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.

Practice

1. What does the "Palindrome Partitioning DP Minimum Cuts" problem aim to find for a given string s?

easy

A. The minimum number of cuts needed to partition s into palindromic substrings

B. The maximum length of a palindrome substring in s

C. The total number of palindrome substrings in s

D. The longest palindrome substring in s

Solution

1. Step 1: Understand the problem goal

   The problem asks for the fewest cuts needed to split the string into parts where each part is a palindrome.

2. Step 2: Clarify what minimum cuts mean

   Minimum cuts means the smallest number of splits to make all parts palindromes.

3. Final Answer:

   The minimum number of cuts needed to partition s into palindromic substrings -> Option A

4. Quick Check:

   Minimum cuts = minimum splits for palindrome parts [OK]

Hint: Focus on splitting string into palindrome parts with fewest cuts [OK]

Common Mistakes:

• Confusing minimum cuts with longest palindrome substring
• Counting total palindrome substrings instead of cuts
• Thinking about maximum palindrome length

2. Which of the following TypeScript function signatures correctly represents a function to compute minimum palindrome partition cuts for a string s?

easy

A. function minCut(s: string): string[]

B. function minCut(s: number): string

C. function minCut(s: string): number

D. function minCut(s: boolean): number

Solution

1. Step 1: Identify input and output types

   Input is a string s, output is a number representing minimum cuts.

2. Step 2: Match correct signature

   Only function minCut(s: string): number matches input string and numeric output.

3. Final Answer:

   function minCut(s: string): number -> Option C

4. Quick Check:

   Input string, output number for cuts [OK]

Hint: Input string, output number for minimum cuts [OK]

Common Mistakes:

• Using wrong input type like number or boolean
• Returning array or string instead of number
• Mixing input and output types

3. What is the output of the following TypeScript code for input "aab"?

function minCut(s: string): number {
  const n = s.length;
  const dp = new Array(n).fill(0);
  const palindrome = Array.from({ length: n }, () => new Array(n).fill(false));

  for (let i = 0; i < n; i++) {
    let minCuts = i;
    for (let j = 0; j <= i; j++) {
      if (s[j] === s[i] && (i - j < 2 || palindrome[j + 1][i - 1])) {
        palindrome[j][i] = true;
        minCuts = j === 0 ? 0 : Math.min(minCuts, dp[j - 1] + 1);
      }
    }
    dp[i] = minCuts;
  }
  return dp[n - 1];
}
console.log(minCut("aab"));

medium

A. 0

B. 1

C. 2

D. 3

Solution

1. Step 1: Trace palindrome checks for "aab"

   Substrings: "a" (palindrome), "aa" (palindrome), "b" (palindrome). Minimum cuts for "aab" is 1 (cut between "aa" and "b").

2. Step 2: Check dp array updates

   dp[0]=0 ("a"), dp[1]=0 ("aa"), dp[2]=1 (cut before "b").

3. Final Answer:

   1 -> Option B

4. Quick Check:

   Minimum cuts for "aab" = 1 [OK]

Hint: Check palindrome substrings and update dp for minimum cuts [OK]

Common Mistakes:

• Assuming no cuts needed for "aab"
• Counting total palindromes instead of cuts
• Incorrect dp index updates

4. Identify the bug in this TypeScript code snippet for minimum palindrome partition cuts:

function minCut(s: string): number {
  const n = s.length;
  const dp = new Array(n).fill(0);
  const palindrome = Array.from({ length: n }, () => new Array(n).fill(false));

  for (let i = 0; i < n; i++) {
    dp[i] = i;
    for (let j = 0; j <= i; j++) {
      if (s[j] === s[i] && (i - j < 2 || palindrome[j + 1][i - 1])) {
        palindrome[j][i] = true;
        dp[i] = Math.min(dp[i], dp[j - 1] + 1);
      }
    }
  }
  return dp[n - 1];
}

medium

A. dp[i] should be initialized to 0 instead of i

B. Inner loop should run from j = 0 to j <= i

C. palindrome array initialization is incorrect

D. dp[j] should be dp[j - 1] when updating dp[i]

Solution

1. Step 1: Analyze dp update logic

   When substring s[j..i] is palindrome, dp[i] should consider dp[j-1] + 1 cuts, not dp[j] + 1.

2. Step 2: Identify correct index for dp

   dp[j-1] represents cuts before substring start; dp[j] is incorrect and causes off-by-one error.

3. Final Answer:

   dp[j] should be dp[j - 1] when updating dp[i] -> Option D

4. Quick Check:

   Use dp[j-1] for correct minimum cuts [OK]

Hint: Use dp[j-1] when substring starts at j to avoid off-by-one error [OK]

Common Mistakes:

• Using dp[j] instead of dp[j-1]
• Incorrect loop bounds causing missed palindromes
• Wrong initialization of dp array

5. Given the string "abccbc", what is the minimum number of cuts needed to partition it into palindromic substrings using the DP approach?

hard

A. 2

B. 1

C. 3

D. 0

Solution

1. Step 1: Identify palindromic substrings in "abccbc"

   Palindromes include "a", "b", "cc", "bcb", "c". Partitioning as "a" | "bccb" | "c" is possible with 2 cuts.

2. Step 2: Calculate minimum cuts

   Minimum cuts = 2 because splitting into "a" | "bccb" | "c" yields all palindromes with 2 cuts.

3. Final Answer:

   2 -> Option A

4. Quick Check:

   Minimum cuts for "abccbc" = 2 [OK]

Hint: Look for largest palindrome substrings to minimize cuts [OK]

Common Mistakes:

• Assuming 0 cuts because string is not fully palindrome
• Counting each character as separate palindrome causing more cuts
• Missing palindrome "bccb" in middle