Palindrome Partitioning DP Minimum Cuts in DSA Typescript - Build from Scratch

Palindrome Partitioning DP Minimum Cuts

📖 Scenario: You are working on a text editor feature that helps users split a string into parts where each part is a palindrome. To make the editor efficient, you want to find the minimum number of cuts needed to split the string so that every substring is a palindrome.

🎯 Goal: Build a program that calculates the minimum number of cuts needed to partition a given string into palindromic substrings using dynamic programming.

📋 What You'll Learn

Create a string variable called inputString with the exact value "aab".

Create a 2D boolean array called isPalindrome to store palindrome checks for substrings.

Create an array called minCuts to store the minimum cuts needed for substrings.

Use nested loops to fill isPalindrome for all substrings of inputString.

Use a loop to calculate minCuts using the isPalindrome array.

Print the minimum cuts needed for the entire string.

💡 Why This Matters

🌍 Real World

Text editors and search tools often need to split strings into meaningful palindromic parts for pattern matching or highlighting.

💼 Career

Understanding palindrome partitioning and dynamic programming is useful for software engineers working on string processing, optimization problems, and algorithm design.

1

Create the input string

Create a string variable called inputString and set it to the exact value "aab".

DSA Typescript

// Create the input string
// Your code here

Hint

Use const inputString: string = "aab"; to create the string.

2

Initialize the palindrome table and minCuts array

Create a 2D boolean array called isPalindrome with size equal to the length of inputString to store palindrome checks. Also create an array called minCuts of the same length to store minimum cuts needed for substrings.

DSA Typescript

const inputString: string = "aab";
// Initialize isPalindrome 2D array and minCuts array
// Your code here

Hint

Use Array.from to create the 2D array and new Array(n).fill(0) for the cuts array.

3

Fill palindrome table and compute minimum cuts

Use nested for loops with variables end and start to fill the isPalindrome table for all substrings of inputString. Then use a for loop with variable i to calculate the minCuts array using the isPalindrome table.

DSA Typescript

const inputString: string = "aab";
const n: number = inputString.length;
const isPalindrome: boolean[][] = Array.from({ length: n }, () => Array(n).fill(false));
const minCuts: number[] = new Array(n).fill(0);
// Fill isPalindrome table and calculate minCuts
// Your code here

Hint

Use the palindrome condition: characters at start and end match and the substring between them is palindrome or length less than 2.

Calculate minCuts by checking all partitions.

4

Print the minimum cuts needed

Print the minimum number of cuts needed for the entire string by printing minCuts[n - 1].

DSA Typescript

const inputString: string = "aab";
const n: number = inputString.length;
const isPalindrome: boolean[][] = Array.from({ length: n }, () => Array(n).fill(false));
const minCuts: number[] = new Array(n).fill(0);

for (let end = 0; end < n; end++) {
    for (let start = 0; start <= end; start++) {
        if (inputString[start] === inputString[end] && (end - start < 2 || isPalindrome[start + 1][end - 1])) {
            isPalindrome[start][end] = true;
        }
    }
}

for (let i = 0; i < n; i++) {
    if (isPalindrome[0][i]) {
        minCuts[i] = 0;
    } else {
        let min = i;
        for (let j = 1; j <= i; j++) {
            if (isPalindrome[j][i] && minCuts[j - 1] + 1 < min) {
                min = minCuts[j - 1] + 1;
            }
        }
        minCuts[i] = min;
    }
}
// Print the minimum cuts needed
// Your code here

Hint

Print minCuts[n - 1] to get the minimum cuts needed for the whole string.