Longest Palindromic Sub-sequence

Competitive Coding/Dynamic Programming/Longest Palindromic Sub-sequence/lps.c

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+#include<stdio.h>
+#include<string.h>
+#define MAXLEN 100
+// A utility function to get max of two integers
+int max (int x, int y) { return (x > y)? x : y; }
+
+// Returns the length of the longest palindromic subsequence in seq
+int lps(char *str)
+{
+   int n = strlen(str);
+   int i, j, len;
+   int mat[n][n];  // Create a table to store results of subproblems
+
+
+   // Strings of length 1 are palindrome of lentgh 1
+   for (i = 0; i < n; i++)
+      mat[i][i] = 1;
+
+    /* Build the table. Note that the lower diagonal values of table are
+    useless and not filled in the process.  len is length of
+    substring*/
+    for (len=2; len<=n; len++)
+    {
+        for (i=0; i<n-len+1; i++)
+        {
+            j = i+len-1;
+            if (str[i] == str[j] && len == 2)
+               mat[i][j] = 2;
+            else if (str[i] == str[j])
+               mat[i][j] = mat[i+1][j-1] + 2;
+            else
+               mat[i][j] = max(mat[i][j-1], mat[i+1][j]);
+        }
+    }
+
+    return mat[0][n-1];
+}
+
+/* main */
+int main()
+{
+	printf("Enter your string\n");
+	char str[MAXLEN];
+	scanf("%99s",str);
+    printf ("The lnegth of the Longest Palindromic Sub-sequence is %d", lps(str));
+    getchar();
+    return 0;
+}

Competitive Coding/Dynamic Programming/Longest Palindromic Sub-sequence/readme_lps.md

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+## Longest Common Subsequence
+  In order to solve this problem using Dynamic Programming, we create a 2-D matrix called mat[n][n], where 'n' is the length of the given string.
+Any entry [i][j] in the matrix represents the length of the longest palindromic sub-sequence from 'i'th charecter of the string to the 'j'th. 
+As the string is always considereed from left to right i<=j always. Hence the lower triangle of the matrix is of no use.
+
+### Filling of the matrix
+  Every single charecter contributes to a palindromic string of length 1 starting and ending at itself, therefore we fill the diagonal of the 
+matrix with 1 for every [i][i] entry. <br/><br/>
+Let str[0..n-1] be the input sequence of length n, then mat[0][n-1] will be the length of the longest palindromic subsequence.<br/>
+For every other entry:<br/>
+If last and first characters of str are same, then mat[i][j] = mat[i+1][j-1] + 2, as it considers [2(for the first and the last chaar)] + 
+[longest palindromic subsequence between these 2 chars].<br/>
+Else mat[i][j] = max(mat[i][j-1], mat[i+1][j]).