LeetCode 2472: Maximum Number of Non-overlapping Palindrome Substrings Solution

Master LeetCode problem 2472 (Maximum Number of Non-overlapping Palindrome Substrings), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2472. Maximum Number of Non-overlapping Palindrome Substrings

Hard

Two Pointers String Dynamic Programming Greedy

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming to find all palindromes in the given string s. We can then use another dynamic programming approach to select non-overlapping palindromes that have a length of at least k. The idea is to iterate through the palindromes and keep track of the maximum number of non-overlapping palindromes found so far.

Find all palindromes in the string s using dynamic programming.
Use dynamic programming to select non-overlapping palindromes of length at least k.
Keep track of the maximum number of non-overlapping palindromes found.

Time complexity: O(n^2) where n is the length of the input string s. Space complexity: O(n^2) for storing the palindrome information.

Solution Code

class Solution {
    public int countPalindromicSubstrings(String s, int k) {
        int n = s.length();
        boolean[][] isPalindrome = new boolean[n][n];
        int count = 0;
        
        // Find all palindromes
        for (int len = 1; len <= n; len++) {
            for (int i = 0; i + len - 1 < n; i++) {
                int j = i + len - 1;
                if (len == 1) {
                    isPalindrome[i][j] = true;
                } else if (len == 2) {
                    isPalindrome[i][j] = (s.charAt(i) == s.charAt(j));
                } else {
                    isPalindrome[i][j] = (s.charAt(i) == s.charAt(j) && isPalindrome[i + 1][j - 1]);
                }
            }
        }
        
        // Select non-overlapping palindromes of length at least k
        int[] dp = new int[n];
        for (int i = 0; i < n; i++) {
            dp[i] = i > 0 ? dp[i - 1] : 0;
            for (int j = 0; j <= i; j++) {
                if (isPalindrome[j][i] && i - j + 1 >= k) {
                    dp[i] = Math.max(dp[i], (j > 0 ? dp[j - 1] : 0) + 1);
                }
            }
            count = Math.max(count, dp[i]);
        }
        
        return count;
    }
}

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