Palindrome Partitioning DP Minimum Cuts in DSA Java - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Minimum Cuts for Palindrome Partitioning

What is the output of the following Java code that calculates the minimum cuts needed to partition the string into palindromes?

DSA Java

public class PalindromePartition {
    public static int minCut(String s) {
        int n = s.length();
        boolean[][] dp = new boolean[n][n];
        int[] cuts = new int[n];
        for (int i = 0; i < n; i++) {
            int minCut = i;
            for (int j = 0; j <= i; j++) {
                if (s.charAt(i) == s.charAt(j) && (i - j < 2 || dp[j + 1][i - 1])) {
                    dp[j][i] = true;
                    minCut = j == 0 ? 0 : Math.min(minCut, cuts[j - 1] + 1);
                }
            }
            cuts[i] = minCut;
        }
        return cuts[n - 1];
    }

    public static void main(String[] args) {
        System.out.println(minCut("aab"));
    }
}

A 1

B 0

C 2

D 3

💡 Hint

Think about how many cuts are needed to split "aab" into palindromes.

The string "aab" can be split into "aa" and "b", both palindromes, with 1 cut.

🧠 Conceptual

intermediate

Understanding DP Table for Palindrome Partitioning

In the DP table used for palindrome partitioning, what does dp[i][j] represent?

A Minimum cuts needed for substring from i to j

B Whether the substring from index i to j is a palindrome

C Length of the longest palindrome substring from i to j

D Number of palindrome partitions from i to j

💡 Hint

Think about what boolean dp array stores in palindrome partitioning.

dp[i][j] is true if substring s[i..j] is palindrome, false otherwise.

🔧 Debug

advanced

Identify the Error in Palindrome Partitioning Code

What error will occur when running this code snippet for palindrome partitioning minimum cuts?

DSA Java

public int minCut(String s) {
    int n = s.length();
    boolean[][] dp = new boolean[n][n];
    int[] cuts = new int[n];
    for (int i = 0; i < n; i++) {
        cuts[i] = i;
        for (int j = 0; j < i; j++) {
            if (s.charAt(i) == s.charAt(j) && (i - j < 2 || dp[j + 1][i - 1])) {
                dp[j][i] = true;
                if (j == 0) {
                    cuts[i] = 0;
                } else {
                    cuts[i] = Math.min(cuts[i], cuts[j - 1] + 1);
                }
            }
        }
    }
    return cuts[n - 1];
}

A ArrayIndexOutOfBoundsException

B No error, code runs correctly

C NullPointerException

D Infinite loop

💡 Hint

Check the loop ranges and array accesses carefully.

The inner loop starts j=0 to i-1, but cuts[j-1] is accessed without checking j > 0 for cuts update, causing index error.

🚀 Application

advanced

Minimum Cuts for Complex Palindrome Partitioning

What is the minimum number of cuts needed to partition the string "ababbbabbababa" into palindromes?

A 5

B 4

C 3

D 2

💡 Hint

Try to find palindrome substrings and count cuts between them.

The minimum cuts for "ababbbabbababa" is 3, partitioning into palindromes like "a|babbbab|b|ababa".

🧠 Conceptual

expert

Time Complexity of Palindrome Partitioning Minimum Cuts DP

What is the time complexity of the dynamic programming solution for palindrome partitioning minimum cuts on a string of length n?

A O(n^3)

B O(n)

C O(n log n)

D O(n^2)

💡 Hint

Consider the nested loops and palindrome checks in the DP solution.

The DP solution uses two nested loops (O(n^2)) and O(1) palindrome checks via the DP table, resulting in O(n^2) time complexity.

Practice

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

easy

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

B. The maximum number of palindromic substrings in the string

C. The length of the longest palindromic substring

D. The total number of substrings in the string

Solution

1. Step 1: Understand palindrome partitioning

   Palindrome partitioning means splitting a string into parts where each part is a palindrome.

2. Step 2: Define minimum cuts

   Minimum cuts is the least number of cuts needed so that every substring after cutting is a palindrome.

3. Final Answer:

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

4. Quick Check:

   Minimum cuts = smallest cuts to get palindromes [OK]

Hint: Minimum cuts = least splits for palindrome parts [OK]

Common Mistakes:

• Confusing minimum cuts with maximum palindromes
• Thinking minimum cuts means longest palindrome length
• Counting total substrings instead of cuts

2. Which of the following Java code snippets correctly initializes the DP array for minimum cuts in palindrome partitioning of a string s of length n?

easy

A. int[] cuts = new int[n]; Arrays.fill(cuts, -1);

B. int[] cuts = new int[n]; for (int i = 0; i <= n; i++) cuts[i] = 0;

C. int[] cuts = new int[n]; for (int i = 0; i < n; i++) cuts[i] = i;

D. int[] cuts = new int[n+1]; Arrays.fill(cuts, Integer.MAX_VALUE);

Solution

1. Step 1: Understand DP array initialization

   We initialize cuts array where cuts[i] = i means max cuts needed for substring s[0..i].

2. Step 2: Check code correctness

   int[] cuts = new int[n]; for (int i = 0; i < n; i++) cuts[i] = i; initializes cuts array of size n and sets cuts[i] = i correctly. Other options have errors like wrong size or wrong initialization.

3. Final Answer:

   int[] cuts = new int[n]; for (int i = 0; i < n; i++) cuts[i] = i; -> Option C

4. Quick Check:

   Initialize cuts with max cuts = index [OK]

Hint: Initialize cuts[i] = i for max cuts before optimization [OK]

Common Mistakes:

• Using wrong array size causing IndexOutOfBounds
• Filling cuts with zero instead of max cuts
• Using negative values which are invalid

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

public class Solution {
  public static int minCut(String s) {
    int n = s.length();
    int[] cuts = new int[n];
    boolean[][] palindrome = new boolean[n][n];
    for (int i = 0; i < n; i++) cuts[i] = i;
    for (int end = 0; end < n; end++) {
      for (int start = 0; start <= end; start++) {
        if (s.charAt(start) == s.charAt(end) && (end - start < 2 || palindrome[start + 1][end - 1])) {
          palindrome[start][end] = true;
          cuts[end] = start == 0 ? 0 : Math.min(cuts[end], cuts[start - 1] + 1);
        }
      }
    }
    return cuts[n - 1];
  }
  public static void main(String[] args) {
    System.out.println(minCut("aab"));
  }
}

medium

A. 0

B. 1

C. 2

D. 3

Solution

1. Step 1: Analyze palindrome substrings in "aab"

   "a", "a", "b" are palindromes. "aa" is palindrome. Minimum cuts needed is 1 (cut between "aa" and "b").

2. Step 2: Trace DP updates

   cuts array updates to [0,0,1]. Final cuts[n-1] = 1.

3. Final Answer:

   1 -> Option B

4. Quick Check:

   Minimum cuts for "aab" = 1 [OK]

Hint: Check palindromes and update cuts with min previous cuts +1 [OK]

Common Mistakes:

• Assuming no cuts needed for "aab"
• Counting cuts as number of palindromes
• Ignoring palindrome "aa" substring

4. Identify the bug in the following Java code snippet for palindrome partitioning minimum cuts:

public int minCut(String s) {
  int n = s.length();
  int[] cuts = new int[n];
  boolean[][] palindrome = new boolean[n][n];
  for (int i = 0; i <= n; i++) cuts[i] = i;
  for (int end = 0; end < n; end++) {
    for (int start = 0; start <= end; start++) {
      if (s.charAt(start) == s.charAt(end) && (end - start < 2 || palindrome[start + 1][end - 1])) {
        palindrome[start][end] = true;
        cuts[end] = start == 0 ? 0 : Math.min(cuts[end], cuts[start - 1] + 1);
      }
    }
  }
  return cuts[n - 1];
}

medium

A. The return statement should be 'cuts[n]' instead of 'cuts[n - 1]'

B. The palindrome check condition is incorrect

C. The cuts array is not initialized properly

D. The loop 'for (int i = 0; i <= n; i++)' causes IndexOutOfBoundsException

Solution

1. Step 1: Check array initialization loop

   cuts array size is n, but loop runs i from 0 to n inclusive, causing IndexOutOfBoundsException at i = n.

2. Step 2: Confirm other parts are correct

   Palindrome check and return statement are correct. Initialization loop must be 'i < n'.

3. Final Answer:

   The loop 'for (int i = 0; i <= n; i++)' causes IndexOutOfBoundsException -> Option D

4. Quick Check:

   Array size n but loop runs to n inclusive causes error [OK]

Hint: Loop to n-1 for array size n to avoid out-of-bounds [OK]

Common Mistakes:

• Using <= n instead of < n in loops
• Misunderstanding palindrome condition
• Returning wrong index from cuts array

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

hard

A. 4

B. 5

C. 3

D. 6

Solution

1. Step 1: Understand the problem and DP approach

   We find minimum cuts so that each substring is palindrome. The string "ababbbabbababa" has palindromic partitions with 4 cuts.

2. Step 2: Trace or recall known result

   Known minimum cuts for this string is 4, splitting into palindromes like "a|babbbab|b|ababa" or similar.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Minimum cuts for "ababbbabbababa" = 4 [OK]

Hint: Use DP to find min cuts; known result for this string is 4 [OK]

Common Mistakes:

• Guessing cuts without checking palindrome substrings
• Counting number of palindromes instead of cuts
• Confusing cuts with substring length