In a given string, we have to find a substring, which is a palindrome and it is longest.
To get the longest palindromic substring, we have to solve many subproblems, some of the subproblems are overlapping. They are needed to be solved for multiple times. For that reason, the Dynamic programming is helpful. Using a table, we can store the result of the previous subproblems, and simply use them to generate further results.
Input and Output
Input: A String. Say “thisispalapsiti” Output: The palindrome substring and the length of the palindrome. Longest palindrome substring is: ispalapsi Length is: 9
Algorithm
findLongPalSubstr(str)
Input − The main string.
Output − Longest palindromic substring and its length.
Begin n := length of the given string create a n x n table named palTab to store true or false value fill patTab with false values maxLen := 1 for i := 0 to n-1, do patTab[i, i] = true //as it is palindrome of length 1 done start := 0 for i := 0 to n-2, do if str[i] = str[i-1], then palTab[i, i+1] := true start := i maxLen := 2 done for k := 3 to n, do for i := 0 to n-k, do j := i + k – 1 if palTab[i+1, j-1] and str[i] = str[j], then palTab[i, j] := true if k > maxLen, then start := i maxLen := k done done display substring from start to maxLen from str, and return maxLen End
Example
#include<iostream> using namespace std; int findLongPalSubstr(string str) { int n = str.size(); // get length of input string bool palCheckTab[n][n]; //true when substring from i to j is palindrome for(int i = 0; i<n; i++) for(int j = 0; j<n; j++) palCheckTab[i][j] = false; //initially set all values to false int maxLength = 1; for (int i = 0; i < n; ++i) palCheckTab[i][i] = true; //as all substring of length 1 is palindrome int start = 0; for (int i = 0; i < n-1; ++i) { if (str[i] == str[i+1]) { //for two character substring both characters are equal palCheckTab[i][i+1] = true; start = i; maxLength = 2; } } for (int k = 3; k <= n; ++k) { //for substrings with length 3 to n for (int i = 0; i < n-k+1 ; ++i) { int j = i + k - 1; if (palCheckTab[i+1][j-1] && str[i] == str[j]) { //if (i,j) and (i+1, j-1) are same, then check palindrome palCheckTab[i][j] = true; if (k > maxLength) { start = i; maxLength = k; } } } } cout << "Longest palindrome substring is: " << str.substr(start, maxLength) << endl; return maxLength; // return length } int main() { char str[] = "thisispalapsiti"; cout << "Length is: "<< findLongPalSubstr(str); }
Output
Longest palindrome substring is: ispalapsi Length is: 9