#2472 - Maximum Number of Non-overlapping Palindrome Substrings

Hard • View on LeetCode • View on GitHub

String Dynamic Programming Greedy Two Pointers

Problem Description

You are given a string s and a positive integer k.

Select a set of non-overlapping substrings from the string s that satisfy the following conditions:

The length of each substring is at least k.
Each substring is a palindrome.

Return the maximum number of substrings in an optimal selection.

A substring is a contiguous sequence of characters within a string.

Solution

/**
 * @param {string} s
 * @param {number} k
 * @return {number}
 */
var maxPalindromes = function(s, k) {
  const n = s.length;
  const isPal = new Array(n).fill().map(() => new Array(n).fill(false));
  const dp = new Array(n + 1).fill(0);

  for (let len = 1; len <= n; len++) {
    for (let start = 0; start + len <= n; start++) {
      const end = start + len - 1;
      if (len === 1) {
        isPal[start][end] = true;
      } else if (len === 2) {
        isPal[start][end] = s[start] === s[end];
      } else {
        isPal[start][end] = s[start] === s[end] && isPal[start + 1][end - 1];
      }
    }
  }

  for (let end = k; end <= n; end++) {
    dp[end] = dp[end - 1];
    for (let start = end - k; start >= 0; start--) {
      if (isPal[start][end - 1]) {
        dp[end] = Math.max(dp[end], dp[start] + 1);
      }
    }
  }

  return dp[n];
};