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

Palindrome Partitioning DP Minimum Cuts

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

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

📋 What You'll Learn

Create a string variable called word with the exact value 'noonabbad'.

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

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

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

Use a loop to calculate minCuts using the palindrome information.

Print the minimum cuts needed for the entire string.

💡 Why This Matters

🌍 Real World

Palindrome partitioning is useful in text processing, DNA sequence analysis, and data compression where symmetrical patterns matter.

💼 Career

Understanding dynamic programming and string manipulation is important for software engineering roles involving algorithms, coding interviews, and problem-solving.

1

Create the input string word

Create a string variable called word and set it to the exact value 'noonabbad'.

DSA Javascript

# Create the string variable word
# Your code here

Hint

Use const word = 'noonabbad'; to create the string.

2

Initialize the palindrome table isPalindrome and minimum cuts array minCuts

Create a 2D array called isPalindrome with size word.length by word.length filled with false. Also, create an array called minCuts of length word.length filled with zeros.

DSA Javascript

const word = 'noonabbad';
// 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 isPalindrome and calculate minCuts

Use nested loops with variables end and start to fill isPalindrome[start][end] as true if the substring word[start..end] is a palindrome. Then, use a loop with variable i to calculate minCuts[i] as the minimum cuts needed for substring word[0..i].

DSA Javascript

const word = 'noonabbad';
const n = word.length;
const isPalindrome = Array.from({ length: n }, () => Array(n).fill(false));
const minCuts = new Array(n).fill(0);

// Fill isPalindrome and minCuts arrays
// Your code here

Hint

Use the palindrome property: characters at start and end match and the inner substring is palindrome or length less than 2.

Calculate minimum cuts by checking all partitions.

4

Print the minimum cuts needed for the entire string

Print the value of minCuts[word.length - 1] to display the minimum cuts needed to partition the entire string into palindromes.

DSA Javascript

const word = 'noonabbad';
const n = word.length;
const isPalindrome = Array.from({ length: n }, () => Array(n).fill(false));
const minCuts = new Array(n).fill(0);

for (let end = 0; end < n; end++) {
    for (let start = 0; start <= end; start++) {
        if (word[start] === word[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 for the entire string
// Your code here

Hint

Use console.log(minCuts[n - 1]) to print the minimum cuts.

Practice

1. What does the term minimum cuts mean in the context of palindrome partitioning?

easy

A. The number of characters to remove to make the string a palindrome

B. The longest palindrome substring in the string

C. The total number of palindromic substrings in the string

D. The smallest number of cuts needed to split the string into palindromic substrings

Solution

1. Step 1: Understand palindrome partitioning

   Palindrome partitioning splits a string into substrings where each substring is a palindrome.

2. Step 2: Define minimum cuts

   Minimum cuts means the least number of cuts needed to divide the string so that every part is a palindrome.

3. Final Answer:

   The smallest number of cuts needed to split the string into palindromic substrings -> Option D

4. Quick Check:

   Minimum cuts = smallest cuts for palindrome parts [OK]

Hint: Minimum cuts split string into palindrome parts with fewest cuts [OK]

Common Mistakes:

• Confusing minimum cuts with longest palindrome substring
• Thinking minimum cuts count characters removed
• Mixing total palindrome substrings with minimum cuts

2. Which of the following is the correct way to initialize a 2D boolean array isPalindrome for a string s of length n in JavaScript?

easy

A. const isPalindrome = Array.from({length: n}, () => Array(n).fill(false));

B. const isPalindrome = Array(n).fill(Array(n).fill(false));

C. const isPalindrome = new Array(n).fill(new Array(n).fill(false));

D. const isPalindrome = Array(n).map(Array(n).fill(false));

Solution

1. Step 1: Understand 2D array initialization in JavaScript

   Using Array.from with a mapping function creates independent inner arrays.

2. Step 2: Compare options

   const isPalindrome = Array.from({length: n}, () => Array(n).fill(false)); correctly creates separate inner arrays filled with false. Options A and C create references to the same inner array, causing bugs. const isPalindrome = Array(n).map(() => Array(n).fill(false)); fails because map on uninitialized array does not work as expected.

3. Final Answer:

   const isPalindrome = Array.from({length: n}, () => Array(n).fill(false)); -> Option A

4. Quick Check:

   Use Array.from with function for independent inner arrays [OK]

Hint: Use Array.from with function to avoid shared references [OK]

Common Mistakes:

• Using fill with array directly causing shared references
• Using map on uninitialized arrays
• Not initializing inner arrays separately

3. What is the output of the following code snippet for s = "aab"?

function minCut(s) {
  const n = s.length;
  const isPalindrome = Array.from({length: n}, () => Array(n).fill(false));
  for (let i = 0; i < n; i++) {
    isPalindrome[i][i] = true;
  }
  for (let length = 2; length <= n; length++) {
    for (let start = 0; start <= n - length; start++) {
      let end = start + length - 1;
      if (s[start] === s[end]) {
        if (length === 2) {
          isPalindrome[start][end] = true;
        } else {
          isPalindrome[start][end] = isPalindrome[start + 1][end - 1];
        }
      }
    }
  }
  const cuts = Array(n).fill(0);
  for (let i = 0; i < n; i++) {
    let minCut = i;
    for (let j = 0; j <= i; j++) {
      if (isPalindrome[j][i]) {
        minCut = j === 0 ? 0 : Math.min(minCut, cuts[j - 1] + 1);
      }
    }
    cuts[i] = minCut;
  }
  return cuts[n - 1];
}
console.log(minCut(s));

medium

A. 0

B. 1

C. 2

D. 3

Solution

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

   "a", "a", "b" are palindromes; "aa" is palindrome; "aab" is not.

2. Step 2: Calculate minimum cuts

   Minimum cuts needed: split "aab" as "aa" | "b" with 1 cut.

3. Final Answer:

   1 -> Option B

4. Quick Check:

   Minimum cuts for "aab" = 1 [OK]

Hint: Check palindrome substrings, then find fewest cuts [OK]

Common Mistakes:

• Assuming no cuts needed for non-palindrome string
• Counting total palindromic substrings instead of cuts
• Misindexing palindrome checks

4. The following code attempts to compute minimum cuts for palindrome partitioning but has a bug. What is the error?

function minCut(s) {
  const n = s.length;
  const isPalindrome = Array(n).fill(Array(n).fill(false));
  for (let i = 0; i < n; i++) {
    isPalindrome[i][i] = true;
  }
  // ... rest of palindrome logic ...
  return 0;
}

medium

A. The function does not return the minimum cuts value

B. Loop for setting isPalindrome[i][i] should start from 1, not 0

C. isPalindrome initialization shares inner arrays causing incorrect updates

D. The string length n is not calculated correctly

Solution

1. Step 1: Analyze isPalindrome array initialization

   Using fill with an array creates references to the same inner array, so updating one row updates all rows.

2. Step 2: Understand impact on palindrome checks

   This causes incorrect palindrome marking because all rows share the same inner array, corrupting data.

3. Final Answer:

   isPalindrome initialization shares inner arrays causing incorrect updates -> Option C

4. Quick Check:

   Shared inner arrays cause bugs in 2D boolean array [OK]

Hint: Avoid fill with arrays; use Array.from with function [OK]

Common Mistakes:

• Ignoring shared reference problem in 2D arrays
• Thinking loop start index causes bug
• Overlooking missing return value as main error

5. Given the string s = "ababbbabbababa", what is the minimum number of cuts needed to partition it into palindromic substrings using dynamic programming?

hard

A. 3

B. 5

C. 4

D. 6

Solution

1. Step 1: Understand palindrome partitions for "ababbbabbababa"

   This string can be partitioned into palindromes with minimum cuts by checking all substrings and using DP to find minimal cuts.

2. Step 2: Use known result or DP approach

   The minimum cuts for this string is 3, as it can be split into palindromic parts like "a|babbbab|b|ababa" or similar partitions.

3. Final Answer:

   3 -> Option A

4. Quick Check:

   Minimum cuts for complex palindrome string = 3 [OK]

Hint: Use DP palindrome checks and cuts array to find minimum cuts [OK]

Common Mistakes:

• Assuming minimum cuts equals number of palindromic substrings
• Miscounting cuts by off-by-one errors
• Not considering overlapping palindrome substrings