all algorithms use mathjax for complexities (algorithm-visualizer#212)

Author: nadr0

algorithm/backtracking/knight's_tour/desc.json

@@ -1,8 +1,8 @@
 {
   "Knight’s tour problem": "A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again immediately, following the same path), the tour is closed, otherwise it is open.",
   "Complexity": {
-    "time": "Worst $$O(8^{N^{2}})$$",
-    "space": "Worst $$O(N^2)$$"
+    "time": "Worst $O(8^{N^{2}})$",
+    "space": "Worst $O(N^2)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Knight%27s_tour'>Wikipedia</a>"

algorithm/backtracking/n_queens/desc.json

@@ -5,8 +5,8 @@
     "Searching"
   ],
   "Complexity": {
-    "time": "Worst $$O(N!)$$",
-    "space": "Worst $$O(N)$$"
+    "time": "Worst $O(N!)$",
+    "space": "Worst $O(N)$"
   },
   "References": [
     "<a href='http://www.geeksforgeeks.org/backtracking-set-3-n-queen-problem/'>geeksforgeeks</a>"

algorithm/cryptography/affine_cipher/desc.json

@@ -5,8 +5,8 @@
     "More complex Variations of Affine Cipher are used in practical cryptography"
   ],
   "Complexity": {
-    "time": "worst O(N), N = length of plain/cipher text",
-    "space": "worst O(N), to create the new mapping (plain->cipher, cipher->plain)"
+    "time": "worst $O(N)$, $N$ = length of plain/cipher text",
+    "space": "worst $O(N)$, to create the new mapping (plain->cipher, cipher->plain)"
   },
   "References": [
     "<a href='http://practicalcryptography.com/ciphers/affine-cipher/'>Practicalcryptography</a>"

algorithm/dp/catalan_number/desc.json

@@ -6,8 +6,8 @@
     "The number of ways to cut an n+2-sided convex polygon in a plane into triangles by connecting vertices with straight, non-intersecting lines is the nth Catalan number. This is the application in which Euler was interested."
   ],
   "Complexity": {
-    "time": " O(N<sup>2</sup>)",
-    "space": "O(N)"
+    "time": " $O(N^2)$",
+    "space": "$O(N)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Catalan_number'>Wikipedia</a>",
@@ -16,4 +16,4 @@
   "files": {
     "catalan_number": "Catalan Number"
   }
-}
+}

algorithm/dp/fibonacci/desc.json

@@ -1,8 +1,8 @@
 {
   "Fibonacci Sequence": "Finding Fibonacci sequence using dynamic programming.",
   "Complexity": {
-    "time": "O(n)",
-    "space": "O(n)"
+    "time": "$O(n)$",
+    "space": "$O(n)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Dynamic_programming#Fibonacci_sequence'>Wikipedia</a>"

algorithm/dp/integer_partition/desc.json

@@ -1,13 +1,13 @@
 {
   "Integer Partition": "In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.",
   "Complexity": {
-    "time": "O(n(log n))",
-    "space": "O(n<sup>2</sup>)"
+    "time": "$O(n(log \\, n))$",
+    "space": "$O(n^2)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Partition_(number_theory)'>Wikipedia</a>"
   ],
   "files": {
     "basic": "Integer partition"
   }
-}
+}

algorithm/dp/knapsack_problem/desc.json

@@ -1,8 +1,8 @@
 {
   "Knapsack Problem": "Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.",
   "Complexity": {
-    "time": "O(n<sup>2</sup>)",
-    "space": "O(n<sup>2</sup>)"
+    "time": "$O(n^2)$",
+    "space": "$O(n^2)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Knapsack_problem'>Wikipedia</a>"

algorithm/dp/longest_common_subsequence/desc.json

@@ -1,13 +1,13 @@
 {
   "Longest Common Subsequence": "The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences)." ,
   "Complexity": {
-    "time": "O(mn)",
-    "space": "O(mn)"
+    "time": "$O(m\\cdot n)$",
+    "space": "$O(m\\cdot n)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Longest_common_subsequence_problem'>Wikipedia</a>"
   ],
   "files": {
     "basic": "Longest common subsequence"
   }
-}
+}

algorithm/dp/longest_increasing_subsequence/desc.json

@@ -1,13 +1,13 @@
 {
   "Longest Increasing Subsequence": "Find the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order",
   "Complexity": {
-    "time": "O(n(log n))",
-    "space": "O(n)"
+    "time": "$O(n(log\\,n))$",
+    "space": "$O(n)$"
   },
   "References": [
     "<a href='https://en.wikipedia.org/wiki/Longest_increasing_subsequence'>Wikipedia</a>"
   ],
   "files": {
     "basic": "Longest increasing subsequence"
   }
-}
+}

algorithm/dp/longest_palindromic_subsequence/desc.json

@@ -1,8 +1,8 @@
 {
   "Longest Palindromic Subsequence": "Find the length of the longest palindromic subsequence in a given sequence",
   "Complexity": {
-    "time": "O(n<sup>2</sup>)",
-    "space": "O(n<sup>2</sup>)"
+"time": "$O(n^2)$",
+"space": "$O(n^2)$"
   },
   "References": [
     "<a href='http://www.geeksforgeeks.org/dynamic-programming-set-12-longest-palindromic-subsequence/'>GeeksForGeeks</a>"