add O(1) space solution for "First Missing Positive" problem. fixed haoel#19

Author: haoel

src/firstMissingPositive/firstMissingPositive.cpp

@@ -14,15 +14,47 @@
 * 
 *               
 **********************************************************************************/
-
+#include <stdlib.h>
+#include <time.h>
 #include <iostream>
 #include <map>
 using namespace std;
 
 #define INT_MAX      2147483647
 
 /*
- *    The idea is simple:
+ *  Idea:
+ * 
+ *    We can move the num to the place whcih the index is the num. 
+ *   
+ *    for example,  (considering the array is zero-based.
+ *       1 => A[0], 2 => A[1], 3=>A[2]
+ *   
+ *    Then, we can go through the array check the i+1 == A[i], if not ,just return i+1;
+ *   
+ *    This solution comes from StackOverflow.com
+ *    http://stackoverflow.com/questions/1586858/find-the-smallest-integer-not-in-a-list
+*/
+int firstMissingPositive_move(int A[], int n) {
+    if (n<=0) return 1;
+    int num;
+    for(int i=0; i<n; i++) {
+        num = A[i];
+        while (num>0 && num<n && A[num-1]!=num) {
+            swap(A[i], A[num-1]);
+            num = A[i];
+        }
+    }
+    for (int i=0; i<n; i++){
+        if (i+1 != A[i]){
+            return i+1;
+        }
+    }
+    return n+1;
+}
+
+/*
+ *    The idea is simple: 
  *
  *    1) put all of number into a map.
  *    2) for each number a[i] in array, remove its continous number in the map
@@ -36,8 +68,10 @@ using namespace std;
  *
  *    However, we missed 1, so, we have to add dummy number 0 whatever.
  *
+ *    NOTE: this solution is not constant space slution!!!!
+ *
  */
-int firstMissingPositive(int A[], int n) {
+int firstMissingPositive_map(int A[], int n) {
     map<int, int> cache;
     for(int i=0; i<n; i++){
         cache[A[i]] = i;
@@ -51,13 +85,13 @@ int firstMissingPositive(int A[], int n) {
     int miss = INT_MAX;
     int x;
     for (int i=-1; i<n && cache.size()>0; i++){
-        
+
         if (i == -1){
             x = 0; //checking dummy
         }else{
             x = A[i];
         } 
-    
+
         if ( cache.find(x)==cache.end() ){
             continue;
         }
@@ -78,32 +112,66 @@ int firstMissingPositive(int A[], int n) {
             miss = num;
         }
     }
-    
+
 
     return miss;
 }
 
+int firstMissingPositive(int A[], int n) {
+    srand(time(0));
+    if (rand()%2){
+        return firstMissingPositive_move(A, n);
+    }
+    return firstMissingPositive_map(A, n);
+}
+
+
+void printArray(int a[], int n){
+    cout << "[ ";
+    for(int i=0; i<n-1; i++) {
+        cout << a[i] << ", ";
+    }
+    cout << a[n-1] << " ]";
+}
+
+void Test(int a[], int n, int expected) {
+    printArray(a, n);
+    int ret = firstMissingPositive(a, n);
+    cout << "\t   missed = " << ret << "  " << (ret==expected?"passed!":"failed!") << endl;
+    //printArray(a, n);
+    //cout <<endl;
+}
+
 int main()
 {
-    #define TEST(a) cout << firstMissingPositive(a, sizeof(a)/sizeof(int)) << endl
+#define TEST(a, e) Test(a, sizeof(a)/sizeof(int), e) 
+
+    int a0[]={1};
+    TEST(a0, 2);
 
     int a1[]={1,2,0};
-    TEST(a1);
+    TEST(a1, 3);
 
     int a2[]={3,4,-1,1};
-    TEST(a2);
+    TEST(a2, 2);
 
     int a3[]={1000,-1};
-    TEST(a3);
+    TEST(a3, 1);
 
     int a4[]={1000, 200};
-    TEST(a4);
+    TEST(a4, 1);
 
-    int a5[]={2,5,4,3,-1};
-    TEST(a5);
+    int a5[]={2,5,3,-1};
+    TEST(a5, 1);
 
     int a6[]={1, 100};
-    TEST(a6);
+    TEST(a6, 2);
+
+    int a7[]={7,8,9,11};
+    TEST(a7, 1);
+
+    int a8[]={4,3,2,1};
+    TEST(a8, 5);
 
     return 0;
 }