Palindrome Partitioning II

Explain the Problem

Given a string s, partition s such that every substring of the partition is a palindrome. Return the minimum cuts needed for a palindrome partitioning of s.

Example:

Input: s = "aab"

Output: 1

Explanation: The palindrome partitioning ["aa","b"] could be produced using 1 cut.

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1) Explain the problem

Given a string s, partition s such that every substring of the partition is a palindrome. Return the minimum cuts needed for a palindrome partitioning of s.

2) Short easy to remember solution/approach

1. Use dynamic programming to determine the minimum cuts required.

2. Use a 2D table to check if substrings are palindromes and a 1D table to store the minimum cuts needed.

3) Solution in JavaScript with code commenting

function minCut(s) {
    const n = s.length;
    const isPalindrome = Array.from({ length: n }, () => Array(n).fill(false));
    const cuts = Array(n).fill(0);

    // Determine if substrings are palindromes
    for (let end = 0; end < n; end++) {
        for (let start = 0; start <= end; start++) {
            if (s[start] === s[end] && (end - start <= 2 || isPalindrome[start + 1][end - 1])) {
                isPalindrome[start][end] = true;
            }
        }
    }

    // Calculate minimum cuts
    for (let end = 0; end < n; end++) {
        if (isPalindrome[0][end]) {
            cuts[end] = 0;
        } else {
            let minCuts = Infinity;
            for (let start = 0; start < end; start++) {
                if (isPalindrome[start + 1][end]) {
                    minCuts = Math.min(minCuts, cuts[start] + 1);
                }
            }
            cuts[end] = minCuts;
        }
    }

    return cuts[n - 1];
}

// Example usage:
const s = "aab";
console.log(minCut(s)); // Output: 1

4) Explanation the solution in an easy-to-understand way with real-life example

Imagine you have a string like "aab" and you want to split it into pieces where each piece is a palindrome. A palindrome is a word that reads the same backward as forward, like "a", "aa", or "aba". Your goal is to make the fewest cuts possible to achieve this.

For example, for "aab", you can cut it after the first "a" to get "a | ab", but "ab" is not a palindrome. Instead, you can cut it to get "aa | b", which means only one cut is needed.

5) Code explanation in pointers

• Initialize palindrome table: Create a 2D array to store if substrings are palindromes.

• Check substrings: Fill the table to check each possible substring.

• Base case for palindromes: A single character is always a palindrome.

• Check if substring is a palindrome: Use previous results to check larger substrings.

• Initialize cuts array: Create an array to store the minimum cuts required.

• Calculate cuts: For each end position, calculate the minimum cuts needed using the palindrome table.

• Return result: The last value in the cuts array will be the minimum cuts needed for the entire string.

6) Complexities

• Time complexity: (O(n^2)) where (n) is the length of the string. This is due to the nested loops for filling the palindrome table and calculating cuts.

• Space complexity: (O(n^2)) for the 2D palindrome table and (O(n)) for the cuts array.when you're ready!

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