher算法） +首先，我们在输入的字符串S的每个字符之间添加一个特殊字符'#'，转换成另一个字符串T。这样做的原因马上向你揭晓。 -An O(N) Solution (Manacher’s Algorithm): -First, we transform the input string, S, to another string T by inserting a special character ‘#’ in between letters. The reason for doing so will be immediately clear to you soon. +举个栗子 S = “abaaba” T = “#a#b#a#a#b#a#” -For example: S = “abaaba”, T = “#a#b#a#a#b#a#”. +为了寻找最长回文子字符串，我们需要扩展每个Ti比如Ti-d...Ti+d或者描述为以Ti为圆心，d为半径的圆，构成一个回文。你立马就发现d就是以Ti为圆心的回文长度。 -To find the longest palindromic substring, we need to expand around each Ti such that Ti-d … Ti+d forms a palindrome. You should immediately see that d is the length of the palindrome itself centered at Ti. +我们把中间结果存到数组P中，那么P[i]就等于以Ti为圆心的回文长度。最长回文子字符串就是P中最大的元素。 -We store intermediate result in an array P, where P[ i ] equals to the length of the palindrome centers at Ti. The longest palindromic substring would then be the maximum element in P. - -Using the above example, we populate P as below (from left to right): +使用上面的栗子，我们填充P如下所示（从左向右）： T = # a # b # a # a # b # a # P = 0 1 0 3 0 1 6 1 0 3 0 1 0 -Looking at P, we immediately see that the longest palindrome is “abaaba”, as indicated by P6 = 6. +看P（傲骄了）我们立马找到最长回文是"abaaba"，如P6 = 6所示。 Did you notice by inserting special characters (#) in between letters, both palindromes of odd and even lengths are handled graciously? (Please note: This is to demonstrate the idea more easily and is not necessarily needed to code the algorithm.) 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Gjiy8`^(eUIJov%ZQEIX+qVjILwVS`ooURx7bu4rZ6!tbn<3Ei*Ik`-hS+fjQ`n zY-czdOb5b8S6oZYCVdYA*1;6=?_G`vtD4-Uxf|B9yz(W2=KAC%lg~!n*qI_p1yqxX z5_QN~P~a>f5_d9LE?gQ2@1~Y4)=TE7WjO8;&i=L<6C0$qI?;lcaY_XZVqk+c`BweT zCpI1N-?740+2y)cMkX_}^*0h@+xCW@Ru#3HAjq35-49;8S%}w4XgqS->Yq6h`>cW} z7yYrzw5nqvE^b?h+&Rz`Xj>H!{84SbuTpMUN$^l8n*G29pU~ zNn{#}bB{d!@Z?k{|83%TE49SycCVV`1x5oIa4^bk39HfnpAtUM}cRtb&ZQ~4ZAHgWRaN2i@@&~Z~49r4dTC= zrw4<4IPZ)0a6hoZgKEd%feG5X-%Mo0=&+EhuT=y)pGf(9O_euAzWSi%yVf7CDNx$^ z{r1M?51n`9h+)@W-nHg)D&a{LSMF%xzN7u+3qjcJGD1 zjFv>n1vrsK{P@FCN=l&sN$EwtgI@x-xs=lru+P43h$TINlR+~ zkrcRVU567vRYr2`e@0ApEt`=hB)@ACGG^O*G;BHIH!qxaec9^RsZeCb>6QawM7vos z%!yTyn#7DRLk56$m16l{)Y8)~D@%^dw|mD_EG^-7?q5NvnLQSdH`Ga(4&s9GYh{?L8sP(eHX5%W-Mb zFmW?cCzmCDxt!E|^Mth8xIpOB~?~_+y=)_vexiX`rHmo9QO+GSx zWp?=Xma5gP(ub+#$H53meLIY(Tpnw1Mj^D2JVyiph?D9;AxVEFJYeSL#l^xz3vm?Wb)B()oHv z?Y($opN6ff&v5g=34YUIUkl{%LH6zFD(lp-gFLaih?N_n$aUTo_qs2x@PpT!;EOyG z#CDHLrdH*Nu?JMtf}&^q^2TOe*5#HZ+udQwapp=$9&^hE6x-1v{)M^Fp0Bg7WQNbR zgxZ8P4nvo)Tlvpo+DjAf*h+JYGkA4k%w+g15*Mnhb7N5A_*Y!v$z&Pga~((16E`wM zaJNup+nLLgByK6|8zYwORsGqm;>-aZvI?cqj&%XF$bN+J#azI@(?t(16rJ%INcBt|3jph`ka*3k2nW``?2) z+Wv~@*W4r&tt?0;W76M1BN0XfCuyri-WSqwc@$uzDzK#PYChko4_=T%aaM=??pyJy z6Ps3&`?MGT2xEI 给定一个字符串S，找出S中最长的回文子字符串。 -# 注意 -这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述一个算法（Manacher算法），可以在线性时间内找出最长回文子字符串。请阅读第一部 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多的内幕（傲骄了）。 +## 注意 +这是[最长回文子字符串]: http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读[第一部]: http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多的内幕。 -Manacher http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 -![ScreenShot](https://raw.github.com/xiangzhai/goaxel/master/image/ManG490.jpg) +[Manacher]: http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 -# 提示 -思考你会如何改进比O(N^2)更简单的方法。考虑最坏情况。最坏的情况是输入了多个盘根错节的回文。举个栗子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/ManG490.jpg) -# 一个O(N)答案（Manacher算法） -首先，我们在输入的字符串S的每个字符之间添加一个特殊字符'#'，转换成另一个字符串T。这样做的原因马上向你揭晓。 +## 提示 +思考如何改进比O(N^2)复杂度更简单的算法。考虑最坏情况。最坏的情况是输入了多个盘根错节的回文。举个例子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 -举个栗子 S = “abaaba” T = “#a#b#a#a#b#a#” +## 一个O(N)复杂度答案（Manacher算法） +首先，我们在输入的字符串S的每个字符之间添加一个特殊字符'#'，转换成另一个字符串T。这样做的原因马上揭晓。 -为了寻找最长回文子字符串，我们需要扩展每个Ti比如Ti-d...Ti+d或者描述为以Ti为圆心，d为半径的圆，构成一个回文。你立马就发现d就是以Ti为圆心的回文长度。 +举个例子 S = “abaaba” T = “#a#b#a#a#b#a#” + +为了寻找最长回文子字符串，我们需要扩展Ti，比如Ti - d...Ti + d，以Ti为圆心，d为半径的圆，构成一个回文。d就是以Ti为圆心的回文长度。 我们把中间结果存到数组P中，那么P[i]就等于以Ti为圆心的回文长度。最长回文子字符串就是P中最大的元素。 -使用上面的栗子，我们填充P如下所示（从左向右）： +使用上面的例子，我们填充P如下所示（从左向右）： +``` T = # a # b # a # a # b # a # P = 0 1 0 3 0 1 6 1 0 3 0 1 0 -看P（傲骄了）我们立马找到最长回文是"abaaba"，如P6 = 6所示。 +``` + +看P我们立马找到最长回文是"abaaba"，如P6 = 6所示。 + +在字母之间插入特殊字符#，可以优雅地处理奇数、偶数长度的回文。（请注意：这是为了更方便地论证解题思路，不需要码代码。） -Did you notice by inserting special characters (#) in between letters, both palindromes of odd and even lengths are handled graciously? (Please note: This is to demonstrate the idea more easily and is not necessarily needed to code the algorithm.) +现在，想像一下在回文"abaaba"的中间画一条竖线。数组P中的数字是中心轴对称的。再试另一个回文"aba"，数组中的数字依旧具有相似的轴对称属性。这是巧合吗？在某一特定条件下是这样的，但是，无论如何，我们没有重复计算P[i]，这就是个进步。 -Now, imagine that you draw an imaginary vertical line at the center of the palindrome “abaaba”. Did you notice the numbers in P are symmetric around this center? That’s not only it, try another palindrome “aba”, the numbers also reflect similar symmetric property. Is this a coincidence? The answer is yes and no. This is only true subjected to a condition, but anyway, we have great progress, since we can eliminate recomputing part of P[ i ]‘s. +让我们看一个稍微有点复杂的例子，有很多盘根错节的回文，比如S = "babcbabcbaccba"。 -Let us move on to a slightly more sophisticated example with more some overlapping palindromes, where S = “babcbabcbaccba”. +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table10.png) +上面图片的T由S = "babcbabcbaccba"转换而来。假设你单步调试到数组P部分形成的状态（比如P[i] < P[N]）。竖实线是回文"babcbabcbaccba"的圆心C。两个竖虚线是左L右R边界。你单步调试到索引i轴对称的i’。怎样才能高效地计算P[i]呢？ -Above image shows T transformed from S = “babcbabcbaccba”. Assumed that you reached a state where table P is partially completed. The solid vertical line indicates the center (C) of the palindrome “abcbabcba”. The two dotted vertical line indicate its left (L) and right (R) edges respectively. You are at index i and its mirrored index around C is i’. How would you calculate P[ i ] efficiently? Assume that we have arrived at index i = 13, and we need to calculate P[ 13 ] (indicated by the question mark ?). We first look at its mirrored index i’ around the palindrome’s center C, which is index i’ = 9. From 74fd1333a3ba88ceb3c7554153088a2ab1a52822 Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 23 Jan 2014 20:26:48 +0800 Subject: [PATCH 06/19] update longest palindromic substring part ii --- .../longest-palindromic-substring-part-ii.md | 143 +++++++++--------- 1 file changed, 75 insertions(+), 68 deletions(-) diff --git a/question/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md index 663eb75..609bfb4 100644 --- a/question/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -3,23 +3,23 @@ > 给定一个字符串S，找出S中最长的回文子字符串。 ## 注意 -这是[最长回文子字符串]: http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读[第一部]: http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多的内幕。 +这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读第一部 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多内幕。 -[Manacher]: http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 +Manacher http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/ManG490.jpg) ## 提示 -思考如何改进比O(N^2)复杂度更简单的算法。考虑最坏情况。最坏的情况是输入了多个盘根错节的回文。举个例子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 +思考如何改进O(N^2)时间复杂度的算法。考虑最坏的情况。最坏的情况是输入了多个重复的回文。举个例子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 -## 一个O(N)复杂度答案（Manacher算法） -首先，我们在输入的字符串S的每个字符之间添加一个特殊字符'#'，转换成另一个字符串T。这样做的原因马上揭晓。 +## 一个O(N)时间复杂度解法（Manacher算法） +首先，我们在输入的字符串S的每个字符之间添加一个特殊字符#，转换成另一个字符串T。这样做的原因马上揭晓。 举个例子 S = “abaaba” T = “#a#b#a#a#b#a#” -为了寻找最长回文子字符串，我们需要扩展Ti，比如Ti - d...Ti + d，以Ti为圆心，d为半径的圆，构成一个回文。d就是以Ti为圆心的回文长度。 +为了寻找最长回文子字符串，我们需要扩展Ti，比如Ti - d...Ti + d，以Ti为中心，d为半径的圆，构成一个回文。d就是以Ti为中心的回文长度。 -我们把中间结果存到数组P中，那么P[i]就等于以Ti为圆心的回文长度。最长回文子字符串就是P中最大的元素。 +我们把中间结果存到数组P中，那么P[i]就等于以Ti为中心的回文长度。最长回文子字符串就是P中最大的元素。 使用上面的例子，我们填充P如下所示（从左向右）： @@ -28,106 +28,113 @@ T = # a # b # a # a # b # a # P = 0 1 0 3 0 1 6 1 0 3 0 1 0 ``` -看P我们立马找到最长回文是"abaaba"，如P6 = 6所示。 +看P我们立马找到最长回文"abaaba"，如P6 = 6所示。 在字母之间插入特殊字符#，可以优雅地处理奇数、偶数长度的回文。（请注意：这是为了更方便地论证解题思路，不需要码代码。） -现在，想像一下在回文"abaaba"的中间画一条竖线。数组P中的数字是中心轴对称的。再试另一个回文"aba"，数组中的数字依旧具有相似的轴对称属性。这是巧合吗？在某一特定条件下是这样的，但是，无论如何，我们没有重复计算P[i]，这就是个进步。 +现在，想像在回文"abaaba"的中间画一条竖线。数组P中的数字是中心轴对称的。再测试另一个回文"aba"，数组中的数字依旧具有相似的轴对称属性。这是巧合吗？在某一特定条件下是这样的，但是，我们至少没有重复计算P[i]，这就是个优化。 -让我们看一个稍微有点复杂的例子，有很多盘根错节的回文，比如S = "babcbabcbaccba"。 +让我们看一个稍微有点复杂的例子，有很多重复的回文，比如S = "babcbabcbaccba" ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table10.png) -上面图片的T由S = "babcbabcbaccba"转换而来。假设你单步调试到数组P部分形成的状态（比如P[i] < P[N]）。竖实线是回文"babcbabcbaccba"的圆心C。两个竖虚线是左L右R边界。你单步调试到索引i轴对称的i’。怎样才能高效地计算P[i]呢？ +上面图片的T由S = "babcbabcbaccba"转换而来。假设你单步调试到数组P暂停在（比如P[i] < P[N]）。竖实线是回文"babcbabcbaccba"的中心C。两个竖虚线是左L右R边界。你单步调试到索引i轴对称的i’。怎样才能高效地计算出P[i]呢？ -Assume that we have arrived at index i = 13, and we need to calculate P[ 13 ] (indicated by the question mark ?). We first look at its mirrored index i’ around the palindrome’s center C, which is index i’ = 9. +假设我们已经单步跟踪到索引i = 13，我们需要计算出P[13]（如蓝色问号所示的位置）。我们首先查看在回文中心旁边，它的镜像索引i’，即索引i’ = 9 +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table11.png) -The two green solid lines above indicate the covered region by the two palindromes centered at i and i’. We look at the mirrored index of i around C, which is index i’. P[ i' ] = P[ 9 ] = 1. It is clear that P[ i ] must also be 1, due to the symmetric property of a palindrome around its center. -As you can see above, it is very obvious that P[ i ] = P[ i' ] = 1, which must be true due to the symmetric property around a palindrome’s center. In fact, all three elements after C follow the symmetric property (that is, P[ 12 ] = P[ 10 ] = 0, P[ 13 ] = P[ 9 ] = 1, P[ 14 ] = P[ 8 ] = 0). +上面的两条绿实线表示中心点i和i’的两个回文的重叠区域。我们看中心点C附近的索引i的镜像i’。P[i'] = P[9] = 1。因为回文中心轴对称属性，P[i]也应该等于1。综上所述，很明显P[i] = P[i'] = 1。事实上，中心C之后的P[12] = P[10] = 0, P[13] = P[9] = 1, P[14] = P[8] = 0都满足该特性。 +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table4.png) -Now we are at index i = 15, and its mirrored index around C is i’ = 7. Is P[ 15 ] = P[ 7 ] = 7? -Now we are at index i = 15. What’s the value of P[ i ]? If we follow the symmetric property, the value of P[ i ] should be the same as P[ i' ] = 7. But this is wrong. If we expand around the center at T15, it forms the palindrome “a#b#c#b#a”, which is actually shorter than what is indicated by its symmetric counterpart. Why? +现在我们单步跟踪到索引i = 15。P[i]的值是多少呢？如果我们遵循对称属性，P[i] = P[i'] = 7。但是这就错了。如果我们以T15为中心，构成回文“a#b#c#b#a”，实际上比中心T11的短。为什么？ +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table5.png) -Colored lines are overlaid around the center at index i and i’. Solid green lines show the region that must match for both sides due to symmetric property around C. Solid red lines show the region that might not match for both sides. Dotted green lines show the region that crosses over the center. -It is clear that the two substrings in the region indicated by the two solid green lines must match exactly. Areas across the center (indicated by dotted green lines) must also be symmetric. Notice carefully that P[ i ' ] is 7 and it expands all the way across the left edge (L) of the palindrome (indicated by the solid red lines), which does not fall under the symmetric property of the palindrome anymore. All we know is P[ i ] ≥ 5, and to find the real value of P[ i ] we have to do character matching by expanding past the right edge (R). In this case, since P[ 21 ] ≠ P[ 1 ], we conclude that P[ i ] = 5. +彩色线段重叠在以索引i和i’中心周围。绿实线所表示的区域是以中心C轴对称必须匹配的两条边。红实线所表示的两条边就不一定匹配了。绿虚线所表示的穿越中心的区域。 -Let’s summarize the key part of this algorithm as below: +在两个绿实线区域内的两个子字符串必须完全匹配。穿越中心的区域（绿虚线所示）也必须相对称。注意P[i'] = 7而且所有穿越左边L的回文（红实线所示），就不再遵循回文的对称属性。我们知道的是P[i] ≥ 5，为了找到P[i]的实际值，我们需要扩展右边R来做字符匹配。当P[21] ≠ P[1]这种情况下，我们得出结论P[i] = 5。 +让我们概括该算法的精髓如下： + +``` if P[ i' ] ≤ R – i, then P[ i ] ← P[ i' ] -else P[ i ] ≥ P[ i' ]. (Which we have to expand past the right edge (R) to find P[ i ]. -See how elegant it is? If you are able to grasp the above summary fully, you already obtained the essence of this algorithm, which is also the hardest part. +else P[ i ] ≥ P[ i' ] 这里我们需要扩展右边R来找到P[i] +``` + +该算法是如此的简洁。如果可以抓到上述要害，就完全领悟了该算法的精髓，也是最难理解的部分。 -The final part is to determine when should we move the position of C together with R to the right, which is easy: +最后我们就要决定何时同时向右移动C和R的坐标： + +``` +如果回文的中心i越过了R，我们就将C更新成i，（该回文的新中心），然后把R扩展到新回文的右边。 +``` -If the palindrome centered at i does expand past R, we update C to i, (the center of this new palindrome), and extend R to the new palindrome’s right edge. -In each step, there are two possibilities. If P[ i ] ≤ R – i, we set P[ i ] to P[ i' ] which takes exactly one step. Otherwise we attempt to change the palindrome’s center to i by expanding it starting at the right edge, R. Extending R (the inner while loop) takes at most a total of N steps, and positioning and testing each centers take a total of N steps too. Therefore, this algorithm guarantees to finish in at most 2*N steps, giving a linear time solution. +论时间复杂度，有两种可能性。如果P[i] ≤ R – i，只需一步，我们设P[i]为P[i']。否则，我们从右边R扩展，改变回文的中心变为i。扩展R（线性while循环）需要花费N步，而且确定坐标也需要花费N步。所以，该算法确保在2*N步内，提供了线性时间复杂度的解法。 ``` -// Transform S into T. -// For example, S = "abba", T = "^#a#b#b#a#$". -// ^ and $ signs are sentinels appended to each end to avoid bounds checking +// 将S转换成T +// 比如，S = "abba", T = "^#a#b#b#a#$" +// ^和$符号用来表示开始和结束。 string preProcess(string s) { - int n = s.length(); - if (n == 0) return "^$"; - string ret = "^"; - for (int i = 0; i < n; i++) - ret += "#" + s.substr(i, 1); + int n = s.length(); + if (n == 0) return "^$"; + string ret = "^"; + for (int i = 0; i < n; i++) + ret += "#" + s.substr(i, 1); - ret += "#$"; - return ret; + ret += "#$"; + return ret; } string longestPalindrome(string s) { - string T = preProcess(s); - int n = T.length(); - int *P = new int[n]; - int C = 0, R = 0; - for (int i = 1; i < n-1; i++) { - int i_mirror = 2*C-i; // equals to i' = C - (i-C) + string T = preProcess(s); + int n = T.length(); + int* P = new int[n]; + int C = 0, R = 0; + for (int i = 1; i < n - 1; i++) { + int i_mirror = 2 * C - i; // 等于i' = C - (i-C) P[i] = (R > i) ? min(R-i, P[i_mirror]) : 0; - // Attempt to expand palindrome centered at i + // 扩展回文中心变为i while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) - P[i]++; + P[i]++; - // If palindrome centered at i expand past R, - // adjust center based on expanded palindrome. + // 如果回文中心i超越了R，调整回文的中心 if (i + P[i] > R) { - C = i; - R = i + P[i]; + C = i; + R = i + P[i]; + } } - } - // Find the maximum element in P. - int maxLen = 0; - int centerIndex = 0; - for (int i = 1; i < n-1; i++) { - if (P[i] > maxLen) { - maxLen = P[i]; - centerIndex = i; + // 找出P中的最大值 + int maxLen = 0; + int centerIndex = 0; + for (int i = 1; i < n-1; i++) { + if (P[i] > maxLen) { + maxLen = P[i]; + centerIndex = i; + } } - } - delete[] P; + delete[] P; - return s.substr((centerIndex - 1 - maxLen)/2, maxLen); + return s.substr((centerIndex - 1 - maxLen)/2, maxLen); } ``` -Note: -This algorithm is definitely non-trivial and you won’t be expected to come up with such algorithm during an interview setting. However, I do hope that you enjoy reading this article and hopefully it helps you in understanding this interesting algorithm. You deserve a pat if you have gone this far! :) +注意： +该算法是不凡的，在面试过程中，你可能想不起来该算法。但是，我希望你喜欢阅读这篇文章，有助于理解这个有趣的算法。 -Further Thoughts: +进一步思考： +事实上，针对该题还有第六种解法——使用后缀树。但是，它并不高效O(N log N)，而且构造后缀树的开销也很大，实践起来也更加复杂。如果你感兴趣，可以阅读维基百科有关最长回文子字符串的文章。 +如果让你找出最长回文序列？（你知道子字符串和序列的区别吗？） -In fact, there exists a sixth solution to this problem — Using suffix trees. However, it is not as efficient as this one (run time O(N log N) and more overhead for building suffix trees) and is more complicated to implement. If you are interested, read Wikipedia’s article about Longest Palindromic Substring. -What if you are required to find the longest palindromic subsequence? (Do you know the difference between substring and subsequence?) -Useful Links: -» Manacher’s Algorithm O(N) 时间求字符串的最长回文子串 (Best explanation if you can read Chinese) -» A simple linear time algorithm for finding longest palindrome sub-string -» Finding Palindromes -» Finding the Longest Palindromic Substring in Linear Time -» Wikipedia: Longest Palindromic Substring +有用的链接： +* Manacher算法O(N)求字符串的最长回文子串 http://www.felix021.com/blog/read.php?2040 +* [需要翻墙]一个简单的找最长回文子字符串的线性时间复杂度算法 http://zhuhongcheng.wordpress.com/2009/08/02/a-simple-linear-time-algorithm-for-finding-longest-palindrome-sub-string/ +* [需要翻墙]寻找回文 http://johanjeuring.blogspot.com/2007/08/finding-palindromes.html +* 在线性时间内寻找最长回文子字符串 http://www.akalin.cx/longest-palindrome-linear-time +* 维基百科：最长回文子字符串 http://en.wikipedia.org/wiki/Longest_palindromic_substring From 710c0f43fdc46ec4925b830993dc1f0d4565c02d Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 23 Jan 2014 20:34:47 +0800 Subject: [PATCH 07/19] use makefile instead of scons --- src/palindrome/Makefile | 14 + src/palindrome/SConstruct | 9 - src/palindrome/dict.txt | 45095 --------------------------------- src/palindrome/find_word.cpp | 160 - src/palindrome/helper.cpp | 39 - src/palindrome/palin_str.cpp | 28 +- 6 files changed, 25 insertions(+), 45320 deletions(-) create mode 100644 src/palindrome/Makefile delete mode 100644 src/palindrome/SConstruct delete mode 100644 src/palindrome/dict.txt delete mode 100644 src/palindrome/find_word.cpp delete mode 100644 src/palindrome/helper.cpp diff --git a/src/palindrome/Makefile b/src/palindrome/Makefile new file mode 100644 index 0000000..0051843 --- /dev/null +++ b/src/palindrome/Makefile @@ -0,0 +1,14 @@ +CC=g++ +CFLAGS=-g -O2 -Wall -fPIC +CPPPATH= +LIBPATH= +LIBS= + +all: palin_str + +palin_str: + $(CC) -o palin_str.o -c $(CFLAGS) $(CPPPATH) palin_str.cpp + $(CC) -o palin_str palin_str.o $(LIBPATH) $(LIBS) + +clean: + rm -rf *.o palin_str diff --git a/src/palindrome/SConstruct b/src/palindrome/SConstruct deleted file mode 100644 index 83b1498..0000000 --- a/src/palindrome/SConstruct +++ /dev/null @@ -1,9 +0,0 @@ -env = Environment(CCFLAGS='-g') - -env.Program('palin_str.cpp') - -env.Program('palin_num.cpp') - -env.Program('find_word.cpp') - -env.Program('helper.cpp') diff --git a/src/palindrome/dict.txt b/src/palindrome/dict.txt deleted file mode 100644 index e7ff971..0000000 --- a/src/palindrome/dict.txt +++ /dev/null @@ -1,45095 +0,0 @@ -a -aardvark -aardwolf -abaca -aback -abacus -abaft -abalone -abandon -abandoned -abandonment -abase -abash -abashed -abask -abate -abatement -abatis -abattoir -abaxial -abbacy -abbatial -abbe -abbess -abbey -abbot -abbreviate -abbreviation -abbreviator -abdicate -abdication -abdomen -abdominal -abdominous -abduce -abducent -abduct -abduction -abductor -abeam -abecedarian -abed -abele -abelmosk -abend -aberrance -aberrant -aberration -abet -abettor -abeyance -abeyant -abhor -abhorrence -abhorrent -abide -abiding -abigail -ability -abiogenesis -abject 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-zwitterion -zygapophysis -zygodactyl -zygogenesis -zygoma -zygomatic -zygomorphic -zygosis -zygospore -zygote -zygotene -zymase -zyme -zymogen -zymogenic -zymology -zymoplastic -zymoscope -zymosis -zymosthenic -zymotic diff --git a/src/palindrome/find_word.cpp b/src/palindrome/find_word.cpp deleted file mode 100644 index 9bba2e8..0000000 --- a/src/palindrome/find_word.cpp +++ /dev/null @@ -1,160 +0,0 @@ -#include -#include -#include -#include -#include -#include -#include - -namespace String -{ - bool IsTheChar(std::string str, int c) - { - str.erase(std::remove(str.begin(), str.end(), c), str.end()); - - if (str.size() == 0) - return true; - - return false; - } - - std::string ToLower(std::string str) - { - std::string ret = ""; - std::locale loc; - - for (std::string::size_type i = 0; i < str.size(); ++i) - ret += std::tolower(str[i], loc); - - return ret; - } - - bool CompareByLength(const std::string & l, const std::string & r) - { - if (l.size() < r.size()) - return true; - - return false; - } -}; - -class Dict -{ -public: - Dict(const char* DictFileName, bool isToLower = true, bool SortByLength = true) - { - std::ifstream DictFile(DictFileName); - std::string strLine; - - while (std::getline(DictFile, strLine)) - { - if (String::IsTheChar(strLine, ' ')) - continue; - - if (isToLower) - m_WordList.push_back(String::ToLower(strLine)); - else - m_WordList.push_back(strLine); - } - - if (SortByLength) - { - std::sort(m_WordList.begin(), m_WordList.end(), String::CompareByLength); - std::reverse(m_WordList.begin(), m_WordList.end()); - } - - std::cout << m_WordList.size() << " words" << std::endl; - } - virtual ~Dict() {} - -public: - std::vector getWordList() { return m_WordList; } - - // 4 DEBUG - void printWordList() - { - for (int i = 0; i < m_WordList.size(); i++) - std::cout << m_WordList[i] << std::endl; - } - -private: - std::vector m_WordList; -}; - -bool isInRange(std::map m, int p, int s) -{ - std::map::iterator iter; - - for (iter = m.begin(); iter != m.end(); iter++) - { - if (iter->first <= p) - { - if (p + s <= iter->first + iter->second) - return true; - } - - if (p <= iter->first) - { - if (iter->first <= p + s) - return true; - } - } - - return false; -} - -void solution(std::string str, std::vector WordList) -{ - std::map PosLengthMap; - std::map::iterator PosLengthIter; - std::string NewStr = ""; - int FindPos; - int i; - - for (i = 0; i < WordList.size(); i++) - { - FindPos = String::ToLower(str).find(WordList[i]); - - if (FindPos != std::string::npos) - { - //if (PosLengthMap.find(FindPos) != PosLengthMap.end()) - // continue; - - if (isInRange(PosLengthMap, FindPos, WordList[i].size())) - continue; - PosLengthMap[FindPos] = WordList[i].size(); - } - } - - for (PosLengthIter = PosLengthMap.begin(); - PosLengthIter != PosLengthMap.end(); PosLengthIter++) - { - //std::cout << PosLengthIter->first << " " << PosLengthIter->second << std::endl; - NewStr += str.substr(PosLengthIter->first, PosLengthIter->second) + " "; - } - - std::cout << NewStr << std::endl; -} - -int main(int argc, char* argv[]) -{ - unsigned t0 = clock(); - // START - //========================================================================= - - Dict objDict("dict.txt"); - //objDict.printWordList(); - - std::ifstream file("gettysburg.txt"); - std::string str; - file >> str; - std::cout << str << std::endl; - solution(str, objDict.getWordList()); - - // END - //========================================================================= - unsigned elapsed = clock() - t0; - std::cout << "elapsed " << elapsed << std::endl; - - return 0; -} diff --git a/src/palindrome/helper.cpp b/src/palindrome/helper.cpp deleted file mode 100644 index 6d09ea8..0000000 --- a/src/palindrome/helper.cpp +++ /dev/null @@ -1,39 +0,0 @@ -#include -#include -#include - -int main(int argc, char* argv[]) -{ - if (argc < 2) - { - std::cout << "usage: a.txt" << std::endl; - return 0; - } - - if (access(argv[1], R_OK) != 0) - { - std::cout << argv[1] << " is not available"<< std::endl; - return 0; - } - - std::ifstream OriFile(argv[1]); - std::ofstream NewFile; - std::string strLine; - int nu = 1; - int i; - - NewFile.open("new.dict.txt", std::ofstream::out | std::ofstream::app); - - while (std::getline(OriFile, strLine)) - { - std::cout << nu << ": " << strLine << std::endl; - NewFile << strLine << '\n'; - - for (i = 0; i < 2; i++) - std::getline(OriFile, strLine); - - nu++; - } - - return 0; -} diff --git a/src/palindrome/palin_str.cpp b/src/palindrome/palin_str.cpp index 0bf8fe2..e029987 100644 --- a/src/palindrome/palin_str.cpp +++ b/src/palindrome/palin_str.cpp @@ -5,7 +5,8 @@ std::string m_preProcess(std::string s) { int n = s.length(); - if (n == 0) return "^$"; + if (n == 0) + return "^$"; std::string ret = "^"; for (int i = 0; i < n; i++) ret += "#" + s.substr(i, 1); @@ -17,36 +18,29 @@ std::string m_preProcess(std::string s) std::string Manacher(std::string s) { std::string T = m_preProcess(s); - std::cout << "PreProcessed: " << T << std::endl; + //std::cout << "预处理：" << T << std::endl; int n = T.length(); int* P = new int[n]; int C = 0, R = 0; - for (int i = 1; i < n - 1; i++) - { - int i_mirror = 2 * C - i; // equals to i' = C - (i - C) - + for (int i = 1; i < n - 1; i++) { + int i_mirror = 2 * C - i; // 等于i' = C - (i - C) P[i] = (R > i) ? std::min(R-i, P[i_mirror]) : 0; - - // Attempt to expand palindrome centered at i + // 扩展回文中心点至i while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) P[i]++; - // If palindrome centered at i expand past R, - // adjust center based on expanded palindrome. - if (i + P[i] > R) - { + // 如果回文中心i超与咯R，就调整回文中心。 + if (i + P[i] > R) { C = i; R = i + P[i]; } } - // Find the maximum element in P. + // 找出P的最大元素 int maxLen = 0; int centerIndex = 0; - for (int i = 1; i < n - 1; i++) - { - if (P[i] > maxLen) - { + for (int i = 1; i < n - 1; i++) { + if (P[i] > maxLen) { maxLen = P[i]; centerIndex = i; } From 64e74b36ae006f710664fdb8cf3c9db33d29d28a Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Thu, 23 Jan 2014 20:36:26 +0800 Subject: [PATCH 08/19] update longest palindromic substring part ii --- question/longest-palindromic-substring-part-ii.md | 12 +++++++----- 1 file changed, 7 insertions(+), 5 deletions(-) diff --git a/question/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md index 609bfb4..ced2f62 100644 --- a/question/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -78,7 +78,8 @@ else P[ i ] ≥ P[ i' ] 这里我们需要扩展右边R来找到P[i] // 将S转换成T // 比如，S = "abba", T = "^#a#b#b#a#$" // ^和$符号用来表示开始和结束。 -string preProcess(string s) { +string preProcess(string s) +{ int n = s.length(); if (n == 0) return "^$"; string ret = "^"; @@ -89,7 +90,8 @@ string preProcess(string s) { return ret; } -string longestPalindrome(string s) { +string longestPalindrome(string s) +{ string T = preProcess(s); int n = T.length(); int* P = new int[n]; @@ -125,14 +127,14 @@ string longestPalindrome(string s) { } ``` -注意： +## 注意 该算法是不凡的，在面试过程中，你可能想不起来该算法。但是，我希望你喜欢阅读这篇文章，有助于理解这个有趣的算法。 -进一步思考： +## 进一步思考 事实上，针对该题还有第六种解法——使用后缀树。但是，它并不高效O(N log N)，而且构造后缀树的开销也很大，实践起来也更加复杂。如果你感兴趣，可以阅读维基百科有关最长回文子字符串的文章。 如果让你找出最长回文序列？（你知道子字符串和序列的区别吗？） -有用的链接： +## 有用的链接 * Manacher算法O(N)求字符串的最长回文子串 http://www.felix021.com/blog/read.php?2040 * [需要翻墙]一个简单的找最长回文子字符串的线性时间复杂度算法 http://zhuhongcheng.wordpress.com/2009/08/02/a-simple-linear-time-algorithm-for-finding-longest-palindrome-sub-string/ * [需要翻墙]寻找回文 http://johanjeuring.blogspot.com/2007/08/finding-palindromes.html From 378ead1ac1e20c705a1dacdf89efeddf47e22c4b Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Mon, 27 Jan 2014 10:41:51 +0800 Subject: [PATCH 09/19] add clone graph part i --- question/clone-graph-part-i.md | 36 ++++++++++++++++++++++++++++++++++ src/clonegraph/Makefile | 14 +++++++++++++ src/clonegraph/SConstruct | 5 ----- 3 files changed, 50 insertions(+), 5 deletions(-) create mode 100644 question/clone-graph-part-i.md create mode 100644 src/clonegraph/Makefile delete mode 100644 src/clonegraph/SConstruct diff --git a/question/clone-graph-part-i.md b/question/clone-graph-part-i.md new file mode 100644 index 0000000..cc410b2 --- /dev/null +++ b/question/clone-graph-part-i.md @@ -0,0 +1,36 @@ +# 克隆图 第一部 + +> 克隆一个图。输入的是一个节点指针。返回的是克隆图的节点指针。 + +一个图定义如下： +``` +struct Node { + std::vector neighbors; +} +``` + +## 提示 +遍历一个图有两种方法。你还记得吗？你能说出一个图是有向图还是无向图吗？ + +## 解法 +遍历一个图主要有两种方法：广度优先和深度优先。让我们先来尝试一下广度优先解法，需要一个队列。关于深度优先解法，请看克隆图第二部。 + +广度优先遍历是如何工作的呢？简单，当我们从队列中弹出一个节点，我们拷贝该节点的邻居，并把邻居压入队列。 + +一个直接了当的广度优先遍历似乎可以工作了。但是依旧遗漏了某些细节。比如，我们如何连接克隆图的节点？ + +在我们继续之前，我们首先需要确认该图是否是有向的。如果你注意到上面是如何定义节点的，很明显该图是有向的。为什么？ + +比如，A可以有一个邻居B。所以，我们可以从A遍历到B。一个无向图说明B总是可以遍历回A。在这里是这样的吗？不是的，因为无论B是否可以遍历回A取决与B是否有个邻居是A。 + +B能遍历回A说明该图可能包含一个环。你必须特别注意处理该情况。设想一下你笔试的时候忘记了考虑该情况，之后被你的面试官指出你的代码中存在一个死循环，讨厌！ + +让我们用下面的例子来进一步分析： + +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/graph.png) + +假设该图的起点是A。首先，你生成节点A的一个副本A2，然后发现A只有一个邻居B。你生成B的一个副本B2，然后压入B2成为A2的邻居，连接A2->B2。接下来，你发现B有一个邻居A，你已经生成过A的副本。这里，我们必须注意不能重复生成A的副本，而是压入A2作为B2的邻居，连接B2->A2。但是，我们怎么知道某个节点已经有副本了呢？ + +简单，我们可以使用一个HASH表！当我们拷贝了一个节点，我们把它插入到表里。如果我们之后发现某个节点的邻居已经在表里，我们就不能生成该邻居的副本，而是压入该邻居的副本做为它的副本。所以，该HASH表需要存储KEY-VALUE映射，这里KEY是原图里的某个节点，而VALUE是该节点的副本。 + +我们就不在这里码代码了，请直接看 https://github.com/xiangzhai/leetcode/blob/master/src/clonegraph/clonegraph.cpp diff --git a/src/clonegraph/Makefile b/src/clonegraph/Makefile new file mode 100644 index 0000000..fbe35f6 --- /dev/null +++ b/src/clonegraph/Makefile @@ -0,0 +1,14 @@ +CC=g++ +CFLAGS=-g -O2 -Wall -fPIC -std=c++0x +CPPPATH= +LIBPATH= +LIBS= + +all: clonegraph + +clonegraph: + $(CC) -o clonegraph.o -c $(CFLAGS) $(CPPPATH) clonegraph.cpp + $(CC) -o clonegraph clonegraph.o $(LIBPATH) $(LIBS) + +clean: + rm -rf *.o clonegraph diff --git a/src/clonegraph/SConstruct b/src/clonegraph/SConstruct deleted file mode 100644 index 0631f8a..0000000 --- a/src/clonegraph/SConstruct +++ /dev/null @@ -1,5 +0,0 @@ -env = Environment(CCFLAGS='-g', - CXXFLAGS="-std=c++0x" - ) - -env.Program('clonegraph.cpp') From 8441d87dd3712a92b97ba0fccc487308448f2236 Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Mon, 27 Jan 2014 10:43:23 +0800 Subject: [PATCH 10/19] add missing image --- image/graph.png | Bin 0 -> 1655 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 image/graph.png diff --git a/image/graph.png b/image/graph.png new file mode 100644 index 0000000000000000000000000000000000000000..34c2dd036133833bca2d9a6325a6aa50c2df8b1c GIT binary patch literal 1655 zcmV--28j8IP)Px#1ZP1_K>z@;j|==^1poj532;bRa{vGi!vFvd!vV){sAK>D1`J6=K~#8N?VIa$ z+&Bz{r;z=*Riq%-lWNjTYSTgz{SPKhaS1T*H1YR;lM2- zY2_>j-iy3~AjW|rFUI%ETI3Z2F%A@YF}_#UBCi;TaiGYH@x8JZdBs4C14Ukp@0GR4 zD+Xd5DDq-_udGF0F%aWGkr(5;f7aXl$6w4nW04nPyHnByZL?oFDf1z3UB6qY7fB?b zErdd=HBVOmMc^;>U&v;q(-*yM#&9+DKX z)o83%*FkwIGI-?05};BrXnO4MJPtgShz*gGCr*hB#0y5U$BxZ|-Q5RV41+v88Q!@J 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diff --git a/.gitignore b/.gitignore index bfa139c..6407987 100644 --- a/.gitignore +++ b/.gitignore @@ -17,3 +17,7 @@ *.exe *.out *.app + +# ignore intelliJ files +*.iml +.idea From 356b97301f1b7b619ebbafbb4f47073e1eb22f0c Mon Sep 17 00:00:00 2001 From: Aphroiai Date: Mon, 27 Jan 2014 11:47:12 +0800 Subject: [PATCH 12/19] do some fine-tuning --- question/clone-graph-part-i.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/question/clone-graph-part-i.md b/question/clone-graph-part-i.md index cc410b2..8d53898 100644 --- a/question/clone-graph-part-i.md +++ b/question/clone-graph-part-i.md @@ -15,13 +15,13 @@ struct Node { ## 解法 遍历一个图主要有两种方法：广度优先和深度优先。让我们先来尝试一下广度优先解法，需要一个队列。关于深度优先解法，请看克隆图第二部。 -广度优先遍历是如何工作的呢？简单，当我们从队列中弹出一个节点，我们拷贝该节点的邻居，并把邻居压入队列。 +广度优先遍历是如何工作的呢？简单，当我们从队列中取出一个节点，我们拷贝该节点的邻居，并把邻居压入队列。 一个直接了当的广度优先遍历似乎可以工作了。但是依旧遗漏了某些细节。比如，我们如何连接克隆图的节点？ -在我们继续之前，我们首先需要确认该图是否是有向的。如果你注意到上面是如何定义节点的，很明显该图是有向的。为什么？ +在我们继续之前，我们首先需要确认该图是否是有向的。如果你注意到之前是如何定义节点的，很明显该图是有向的。为什么？ -比如，A可以有一个邻居B。所以，我们可以从A遍历到B。一个无向图说明B总是可以遍历回A。在这里是这样的吗？不是的，因为无论B是否可以遍历回A取决与B是否有个邻居是A。 +比如，A可以有一个邻居B。所以，我们可以从A遍历到B。一个无向图说明B总是可以遍历回A。在这里是这样的吗？不是的，因为B是否可以遍历回A取决与B是否有个邻居是A。 B能遍历回A说明该图可能包含一个环。你必须特别注意处理该情况。设想一下你笔试的时候忘记了考虑该情况，之后被你的面试官指出你的代码中存在一个死循环，讨厌！ @@ -29,7 +29,7 @@ B能遍历回A说明该图可能包含一个环。你必须特别注意处理该 ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/graph.png) -假设该图的起点是A。首先，你生成节点A的一个副本A2，然后发现A只有一个邻居B。你生成B的一个副本B2，然后压入B2成为A2的邻居，连接A2->B2。接下来，你发现B有一个邻居A，你已经生成过A的副本。这里，我们必须注意不能重复生成A的副本，而是压入A2作为B2的邻居，连接B2->A2。但是，我们怎么知道某个节点已经有副本了呢？ +假设该图的起点是A。首先，你生成节点A的一个副本A2，然后发现A只有一个邻居B。你生成B的一个副本B2，然后通过压入B2成为A2的邻居来连接A2->B2。接下来，你发现B有一个邻居A，你已经生成过A的副本。这里，我们必须注意不能重复生成A的副本，而是通过压入A2作为B2的邻居来连接B2->A2。但是，我们怎么知道某个节点已经有副本了呢？ 简单，我们可以使用一个HASH表！当我们拷贝了一个节点，我们把它插入到表里。如果我们之后发现某个节点的邻居已经在表里，我们就不能生成该邻居的副本，而是压入该邻居的副本做为它的副本。所以，该HASH表需要存储KEY-VALUE映射，这里KEY是原图里的某个节点，而VALUE是该节点的副本。 From cb3758f673731ec3d0074f5cac14bab34802a70e Mon Sep 17 00:00:00 2001 From: xiangzhai Date: Mon, 27 Jan 2014 14:41:42 +0800 Subject: [PATCH 13/19] update question --- README.md | 2 +- question/clone-graph-part-i.md | 2 + .../longest-palindromic-substring-part-ii.md | 2 + question/palindrome-number.md | 76 +++++++++++++++++++ 4 files changed, 81 insertions(+), 1 deletion(-) create mode 100644 question/palindrome-number.md diff --git a/README.md b/README.md index e6140ac..6baaf65 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ LeetCode中文 ============ -LeetCodeedoCteeL +翻译 http://www.leetcode.com 的题目 diff --git a/question/clone-graph-part-i.md b/question/clone-graph-part-i.md index 8d53898..6a3ea70 100644 --- a/question/clone-graph-part-i.md +++ b/question/clone-graph-part-i.md @@ -1,5 +1,7 @@ # 克隆图 第一部 +http://leetcode.com/2012/05/clone-graph-part-i.html + > 克隆一个图。输入的是一个节点指针。返回的是克隆图的节点指针。 一个图定义如下： diff --git a/question/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md index ced2f62..01743b6 100644 --- a/question/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -1,5 +1,7 @@ # 最长回文子字符串 第二部 +http://leetcode.com/2011/11/longest-palindromic-substring-part-ii.html + > 给定一个字符串S，找出S中最长的回文子字符串。 ## 注意 diff --git a/question/palindrome-number.md b/question/palindrome-number.md new file mode 100644 index 0000000..d92272a --- /dev/null +++ b/question/palindrome-number.md @@ -0,0 +1,76 @@ +# 回文数 + +http://leetcode.com/2012/01/palindrome-number.html + +> 确定一个整型是否是回文。不能使用额外的空间。 + +在之前的题目中（最长回文子字符串 第一部 第） +In previous posts (Longest Palindromic Substring Part I, Part II) we have discussed multiple approaches on finding the longest palindrome in a string. In this post we discuss ways to determine whether an integer is a palindrome. Sounds easy? + +Hint: +Don’t be deceived by this problem which seemed easy to solve. Also note the restriction of doing it without extra space. Think of a generic solution that is not language/platform specific. Also, consider cases where your solution might go wrong. + +Solution: +First, the problem statement did not specify if negative integers qualify as palindromes. Does negative integer such as -1 qualify as a palindrome? Finding out the full requirements of a problem before coding is what every programmer must do. For the purpose of discussion here, we define negative integers as non-palindromes. + +The most intuitive approach is to first represent the integer as a string, since it is more convenient to manipulate. Although this certainly does work, it violates the restriction of not using extra space. (ie, you have to allocate n characters to store the reversed integer as string, where n is the maximum number of digits). I know, this sound like an unreasonable requirement (since it uses so little space), but don’t most interview problems have such requirements? + +Another approach is to first reverse the number. If the number is the same as its reversed, then it must be a palindrome. You could reverse a number by doing the following: + +``` +int reverse(int num) { + assert(num >= 0); // for non-negative integers only. + int rev = 0; + while (num != 0) { + rev = rev * 10 + num % 10; + num /= 10; + } + return rev; +} +``` +This seemed to work too, but did you consider the possibility that the reversed number might overflow? If it overflows, the behavior is language specific (For Java the number wraps around on overflow, but in C/C++ its behavior is undefined). Yuck. + +Of course, we could avoid overflow by storing and returning a type that has larger size than int (ie, long long). However, do note that this is language specific, and the larger type might not always be available on all languages. + +We could construct a better and more generic solution. One pointer is that, we must start comparing the digits somewhere. And you know there could only be two ways, either expand from the middle or compare from the two ends. + +It turns out that comparing from the two ends is easier. First, compare the first and last digit. If they are not the same, it must not be a palindrome. If they are the same, chop off one digit from both ends and continue until you have no digits left, which you conclude that it must be a palindrome. + +Now, getting and chopping the last digit is easy. However, getting and chopping the first digit in a generic way requires some thought. I will leave this to you as an exercise. Please think your solution out before you peek on the solution below. + +``` +bool isPalindrome(int x) { + if (x < 0) return false; + int div = 1; + while (x / div >= 10) { + div *= 10; + } + while (x != 0) { + int l = x / div; + int r = x % 10; + if (l != r) return false; + x = (x % div) / 10; + div /= 100; + } + return true; +} +``` + +Alternative Solution: +Credits go to Dev who suggested a recursive solution (if extra stack space does not count as extra space), which is pretty neat too. + +``` +bool isPalindrome(int x, int &y) { + if (x < 0) return false; + if (x == 0) return true; + if (isPalindrome(x/10, y) && (x%10 == y%10)) { + y /= 10; + return true; + } else { + return false; + } +} +bool isPalindrome(int x) { + return isPalindrome(x, x); +} +``` From e7d7610214bde6d3da285520cdeef87278ea1010 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=BF=9F=E7=BF=94=20Leslie=20Zhai?= Date: Tue, 28 Jan 2014 12:57:10 +0800 Subject: [PATCH 14/19] update palindrome number --- question/palindrome-number.md | 106 ++++++++++++++++++---------------- 1 file changed, 57 insertions(+), 49 deletions(-) diff --git a/question/palindrome-number.md b/question/palindrome-number.md index d92272a..b19fedb 100644 --- a/question/palindrome-number.md +++ b/question/palindrome-number.md @@ -2,75 +2,83 @@ http://leetcode.com/2012/01/palindrome-number.html -> 确定一个整型是否是回文。不能使用额外的空间。 +> 确定一个整数是否是回文。不能使用额外的空间。 -在之前的题目中（最长回文子字符串 第一部 第） -In previous posts (Longest Palindromic Substring Part I, Part II) we have discussed multiple approaches on finding the longest palindrome in a string. In this post we discuss ways to determine whether an integer is a palindrome. Sounds easy? +在之前的题目中（最长回文子字符串 第一部 第二部）我们讨论过在字符串中寻找最长回文的多种解法。在这道题里，我们讨论确定一个整数是否是回文。听起来容易？ -Hint: -Don’t be deceived by this problem which seemed easy to solve. Also note the restriction of doing it without extra space. Think of a generic solution that is not language/platform specific. Also, consider cases where your solution might go wrong. +## 提示 +不要被忽悠了该题不容易解。还要注意约束条件不能使用额外空间。考虑通用的解法任何语言/平台都支持。也考虑什么情况下你的解法可能出错。 -Solution: -First, the problem statement did not specify if negative integers qualify as palindromes. Does negative integer such as -1 qualify as a palindrome? Finding out the full requirements of a problem before coding is what every programmer must do. For the purpose of discussion here, we define negative integers as non-palindromes. +## 解法 +首先，该题没有描述清楚负数是否属于回文。比如负数-1是否是回文？每个程序员必须在码代码之前弄清楚该题的所有需求。我们在这里讨论的，定义负数不是回文。 -The most intuitive approach is to first represent the integer as a string, since it is more convenient to manipulate. Although this certainly does work, it violates the restriction of not using extra space. (ie, you have to allocate n characters to store the reversed integer as string, where n is the maximum number of digits). I know, this sound like an unreasonable requirement (since it uses so little space), but don’t most interview problems have such requirements? +最直观的解法是首先将整数转换成字符串，那样就更加容易操作。虽然这种解法可以工作，但是它违反了不能使用额外空间的约束。（比如，你需要申请n个字符空间来存储反转后的整数字符串，n是整数的最大位数）我知道，这听上去是不合理的需求（尽管它只使用了很少的空间），但是大多数面试题都会有如此需求吧？ -Another approach is to first reverse the number. If the number is the same as its reversed, then it must be a palindrome. You could reverse a number by doing the following: +另一个解法是首先反转整数。如果原始整数等于反转后的整数，那么它肯定是回文。你可以反转整数如下所示： ``` -int reverse(int num) { - assert(num >= 0); // for non-negative integers only. - int rev = 0; - while (num != 0) { - rev = rev * 10 + num % 10; - num /= 10; - } - return rev; +int reverse(int num) +{ + assert(num >= 0); // 只考虑正整数 + int rev = 0; + while (num != 0) { + rev = rev * 10 + num % 10; + num /= 10; + } + return rev; } ``` -This seemed to work too, but did you consider the possibility that the reversed number might overflow? If it overflows, the behavior is language specific (For Java the number wraps around on overflow, but in C/C++ its behavior is undefined). Yuck. -Of course, we could avoid overflow by storing and returning a type that has larger size than int (ie, long long). However, do note that this is language specific, and the larger type might not always be available on all languages. +这个看上去也能工作，但是你考虑到反转整数有可能溢出吗？如果溢出了，取决于编程语言（Java封装了溢出，但是C/C++就会段错误）。讨厌！ -We could construct a better and more generic solution. One pointer is that, we must start comparing the digits somewhere. And you know there could only be two ways, either expand from the middle or compare from the two ends. +当然，我们可以返回比int（比如long long）存储空间更大的类型来防止溢出。但是，注意这也取决于编程语言，不是所有的编程语言都支持大数据类型。 -It turns out that comparing from the two ends is easier. First, compare the first and last digit. If they are not the same, it must not be a palindrome. If they are the same, chop off one digit from both ends and continue until you have no digits left, which you conclude that it must be a palindrome. +我们可以构造一个更好的更加通用的解法。关键在于，我们必须按位比较。而且你知道只有两种方法，从中间开始或从两端开始比较。 -Now, getting and chopping the last digit is easy. However, getting and chopping the first digit in a generic way requires some thought. I will leave this to you as an exercise. Please think your solution out before you peek on the solution below. +从两端开始比较比较简单。首先，按位比较第一个和最后一个。如果它们不相等，它就不是回文。如果相等，从两端各砍掉一位，继续比较，直到按位比较完所有的数，你就可以得出结论它是回文。 + +获取、砍掉最后一位很简单。但是，如何使用通用方法砍掉第一位。我把这个问题留给你做个练习。请先思考你的解法，在偷看下面的。 ``` -bool isPalindrome(int x) { - if (x < 0) return false; - int div = 1; - while (x / div >= 10) { - div *= 10; - } - while (x != 0) { - int l = x / div; - int r = x % 10; - if (l != r) return false; - x = (x % div) / 10; - div /= 100; - } - return true; +bool isPalindrome(int x) +{ + if (x < 0) + return false; + int div = 1; + while (x / div >= 10) + div *= 10; + while (x != 0) { + int l = x / div; + int r = x % 10; + if (l != r) + return false; + x = (x % div) / 10; + div /= 100; + } + return true; } ``` -Alternative Solution: -Credits go to Dev who suggested a recursive solution (if extra stack space does not count as extra space), which is pretty neat too. +## 另一种解法 +递归解法（如果额外的栈空间不算额外空间）非常简洁。 ``` -bool isPalindrome(int x, int &y) { - if (x < 0) return false; - if (x == 0) return true; - if (isPalindrome(x/10, y) && (x%10 == y%10)) { - y /= 10; - return true; - } else { - return false; - } +bool isPalindrome(int x, int &y) +{ + if (x < 0) + return false; + if (x == 0) + return true; + if (isPalindrome(x / 10, y) && (x % 10 == y % 10)) { + y /= 10; + return true; + } else { + return false; + } } -bool isPalindrome(int x) { - return isPalindrome(x, x); + +bool isPalindrome(int x) +{ + return isPalindrome(x, x); } ``` From ffcb12ccfab8beb4ece3a4353d4de439606b1825 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=BF=9F=E7=BF=94=20Leslie=20Zhai?= Date: Tue, 4 Feb 2014 15:02:12 +0800 Subject: [PATCH 15/19] question: add longest palindromic substring part i --- .../longest-palindromic-substring-part-i.md | 134 ++++++++++++++++++ .../longest-palindromic-substring-part-ii.md | 2 +- 2 files changed, 135 insertions(+), 1 deletion(-) create mode 100644 question/longest-palindromic-substring-part-i.md diff --git a/question/longest-palindromic-substring-part-i.md b/question/longest-palindromic-substring-part-i.md new file mode 100644 index 0000000..e57d844 --- /dev/null +++ b/question/longest-palindromic-substring-part-i.md @@ -0,0 +1,134 @@ +# 最长回文子字符串 第一部 + +http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html + +> 给定一个字符串S，找出S中最长的回文子字符串。 + +这道有趣的题目已经成为著名的Greplin http://baike.baidu.com/view/5302414.htm?fr=iciba 编程挑战的专题，而且多次在面试中被问起。为什么？因为该题有多少解法。我知道的解法就有5种。你准备接受挑战吗？ + +## 提示 +首先，确保你明白回文的意思。回文是一个字符串，正着读反着读都一样。比如，aba是一个回文，abc就不是。 + +## 通病 +试图想出快速解法的，都不幸的答错了（但是很容易被纠正）： + +``` +反转S变成S’。找出S和S’最长的公共子字符串 http://en.wikipedia.org/wiki/Longest_common_substring 就是最长回文子字符串。 +``` + +看上去可以工作，让我们看下面的例子。 + +例如， +S = “caba” S’ = “abac” +S和S’最长的公共子字符串是“aba”。 + +让我们试试另一个例子： +S = “abacdfgdcaba” S’ = “abacdgfdcaba” +S和S’最长的公共子字符串是“abacd”。很明显这不是一个回文。 + +我们发现只要在S中存在一个反转的非回文子字符串，最长公共子字符串的解法就失败了。修正该解法，每次我们找到一个最长公共子字符串，我们检查一下该子字符串和反转子字符串之前的原始字符串是否一样。如果一样，我们更新当前找到的最长公共子字符串；如果不一样，我们跳过它寻找下一个。 + +该解法时间复杂度是O(N2)使用O(N2)空间（可以改进只使用O(N)空间）。请阅读最长公共子字符串 http://en.wikipedia.org/wiki/Longest_common_substring + +## 暴力解法，时间复杂度O(N3) +暴力解法就是穷举所有可能的子字符串的起止位置，然后挨个检查是否是回文。总共C(N, 2)子字符串（单个字符除外，它不算回文）。 + +挨个检查每个子字符串的时间复杂度是O(N)，运行时复杂度是O(N3)。 + +## 动态编程解法 O(N2)时间复杂度 O(N2)空间复杂度 +改进数据处理的暴力解法，首先考虑我们如何省去检查是否是回文的不必要的重复计算。考虑“ababa”。如果我们已经知道“bab”是回文，很明显“ababa”肯定是回文，因为左右两端的字母是一样的。 + +公式化如下所示： + +``` +定义P[ i, j ] ← true 如果子字符串Si … Sj是回文，否则false. +``` + +所以， + +``` +P[ i, j ] ← ( P[ i+1, j-1 ] && Si = Sj ) +``` + +基本如下： + +``` +P[ i, i ] ← true +P[ i, i+1 ] ← ( Si = Si+1 ) +``` + +这就产生了一个直接的数据处理解法，我们首先初始化一个和两个字母的回文，然后找出所有三个字母的回文，N个... + +时间复杂度O(N2)，空间复杂度O(N2) + +``` +string longestPalindromeDP(string s) { + int n = s.length(); + int longestBegin = 0; + int maxLen = 1; + bool table[1000][1000] = {false}; + for (int i = 0; i < n; i++) + table[i][i] = true; + for (int i = 0; i < n-1; i++) { + if (s[i] == s[i+1]) { + table[i][i+1] = true; + longestBegin = i; + maxLen = 2; + } + } + for (int len = 3; len <= n; len++) { + for (int i = 0; i < n-len+1; i++) { + int j = i + len - 1; + if (s[i] == s[j] && table[i+1][j-1]) { + table[i][j] = true; + longestBegin = i; + maxLen = len; + } + } + } + return s.substr(longestBegin, maxLen); +} +``` + +## 附加题 +你能改进上面的解法，如何减少空间复杂度？ + +## 一个更加简单的解法O(N2)时间复杂度O(1)空间复杂度 +实际上，我们可以在O(N2)时间复杂度，不使用额外空间的前提下解题。 + +我们发现一个回文是中心点对称的。所以，一个回文可以由中心点扩展，而且只有2N - 1个中心点。 + +你可能会问为什么有2N - 1个中心点，而不是N个？这是因为一个回文的中心点可能在两个字母之间。有偶数个字母的回文（比如“abba”）它的中心点在两个b之间。 + +由回文中心点扩展开来，时间复杂度变为O(N)，总复杂度是O(N2)。 + +``` +string expandAroundCenter(string s, int c1, int c2) { + int l = c1, r = c2; + int n = s.length(); + while (l >= 0 && r <= n-1 && s[l] == s[r]) { + l--; + r++; + } + return s.substr(l+1, r-l-1); +} + +string longestPalindromeSimple(string s) { + int n = s.length(); + if (n == 0) return ""; + string longest = s.substr(0, 1); // 单个字符本身是个回文 + for (int i = 0; i < n-1; i++) { + string p1 = expandAroundCenter(s, i, i); + if (p1.length() > longest.length()) + longest = p1; + + string p2 = expandAroundCenter(s, i, i+1); + if (p2.length() > longest.length()) + longest = p2; + } + return longest; +} +``` + +## 进一步思考 +是否存在O(N)的解法？你打赌！但是，它需要非常聪明的洞察力。第二部 https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-ii.md 将讲解O(N)的解法。 diff --git a/question/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md index 01743b6..ba379fc 100644 --- a/question/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -5,7 +5,7 @@ http://leetcode.com/2011/11/longest-palindromic-substring-part-ii.html > 给定一个字符串S，找出S中最长的回文子字符串。 ## 注意 -这是最长回文子字符串 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读第一部 http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html 了解更多内幕。 +这是最长回文子字符串 https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-i.md 的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读第一部 https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-i.md 了解更多内幕。 Manacher http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 From 176311ab419c9ec80ded70a5851199973d7f1393 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=BF=9F=E7=BF=94=20Leslie=20Zhai?= Date: Tue, 4 Feb 2014 15:07:32 +0800 Subject: [PATCH 16/19] question: add readme --- question/README.md | 4 ++++ 1 file changed, 4 insertions(+) create mode 100644 question/README.md diff --git a/question/README.md b/question/README.md new file mode 100644 index 0000000..6908217 --- /dev/null +++ b/question/README.md @@ -0,0 +1,4 @@ +* clone-graph-part-i 克隆图第一部 +* palindrome-number 回文数 +* longest-palindromic-substring-part-ii 最长回文子字符串第二部 +* longest-palindromic-substring-part-i 最长回文子字符串第一部 From e35b7593a1d266641637c0b6c63ae7b2fb61d87f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E7=BF=9F=E7=BF=94=20Leslie=20Zhai?= 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zkSE|$@nx;{{yS~%rsdtjA_O1+fo1}=>eO^>x%5t3t<5H};~+Fi2muHvAuvFuy0tI$ zjapAhfawMVAmC1*y*_g~<3fq&j+-kX009jII#tU_`%+Ij4QcR}K0p8h5OCBhr#Y`p zlld>X1px?XCg518_13=3XB1F#?CBc>7D&KR@(MBowQqrBaTx*-m=gil^}adzj4u#? s00huJasUDlSRw(mZ;4UIX9z&xe-^@Y{Nm$Ix&QzG07*qoM6N<$f--pu?EnA( literal 0 HcmV?d00001 diff --git a/question/insert-into-a-cyclic-sorted-list.md b/question/insert-into-a-cyclic-sorted-list.md new file mode 100644 index 0000000..2ab6fca --- /dev/null +++ b/question/insert-into-a-cyclic-sorted-list.md @@ -0,0 +1,65 @@ +# 向循环有序链表插入节点 + +http://leetcode.com/2011/08/insert-into-a-cyclic-sorted-list.html + +> 给一个循环有序链表中的某个节点，写一个函数，向该链表插入一个节点，依然保持循环有序。给的节点可以是链表中的任意单个节点。 + +## 循环有序链表定义 +设想你有一个有序链表，但是它的尾指针指回到头指针。换言之，该链表必须有一个最小的节点，升序排列，最后指针指回到这个最小节点。访问该链表的唯一方法是通过节点，可以指向任意节点，但是没有必要一定指向最小节点。 + +首先，你明白什么是循环链表很重要。一个循环链表不同于普通的链表，循环链表的尾指针指回它的头指针，而普通的链表指向NULL指针。 + +该题出得有点狡猾，因为给的节点不一定是该链表的头指针（具有最小元素的节点）。你立马就能想出一个点子，但是注意。该题有陷阱，如果你不小心就会犯错。 + +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/cyclic_list1.png) + +一个循环有序链表。注意尾指针指回到头指针。该链表唯独可以参考的是给定一个节点，可以是该链表中的任意一个节点。假设你需要向该链表插入4。 + +![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/cyclic_list2.png) + +This is how the cyclic list becomes after inserting 4. Note that the cyclic linked list remained in sorted order. + +Hints: +It is best to list all kinds of cases first before you jump into coding. Then, it is much easier to reduce the number of cases your code need to handle by combining some of them into a more generic case. Try to also list down all possible edge cases if you have time. You might discover a bug before you even start coding! + +Solution: +Basically, you would have a loop that traverse the cyclic sorted list and find the point where you insert the value (Let’s assume the value being inserted called x). You would only need to consider the following three cases: + +prev→val ≤ x ≤ current→val: +Insert between prev and current. +x is the maximum or minimum value in the list: +Insert before the head. (ie, the head has the smallest value and its prev→val > head→val. +Traverses back to the starting point: +Insert before the starting point. +Most people have no problem getting case 1) working, while case 2) is easy to miss or being handled incorrectly. Case 3), on the other hand is more subtle and is not immediately clear what kind of test cases would hit this condition. It seemed that case 1) and 2) should take care of all kinds of cases and case 3) is not needed. Think again… How can you be sure of that? Could you come up with one case where it hits case 3)? + +Q: What if the list has only one value? +A: Handled by case 1). Handled by case 3). +Q: What if the list is passed in as NULL? +A: Then handle this special case by creating a new node pointing back to itself and return. +Q: What if the list contains all duplicates? +A: Then it has been handled by case 3). +Below is the code. You could combine both negation of case 1) and case 2) in the while loop’s condition, but I prefer to use break statements here to illustrate the above idea clearer. + +``` +void insert(Node *& aNode, int x) { + if (!aNode) { + aNode = new Node(x); + aNode->next = aNode; + return; + } + + Node *p = aNode; + Node *prev = NULL; + do { + prev = p; + p = p->next; + if (x <= p->data && x >= prev->data) break; // For case 1) + if ((prev->data > p->data) && (x < p->data || x > prev->data)) break; // For case 2) + } while (p != aNode); // when back to starting point, then stop. For case 3) + + Node *newNode = new Node(x); + newNode->next = p; + prev->next = newNode; +} +``` From cfd9484a320cb0780aaeadd46124612119c3e94d Mon Sep 17 00:00:00 2001 From: Aphroiai Date: Wed, 12 Feb 2014 18:25:25 +0800 Subject: [PATCH 18/19] update longest-palindromic-substring-part-i.md --- .../longest-palindromic-substring-part-i.md | 40 +++++++++---------- 1 file changed, 20 insertions(+), 20 deletions(-) diff --git a/question/longest-palindromic-substring-part-i.md b/question/longest-palindromic-substring-part-i.md index e57d844..b7914ba 100644 --- a/question/longest-palindromic-substring-part-i.md +++ b/question/longest-palindromic-substring-part-i.md @@ -4,19 +4,19 @@ http://leetcode.com/2011/11/longest-palindromic-substring-part-i.html > 给定一个字符串S，找出S中最长的回文子字符串。 -这道有趣的题目已经成为著名的Greplin http://baike.baidu.com/view/5302414.htm?fr=iciba 编程挑战的专题，而且多次在面试中被问起。为什么？因为该题有多少解法。我知道的解法就有5种。你准备接受挑战吗？ +这道有趣的题目已经成为著名的[Greplin](http://baike.baidu.com/view/5302414.htm?fr=iciba)编程挑战的专题，而且多次在面试中被问起。为什么？因为该题有多种解法。我知道的解法就有5种。你准备接受挑战吗？ + +到[在线评测](http://www.leetcode.com/onlinejudge)去解决这个问题（你可以提交C++或Java代码来解决） ## 提示 -首先，确保你明白回文的意思。回文是一个字符串，正着读反着读都一样。比如，aba是一个回文，abc就不是。 +首先，确保你明白回文的意思。回文是一个字符串，正着读反着读都一样。比如，"aba"是一个回文，"abc"就不是。 ## 通病 -试图想出快速解法的，都不幸的答错了（但是很容易被纠正）： +许多人倾向于找出一个快速解决方案，都不幸的答错了（但是很容易纠正）： -``` -反转S变成S’。找出S和S’最长的公共子字符串 http://en.wikipedia.org/wiki/Longest_common_substring 就是最长回文子字符串。 -``` +>反转S变成S’。找出S和S’[最长的公共子字符串](http://en.wikipedia.org/wiki/Longest_common_substring)就是最长回文子字符串。 -看上去可以工作，让我们看下面的例子。 +看上去可以工作，让我们看下面的一些例子。 例如， S = “caba” S’ = “abac” @@ -26,22 +26,22 @@ S和S’最长的公共子字符串是“aba”。 S = “abacdfgdcaba” S’ = “abacdgfdcaba” S和S’最长的公共子字符串是“abacd”。很明显这不是一个回文。 -我们发现只要在S中存在一个反转的非回文子字符串，最长公共子字符串的解法就失败了。修正该解法，每次我们找到一个最长公共子字符串，我们检查一下该子字符串和反转子字符串之前的原始字符串是否一样。如果一样，我们更新当前找到的最长公共子字符串；如果不一样，我们跳过它寻找下一个。 +我们发现只要在S中存在一个反转的非回文子字符串的反转的子串，最长公共子字符串的解法就失败了。为了修正该解法，每次我们找到一个最长公共子字符串，我们检查一下该子字符串和反转子字符串之前的原始字符串是否一样。如果一样，我们更新当前找到的最长公共子字符串；如果不一样，我们跳过它寻找下一个。 -该解法时间复杂度是O(N2)使用O(N2)空间（可以改进只使用O(N)空间）。请阅读最长公共子字符串 http://en.wikipedia.org/wiki/Longest_common_substring +该解法给出了一个时间复杂度是O(N2)的动态规划解法，使用O(N2)空间（可以改进只使用O(N)空间）。请阅读[最长公共子字符串](http://en.wikipedia.org/wiki/Longest_common_substring)。 ## 暴力解法，时间复杂度O(N3) 暴力解法就是穷举所有可能的子字符串的起止位置，然后挨个检查是否是回文。总共C(N, 2)子字符串（单个字符除外，它不算回文）。 -挨个检查每个子字符串的时间复杂度是O(N)，运行时复杂度是O(N3)。 +挨个检查每个子字符串的时间复杂度是O(N)，总共时间复杂度是O(N3)。 -## 动态编程解法 O(N2)时间复杂度 O(N2)空间复杂度 -改进数据处理的暴力解法，首先考虑我们如何省去检查是否是回文的不必要的重复计算。考虑“ababa”。如果我们已经知道“bab”是回文，很明显“ababa”肯定是回文，因为左右两端的字母是一样的。 +## 动态规划解法 O(N2)时间复杂度 O(N2)空间复杂度 +通过动态规划方法来改进暴力解法，首先考虑我们如何避免检查是否是回文的不必要的重复计算。考虑“ababa”。如果我们已经知道“bab”是回文，很明显“ababa”肯定是回文，因为左右两端的字母是一样的。 -公式化如下所示： +更严谨的陈述如下所示： ``` -定义P[ i, j ] ← true 如果子字符串Si … Sj是回文，否则false. +定义P[ i, j ] ← true 当且仅当子字符串Si … Sj是回文，否则false. ``` 所以， @@ -50,14 +50,14 @@ S和S’最长的公共子字符串是“abacd”。很明显这不是一个回 P[ i, j ] ← ( P[ i+1, j-1 ] && Si = Sj ) ``` -基本如下： +边界条件如下： ``` P[ i, i ] ← true P[ i, i+1 ] ← ( Si = Si+1 ) ``` -这就产生了一个直接的数据处理解法，我们首先初始化一个和两个字母的回文，然后找出所有三个字母的回文，N个... +这就产生了一个直观的动态规划解法，我们首先初始化一个和两个字母的回文，然后找出所有三个字母的回文，N个... 时间复杂度O(N2)，空间复杂度O(N2) @@ -67,7 +67,7 @@ string longestPalindromeDP(string s) { int longestBegin = 0; int maxLen = 1; bool table[1000][1000] = {false}; - for (int i = 0; i < n; i++) + for (int i = 0; i < n; i++) table[i][i] = true; for (int i = 0; i < n-1; i++) { if (s[i] == s[i+1]) { @@ -112,7 +112,7 @@ string expandAroundCenter(string s, int c1, int c2) { } return s.substr(l+1, r-l-1); } - + string longestPalindromeSimple(string s) { int n = s.length(); if (n == 0) return ""; @@ -121,7 +121,7 @@ string longestPalindromeSimple(string s) { string p1 = expandAroundCenter(s, i, i); if (p1.length() > longest.length()) longest = p1; - + string p2 = expandAroundCenter(s, i, i+1); if (p2.length() > longest.length()) longest = p2; @@ -131,4 +131,4 @@ string longestPalindromeSimple(string s) { ``` ## 进一步思考 -是否存在O(N)的解法？你打赌！但是，它需要非常聪明的洞察力。第二部 https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-ii.md 将讲解O(N)的解法。 +是否存在O(N)的解法？你打赌！但是，它需要非常聪明的洞察力。[第二部](https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-ii.md)将讲解O(N)的解法。 From 6b684c9de0da7de4dc306df8cfc131b0bcfb4742 Mon Sep 17 00:00:00 2001 From: Aphroiai Date: Fri, 14 Feb 2014 16:59:10 +0800 Subject: [PATCH 19/19] update longest-palindromic-substring-part-ii.md --- .../longest-palindromic-substring-part-ii.md | 52 ++++++++++--------- 1 file changed, 28 insertions(+), 24 deletions(-) diff --git a/question/longest-palindromic-substring-part-ii.md b/question/longest-palindromic-substring-part-ii.md index ba379fc..463b42e 100644 --- a/question/longest-palindromic-substring-part-ii.md +++ b/question/longest-palindromic-substring-part-ii.md @@ -5,14 +5,18 @@ http://leetcode.com/2011/11/longest-palindromic-substring-part-ii.html > 给定一个字符串S，找出S中最长的回文子字符串。 ## 注意 -这是最长回文子字符串 https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-i.md 的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读第一部 https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-i.md 了解更多内幕。 +这是[最长回文子字符串][part-i]的第二部。这里，我们要描述Manacher算法，可以在线性时间内找出最长回文子字符串。请阅读[第一部][part-i]了解更多内幕。 + +在我的[上一个帖子][part-i]里面我们一共讨论了四种不同的方法，其中包括一个只使用O(N2)时间复杂度和常数空间复杂的的简单的方法，这里我们将讨论一个使用线性时间和线性空间的算法，也就是Manacher算法。 + +[part-i]: https://github.com/xiangzhai/leetcode/blob/master/question/longest-palindromic-substring-part-i.md Manacher http://en.wikipedia.org/wiki/Longest_palindromic_substring#CITEREFManacher1975 ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/ManG490.jpg) ## 提示 -思考如何改进O(N^2)时间复杂度的算法。考虑最坏的情况。最坏的情况是输入了多个重复的回文。举个例子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 +思考如何改进O(N^2)时间复杂度的算法。考虑最坏的情况。最坏的情况是输入了多个相互重叠的回文。举个例子，输入："aaaaaaaaa" 和 “cabcbabcbabcba”。事实上，我们应该利用回文的对称属性，减少一些不必要的计算量。 ## 一个O(N)时间复杂度解法（Manacher算法） 首先，我们在输入的字符串S的每个字符之间添加一个特殊字符#，转换成另一个字符串T。这样做的原因马上揭晓。 @@ -30,23 +34,23 @@ T = # a # b # a # a # b # a # P = 0 1 0 3 0 1 6 1 0 3 0 1 0 ``` -看P我们立马找到最长回文"abaaba"，如P6 = 6所示。 +通过P我们立马找到最长回文"abaaba"，如P6 = 6所示。 在字母之间插入特殊字符#，可以优雅地处理奇数、偶数长度的回文。（请注意：这是为了更方便地论证解题思路，不需要码代码。） 现在，想像在回文"abaaba"的中间画一条竖线。数组P中的数字是中心轴对称的。再测试另一个回文"aba"，数组中的数字依旧具有相似的轴对称属性。这是巧合吗？在某一特定条件下是这样的，但是，我们至少没有重复计算P[i]，这就是个优化。 -让我们看一个稍微有点复杂的例子，有很多重复的回文，比如S = "babcbabcbaccba" +让我们看一个稍微有点复杂的例子，有很多相互重叠的回文，比如S = "babcbabcbaccba" ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table10.png) -上面图片的T由S = "babcbabcbaccba"转换而来。假设你单步调试到数组P暂停在（比如P[i] < P[N]）。竖实线是回文"babcbabcbaccba"的中心C。两个竖虚线是左L右R边界。你单步调试到索引i轴对称的i’。怎样才能高效地计算出P[i]呢？ +上面图片的T由S = "babcbabcbaccba"转换而来。假设你到达了一个数组P部分已完成的状态。竖实线是回文"babcbabcbaccba"的中心C。两个竖虚线是左L右R边界。你单步调试到索引i并且它的轴对称的索引为i’。怎样才能高效地计算出P[i]呢？ -假设我们已经单步跟踪到索引i = 13，我们需要计算出P[13]（如蓝色问号所示的位置）。我们首先查看在回文中心旁边，它的镜像索引i’，即索引i’ = 9 +假设我们已经单步跟踪到索引i = 13，我们需要计算出P[13]（如蓝色问号所示的位置）。我们首先查看在回文中心旁边的镜像索引i’，即索引i’ = 9。 ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table11.png) -上面的两条绿实线表示中心点i和i’的两个回文的重叠区域。我们看中心点C附近的索引i的镜像i’。P[i'] = P[9] = 1。因为回文中心轴对称属性，P[i]也应该等于1。综上所述，很明显P[i] = P[i'] = 1。事实上，中心C之后的P[12] = P[10] = 0, P[13] = P[9] = 1, P[14] = P[8] = 0都满足该特性。 +上面的两条绿实线表示中心点i和i’的两个回文的覆盖区域。我们看中心点C附近的索引i的镜像i’。P[i'] = P[9] = 1。因为回文中心轴对称属性，P[i]也应该等于1。综上所述，很明显P[i] = P[i'] = 1。事实上，中心C之后的P[12] = P[10] = 0, P[13] = P[9] = 1, P[14] = P[8] = 0都满足该特性。 ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table4.png) @@ -54,32 +58,32 @@ P = 0 1 0 3 0 1 6 1 0 3 0 1 0 ![ScreenShot](https://raw.github.com/xiangzhai/leetcode/master/image/palindrome_table5.png) -彩色线段重叠在以索引i和i’中心周围。绿实线所表示的区域是以中心C轴对称必须匹配的两条边。红实线所表示的两条边就不一定匹配了。绿虚线所表示的穿越中心的区域。 +彩色线段覆盖在以索引i和i’中心周围。绿实线所表示的区域是以中心C轴对称肯定匹配的两条边。红实线所表示的两条边就不一定匹配了。绿虚线所表示的穿越中心的区域。 -在两个绿实线区域内的两个子字符串必须完全匹配。穿越中心的区域（绿虚线所示）也必须相对称。注意P[i'] = 7而且所有穿越左边L的回文（红实线所示），就不再遵循回文的对称属性。我们知道的是P[i] ≥ 5，为了找到P[i]的实际值，我们需要扩展右边R来做字符匹配。当P[21] ≠ P[1]这种情况下，我们得出结论P[i] = 5。 +在两个绿实线区域内的两个子字符串肯定完全匹配。穿越中心的区域（绿虚线所示）也肯定是对称的。注意P[i'] = 7和所有穿越左边L的回文（红实线所示），就不再遵循回文的对称属性。我们知道的是P[i] ≥ 5，为了找到P[i]的实际值，我们需要越过右边边界R来做字符匹配。当T[21] ≠ T[1]这种情况下，我们得出结论P[i] = 5。(译者注：原文写的是P[21] ≠ P[1]，有误) 让我们概括该算法的精髓如下： ``` if P[ i' ] ≤ R – i, then P[ i ] ← P[ i' ] -else P[ i ] ≥ P[ i' ] 这里我们需要扩展右边R来找到P[i] +else P[ i ] ≥ P[ i' ] 这里我们需要越过右边边界R来找到P[i] ``` -该算法是如此的简洁。如果可以抓到上述要害，就完全领悟了该算法的精髓，也是最难理解的部分。 +该算法是如此的优雅。如果可以掌握上述要害，就完全领悟了该算法的精髓，也是最难理解的部分。 最后我们就要决定何时同时向右移动C和R的坐标： ``` -如果回文的中心i越过了R，我们就将C更新成i，（该回文的新中心），然后把R扩展到新回文的右边。 +如果中心为i的回文越过了R，我们就将C更新成i，（该新回文的中心），然后把R扩展到新回文的右边边界。 ``` -论时间复杂度，有两种可能性。如果P[i] ≤ R – i，只需一步，我们设P[i]为P[i']。否则，我们从右边R扩展，改变回文的中心变为i。扩展R（线性while循环）需要花费N步，而且确定坐标也需要花费N步。所以，该算法确保在2*N步内，提供了线性时间复杂度的解法。 +论时间复杂度，有两种可能性。如果P[i] ≤ R – i，只需一步，我们设P[i]为P[i']。否则，我们通过从右边边界R进行扩展来尝试将回文的中心变为i。扩展R（线性while循环）需要花费最多N步，而且确定坐标也需要总共花费N步。所以，该算法确保在2*N步内，由此给出了一个线性时间复杂度的解法。 ``` // 将S转换成T // 比如，S = "abba", T = "^#a#b#b#a#$" -// ^和$符号用来表示开始和结束。 +// ^和$符号用来表示开始和结束，并且避免边界检查。 string preProcess(string s) { int n = s.length(); @@ -103,11 +107,11 @@ string longestPalindrome(string s) P[i] = (R > i) ? min(R-i, P[i_mirror]) : 0; - // 扩展回文中心变为i + // 尝试扩展中心为i的回文 while (T[i + 1 + P[i]] == T[i - 1 - P[i]]) P[i]++; - // 如果回文中心i超越了R，调整回文的中心 + // 如果中心为i的回文超越了R，根据已扩展的回文来调整中心 if (i + P[i] > R) { C = i; R = i + P[i]; @@ -130,15 +134,15 @@ string longestPalindrome(string s) ``` ## 注意 -该算法是不凡的，在面试过程中，你可能想不起来该算法。但是，我希望你喜欢阅读这篇文章，有助于理解这个有趣的算法。 +该算法当然是不简单的，在面试过程中，你可能想不起来该算法。但是，我希望你喜欢阅读这篇文章，有助于理解这个有趣的算法。如果你看到了这里，值得表扬哦！ ## 进一步思考 -事实上，针对该题还有第六种解法——使用后缀树。但是，它并不高效O(N log N)，而且构造后缀树的开销也很大，实践起来也更加复杂。如果你感兴趣，可以阅读维基百科有关最长回文子字符串的文章。 -如果让你找出最长回文序列？（你知道子字符串和序列的区别吗？） +事实上，针对该题还有第六种解法——使用后缀树。但是，它并不高效O(N log N)，而且构造后缀树的开销也很大，实现起来也更加复杂。如果你感兴趣，可以阅读维基百科有关[最长回文子字符串的文章](http://en.wikipedia.org/wiki/Longest_palindromic_substring)。 +如果让你找出最长回文子序列你该怎么办呢？（你知道子字符串和子序列的区别吗？） ## 有用的链接 -* Manacher算法O(N)求字符串的最长回文子串 http://www.felix021.com/blog/read.php?2040 -* [需要翻墙]一个简单的找最长回文子字符串的线性时间复杂度算法 http://zhuhongcheng.wordpress.com/2009/08/02/a-simple-linear-time-algorithm-for-finding-longest-palindrome-sub-string/ -* [需要翻墙]寻找回文 http://johanjeuring.blogspot.com/2007/08/finding-palindromes.html -* 在线性时间内寻找最长回文子字符串 http://www.akalin.cx/longest-palindrome-linear-time -* 维基百科：最长回文子字符串 http://en.wikipedia.org/wiki/Longest_palindromic_substring +* [Manacher算法O(N)求字符串的最长回文子串](http://www.felix021.com/blog/read.php?2040) +* [需要翻墙]. [一个简单的找最长回文子字符串的线性时间复杂度算法](http://zhuhongcheng.wordpress.com/2009/08/02/a-simple-linear-time-algorithm-for-finding-longest-palindrome-sub-string/) +* [需要翻墙]. [寻找回文](http://johanjeuring.blogspot.com/2007/08/finding-palindromes.html) +* [在线性时间内寻找最长回文子字符串](http://www.akalin.cx/longest-palindrome-linear-time) +* [维基百科：最长回文子字符串](http://en.wikipedia.org/wiki/Longest_palindromic_substring)