Palindrome Substrings Count
Last Updated :
04 Aug, 2025
Given a string s, find the total number of palindromic substrings of length greater than or equal to 2 present in the string.
A substring is palindromic if it reads the same forwards and backwards.
Examples:
Input: s = "abaab"
Output: 3
Explanation: Palindromic substrings with length greater than 1, are "aba", "aa", and "baab".
Input: s = "aaa"
Output: 3
Explanation: Palindromic substrings with length greater than 1, are "aa" , "aa" , "aaa" .
Input: s = "abbaeae"
Output: 4
Explanation: Palindromic substrings with length greater than 1, are "bb" , "abba" , "aea", "eae".
[Naive Approach] By Generating All Possible Substrings - O(n^3) Time and O(1) Space
The idea is to generate all possible substrings using two nested loops and for every substring check if it is palindrome or not.
C++
// C++ program to count all palindromic substring of
// given string by generating all possible substrings
#include <iostream>
#include <string>
using namespace std;
// Function to check if a substring
// s[i..j] is a palindrome
bool isPalindrome(string& s, int i, int j) {
while (i < j) {
if (s[i] != s[j]) return false;
i++;
j--;
}
return true;
}
int countPS(string& s) {
int n = s.length();
// Consider all possible substrings of lengths
// more than 1
int res = 0;
for (int i = 0; i < n; i++) {
for (int j = i+1; j < n; j++) {
// If substring from i to j is palindrome
// increment the result
if (isPalindrome(s, i, j))
res++;
}
}
return res;
}
int main() {
string s = "abaab";
cout << countPS(s);
return 0;
}
// Java program to count all palindromic substring of
// given string by generating all possible substrings
class GfG {
// Function to check if a substring
// s[i..j] is a palindrome
static boolean isPalindrome(String s, int i, int j) {
while (i < j) {
if (s.charAt(i) != s.charAt(j)) return false;
i++;
j--;
}
return true;
}
static int countPS(String s) {
int n = s.length();
// Consider all possible substrings of lengths
// more than 1
int res = 0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
// If substring from i to j is palindrome
// increment the result
if (isPalindrome(s, i, j))
res++;
}
}
return res;
}
public static void main(String[] args) {
String s = "abaab";
System.out.println(countPS(s));
}
}
# Python program to count all palindromic substring of
# given string by generating all possible substrings
# Function to check if a substring
# s[i..j] is a palindrome
def isPalindrome(s, i, j):
while i < j:
if s[i] != s[j]:
return False
i += 1
j -= 1
return True
def countPS(s):
n = len(s)
# Consider all possible substrings of lengths
# more than 1
res = 0
for i in range(n):
for j in range(i + 1, n):
# If substring from i to j is palindrome
# increment the result
if isPalindrome(s, i, j):
res += 1
return res
if __name__ == "__main__":
s = "abaab"
print(countPS(s))
// C# program to count all palindromic substring of
// given string by generating all possible substrings
using System;
class GfG {
// Function to check if a substring
// s[i..j] is a palindrome
static bool isPalindrome(string s, int i, int j) {
while (i < j) {
if (s[i] != s[j]) return false;
i++;
j--;
}
return true;
}
static int countPS(string s) {
int n = s.Length;
// Consider all possible substrings of lengths
// more than 1
int res = 0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
// If substring from i to j is palindrome
// increment the result
if (isPalindrome(s, i, j))
res++;
}
}
return res;
}
static void Main() {
string s = "abaab";
Console.WriteLine(countPS(s));
}
}
// JavaScript program to count all palindromic substring
// of given string by generating all possible substrings
function isPalindrome(s, i, j) {
while (i < j) {
if (s[i] !== s[j]) return false;
i++;
j--;
}
return true;
}
function countPS(s) {
let n = s.length;
// Consider all possible substrings of lengths
// more than 1
let res = 0;
for (let i = 0; i < n; i++) {
for (let j = i + 1; j < n; j++) {
// If substring from i to j is palindrome
// increment the result
if (isPalindrome(s, i, j))
res++;
}
}
return res;
}
// Driver Code
let s = "abaab";
console.log(countPS(s));
[Better Approach 1] Using Memoization - O(n^2) Time and O(n^2) Space
If we notice carefully, we can observe that this recursive solution holds the following two properties of Dynamic Programming:
1.Optimal Substructure: The solution for the problem isPalindrome(i, j) depends on the optimal solution of the subproblem isPalindrome(i + 1, j - 1). By solving the smaller substructures, we can efficiently find if the entire substring is a palindrome or not.
2.Overlapping Subproblems: We can see that we are computing the same subproblems multiple times, isPalindrome(i + 2, j - 2) will be computed in isPalindrome(i, j) as well as isPalindrome(i + 1, j - 1). This redundancy leads to overlapping subproblems.
- There are two parameters(i and j) that change in the recursive solution and then can go from 0 to n. So we create a 2D array of size n x n for memoization.
- We initialize this array as -1 to indicate nothing is computed initially. We first check if the value is -1, then only we make recursive calls.
- If the substring from i to j is a palindrome, we store memo[i][j] = 1, otherwise 0.
C++
// C++ program to count all palindromic substring of
// given string using memoization
#include <iostream>
#include <vector>
#include <string>
using namespace std;
int isPalindrome(int i, int j, string& s,
vector<vector<int>>& memo) {
// One length string is always palindrome
if (i == j)
return 1;
// Two length string is plaindrome if
// both characters are same
if (j == i + 1 && s[i] == s[j])
return 1;
// if current substring is already checked
if (memo[i][j] != -1)
return memo[i][j];
// Check if the characters at i and j are equal
// and the substring inside is palindrome
memo[i][j] = (s[i] == s[j] &&
isPalindrome(i + 1, j - 1, s, memo));
return memo[i][j];
}
int countPS(string& s) {
int n = s.length();
// Memoization table
vector<vector<int>> memo(n, vector<int>(n, -1));
int res = 0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
// Check if the substring is palindrome
if (isPalindrome(i, j, s, memo)) {
res++;
}
}
}
return res;
}
int main() {
string s = "abaab";
cout << countPS(s);
return 0;
}
// Java program to count all palindromic substring of given
// string using memoization
import java.util.Arrays;
class GfG {
static int isPalindrome(int i, int j, String s,
int[][] memo) {
// One length string is always palindrome
if (i == j)
return 1;
// Two length string is palindrome if
// both characters are same
if (j == i + 1 && s.charAt(i) == s.charAt(j))
return 1;
// if current substring is already checked
if (memo[i][j] != -1)
return memo[i][j];
// Check if the characters at i and j are equal
// and the substring inside is palindrome
if(s.charAt(i) == s.charAt(j) &&
isPalindrome(i + 1, j - 1, s, memo) == 1)
memo[i][j] = 1;
else
memo[i][j] = 0;
return memo[i][j];
}
static int countPS(String s) {
int n = s.length();
// Memoization table
int[][] memo = new int[n][n];
for (int[] row : memo) {
Arrays.fill(row, -1);
}
int res = 0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
// Check if the substring is palindrome
if (isPalindrome(i, j, s, memo) == 1) {
res++;
}
}
}
return res;
}
public static void main(String[] args) {
String s = "abaab";
System.out.println(countPS(s));
}
}
# Python program to count all palindromic substrings of
# a given string using memoization
def isPalindrome(i, j, s, memo):
# One length string is always palindrome
if i == j:
return 1
# Two length string is palindrome if
# both characters are same
if j == i + 1 and s[i] == s[j]:
return 1
# if current substring is already checked
if memo[i][j] != -1:
return memo[i][j]
# Check if the characters at i and j are equal
# and the substring inside is palindrome
if s[i] == s[j] and isPalindrome(i + 1, j - 1, s, memo) == 1:
memo[i][j] = 1
else:
memo[i][j] = 0
return memo[i][j]
def countPS(s):
n = len(s)
# Memoization table
memo = [[-1 for i in range(n)] for i in range(n)]
res = 0
for i in range(n):
for j in range(i + 1, n):
# Check if the substring is palindrome
if isPalindrome(i, j, s, memo) == 1:
res += 1
return res
if __name__ == "__main__":
s = "abaab"
print(countPS(s))
// C# program to count all palindromic substrings of
// a given string using memoization
using System;
class GfG {
static int IsPalindrome(int i, int j, string s,
int[,] memo) {
// One length string is always palindrome
if (i == j)
return 1;
// Two length string is palindrome if
// both characters are same
if (j == i + 1 && s[i] == s[j])
return 1;
// if current substring is already checked
if (memo[i, j] != -1)
return memo[i, j];
// Check if the characters at i and j are equal
// and the substring inside is palindrome
if (s[i] == s[j] &&
IsPalindrome(i + 1, j - 1, s, memo) == 1) {
memo[i, j] = 1;
}
else {
memo[i, j] = 0;
}
return memo[i, j];
}
static int CountPS(string s) {
int n = s.Length;
// Memoization table
int[,] memo = new int[n, n];
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
memo[i, j] = -1;
}
}
int res = 0;
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
// Check if the substring is palindrome
if (IsPalindrome(i, j, s, memo) == 1) {
res++;
}
}
}
return res;
}
static void Main() {
string s = "abaab";
Console.WriteLine(CountPS(s));
}
}
// JavaScript program to count all palindromic substrings of
// a given string using memoization
function isPalindrome(i, j, s, memo) {
// One length string is always palindrome
if (i === j)
return 1;
// Two length string is palindrome if
// both characters are same
if (j === i + 1 && s[i] === s[j])
return 1;
// if current substring is already checked
if (memo[i][j] !== -1)
return memo[i][j];
// Check if the characters at i and j are equal
// and the substring inside is palindrome
if (s[i] === s[j] &&
isPalindrome(i + 1, j - 1, s, memo) === 1)
memo[i][j] = 1;
else
memo[i][j] = 0;
return memo[i][j];
}
function countPS(s) {
const n = s.length;
// Memoization table
const memo = Array.from({ length: n }, () => Array(n).fill(-1));
let res = 0;
for (let i = 0; i < n; i++) {
for (let j = i + 1; j < n; j++) {
// Check if the substring is palindrome
if (isPalindrome(i, j, s, memo) === 1) {
res++;
}
}
}
return res;
}
// Driver Code
const s = "abaab";
console.log(countPS(s));
[Better Approach 2] Using Bottom-Up DP (Tabulation) - O(n^2) Time and O(n^2) Space
We create a dp array of size n x n. However, we cannot simply fill the dp table from i = 0 to n-1 and j from i to n-1. To compute the value for (i, j), we need the value from (i+1, j-1). Similar to Matrix Chain Multiplication, we need to fill the table diagonally using a gap variable.
1. Base Cases:
=> A single character string is always palindrome, i.e. dp[i][i] = true.
=> Strings having two characters are palindrome, if both the characters are same. i.e. dp[i][i+1] = true if s[i] == s[i+1].
2. Any substring s[i...j] will be palindrome if:
=> If first and last characters of string are same
=> Remaining substring (excluding first and last character) is palindrome. I.e. dp[i+1][j-1] = true.
Illustration:
C++
// C++ program to count all palindromic substring of
// given string using bottom up DP
#include <iostream>
#include <vector>
#include <string>
using namespace std;
int countPS(string& s) {
int n = s.length();
int res = 0;
vector<vector<bool>> dp(n, vector<bool>(n, false));
// One length string is always palindrome
for (int i = 0; i < n; i++) {
dp[i][i] = true;
}
// Two length string is plaindrome if
// both characters are same
for (int i = 0; i < n - 1; i++) {
if (s[i] == s[i + 1]) {
dp[i][i + 1] = true;
res++;
}
}
// Handle palindromes of length
// greater than 2 (gap >= 2)
for (int gap = 2; gap < n; gap++) {
for (int i = 0; i < n - gap; i++) {
int j = i + gap;
// Check if the current string is a palindrome
if (s[i] == s[j] && dp[i + 1][j - 1]) {
dp[i][j] = true;
res++;
}
}
}
return res;
}
int main() {
string s = "abaab";
cout << countPS(s) << endl;
return 0;
}
// Java program to count all palindromic substrings of
// given string using bottom-up DP
import java.util.*;
class GfG {
static int countPS(String s) {
int n = s.length();
int res = 0;
boolean[][] dp = new boolean[n][n];
// One length string is always palindrome
for (int i = 0; i < n; i++) {
dp[i][i] = true;
}
// Two length string is palindrome if
// both characters are same
for (int i = 0; i < n - 1; i++) {
if (s.charAt(i) == s.charAt(i + 1)) {
dp[i][i + 1] = true;
res++;
}
}
// Handle palindromes of length greater than 2
for (int gap = 2; gap < n; gap++) {
for (int i = 0; i < n - gap; i++) {
int j = i + gap;
// Check if the current string is a palindrome
if (s.charAt(i) == s.charAt(j) && dp[i + 1][j - 1]) {
dp[i][j] = true;
res++;
}
}
}
return res;
}
public static void main(String[] args) {
String s = "abaab";
System.out.println(countPS(s));
}
}
# Python program to count all palindromic substrings of
# given string using bottom-up DP
def countPS(s):
n = len(s)
res = 0
dp = [[False] * n for i in range(n)]
# One length string is always palindrome
for i in range(n):
dp[i][i] = True
# Two length string is palindrome if
# both characters are same
for i in range(n - 1):
if s[i] == s[i + 1]:
dp[i][i + 1] = True
res += 1
# Handle palindromes of length
# greater than 2 (gap >= 2)
for gap in range(2, n):
for i in range(n - gap):
j = i + gap
# Check if the current string is a palindrome
if s[i] == s[j] and dp[i + 1][j - 1]:
dp[i][j] = True
res += 1
return res
if __name__ == "__main__":
s = "abaab"
print(countPS(s))
// C# program to count all palindromic substrings of
// given string using bottom-up DP
using System;
class GfG {
static int countPS(string s) {
int n = s.Length;
int res = 0;
bool[,] dp = new bool[n, n];
// One length string is always palindrome
for (int i = 0; i < n; i++) {
dp[i, i] = true;
}
// Two length string is palindrome if
// both characters are same
for (int i = 0; i < n - 1; i++) {
if (s[i] == s[i + 1]) {
dp[i, i + 1] = true;
res++;
}
}
// Handle palindromes of length
// greater than 2 (gap >= 2)
for (int gap = 2; gap < n; gap++) {
for (int i = 0; i < n - gap; i++) {
int j = i + gap;
// Check if the current string is a palindrome
if (s[i] == s[j] && dp[i + 1, j - 1]) {
dp[i, j] = true;
res++;
}
}
}
return res;
}
static void Main() {
string s = "abaab";
Console.WriteLine(countPS(s));
}
}
// JavaScript program to count all palindromic substrings of
// given string using bottom-up DP
function countPS(s) {
const n = s.length;
let res = 0;
const dp = Array.from({ length: n }, () => Array(n).fill(false));
// One length string is always palindrome
for (let i = 0; i < n; i++) {
dp[i][i] = true;
}
// Two length string is palindrome if
// both characters are same
for (let i = 0; i < n - 1; i++) {
if (s[i] === s[i + 1]) {
dp[i][i + 1] = true;
res++;
}
}
// Handle palindromes of length
// greater than 2 (gap >= 2)
for (let gap = 2; gap < n; gap++) {
for (let i = 0; i < n - gap; i++) {
const j = i + gap;
// Check if the current string is a palindrome
if (s[i] === s[j] && dp[i + 1][j - 1]) {
dp[i][j] = true;
res++;
}
}
}
return res;
}
// Driver Code
const s = "abaab";
console.log(countPS(s));
This problem can be solved more efficiently using Manacher’s algorithm or the center expansion technique.
See: Count All Palindrome Sub-Strings Set 2
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