Palindrome Partitioning DP Minimum Cuts in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the minimum cuts array with the maximum possible cuts.

DSA C#

int n = s.Length;
int[] cuts = new int[n];
for (int i = 0; i < n; i++) {
    cuts[i] = [1];
}

Drag options to blanks, or click blank then click option'

Ai

Bi - 1

C0

Dn - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using i or i - 1 instead of n - 1 causes incorrect initialization.

Setting cuts[i] to 0 assumes no cuts needed initially.

We initialize cuts[i] with the maximum cuts possible, which is n - 1 (cutting between every character).

2fill in blank

medium

Complete the code to mark single characters as palindromes in the DP table.

DSA C#

bool[,] dp = new bool[n, n];
for (int i = 0; i < n; i++) {
    dp[i, i] = [1];
}

Drag options to blanks, or click blank then click option'

Afalse

Bi == 0

Ctrue

Ds[i] == s[i]

Attempts:

3 left

💡 Hint

Common Mistakes

Setting dp[i, i] to false causes incorrect palindrome detection.

Using conditions like s[i] == s[i] is redundant.

Every single character is a palindrome, so dp[i, i] should be true.

3fill in blank

hard

Fix the error in the palindrome check condition inside the nested loops.

DSA C#

for (int length = 2; length <= n; length++) {
    for (int start = 0; start <= n - length; start++) {
        int end = start + length - 1;
        if (s[start] == s[end] && (length == 2 || [1])) {
            dp[start, end] = true;
        }
    }
}

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Adp[start, end - 1]

Bdp[start + 1, end - 1]

Cdp[start + 1, end]

Ddp[start, end]

Attempts:

3 left

💡 Hint

Common Mistakes

Using dp[start, end - 1] or dp[start + 1, end] checks wrong substring parts.

Using dp[start, end] causes infinite recursion or wrong results.

For substrings longer than 2, check if the inner substring is palindrome using dp[start + 1, end - 1].

4fill in blank

hard

Fill both blanks to update the minimum cuts correctly when a palindrome substring is found.

DSA C#

for (int i = 0; i < n; i++) {
    if (dp[0, i]) {
        cuts[i] = 0;
    } else {
        for (int j = 0; j < i; j++) {
            if (dp[j + 1, i]) {
                cuts[i] = Math.Min(cuts[i], cuts[[1]] + [2]);
            }
        }
    }
}

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Aj

Bi

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using i instead of j causes wrong indexing.

Adding 0 instead of 1 misses the new cut.

We update cuts[i] by checking cuts[j] + 1 because we cut after position j.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each palindrome substring to its minimum cuts.

DSA C#

var result = new Dictionary<string, int>();
for (int start = 0; start < n; start++) {
    for (int end = start; end < n; end++) {
        if (dp[start, end]) {
            string substring = s.Substring(start, end - start + 1);
            result[[1]] = cuts[[2]];
        }
    }
}
return result;

Drag options to blanks, or click blank then click option'

Asubstring

Bend

Dstart

Attempts:

3 left

💡 Hint

Common Mistakes

Using start as key instead of substring.

Using cuts[start] instead of cuts[end].

Use substring as key, cuts[end] as value, and start for clarity in code.

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 longest palindromic substring in s

C. The total number of palindromic substrings in s

D. The maximum number of cuts possible 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 mean the smallest number of splits so that every substring after splitting is a palindrome.

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 length
• Counting total palindromic substrings instead of cuts
• Thinking maximum cuts is the goal

2. Which of the following C# code snippets correctly initializes the DP array to store minimum cuts for a string s of length n?

easy

A. int[] cuts = new int[n + 1]; for (int i = 0; i < n; i++) cuts[i] = n;

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

C. int[] cuts = new int[n + 1]; for (int i = 0; i <= n; i++) cuts[i] = i - 1;

D. int[] cuts = new int[n + 1]; for (int i = 0; i <= n; i++) cuts[i] = 0;

Solution

1. Step 1: Understand DP array purpose

   The DP array stores minimum cuts needed for substring up to index i, so size is n+1.

2. Step 2: Initialize cuts array correctly

   Initialize cuts[i] = i - 1 means worst case: each character is a palindrome, so max cuts = i-1.

3. Final Answer:

   int[] cuts = new int[n + 1]; for (int i = 0; i <= n; i++) cuts[i] = i - 1; -> Option C

4. Quick Check:

   DP array size n+1, initialized to max cuts i-1 [OK]

Hint: Initialize cuts[i] = i - 1 for worst case cuts [OK]

Common Mistakes:

• Using array size n instead of n+1
• Initializing all cuts to zero
• Starting loop from 0 but using wrong index in initialization

3. What is the output of the following C# code snippet for input string "aab"?

string s = "aab";
int n = s.Length;
int[] cuts = new int[n + 1];
for (int i = 0; i <= n; i++) cuts[i] = i - 1;
for (int i = 1; i <= n; i++) {
    for (int j = 0; j < i; j++) {
        if (IsPalindrome(s, j, i - 1)) {
            cuts[i] = Math.Min(cuts[i], cuts[j] + 1);
        }
    }
}
Console.WriteLine(cuts[n]);

bool IsPalindrome(string str, int left, int right) {
    while (left < right) {
        if (str[left] != str[right]) return false;
        left++;
        right--;
    }
    return true;
}

medium

A. 0

B. 3

C. 2

D. 1

Solution

1. Step 1: Trace DP initialization and loops

   cuts array initialized as [-1,0,1,2] for indices 0 to 3. Then loops check palindromes and update cuts.

2. Step 2: Check palindrome partitions for "aab"

   Partitions: "aa" (palindrome) + "b" (palindrome). Minimum cuts = 1.

3. Final Answer:

   1 -> Option D

4. Quick Check:

   Minimum cuts for "aab" = 1 [OK]

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

Common Mistakes:

• Assuming no cuts needed for "aab"
• Counting total palindromic substrings instead of cuts
• Off-by-one errors in loops

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

string s = "abc";
int n = s.Length;
int[] cuts = new int[n + 1];
for (int i = 0; i < n; i++) cuts[i] = i - 1;
for (int i = 1; i <= n; i++) {
    for (int j = 0; j < i; j++) {
        if (IsPalindrome(s, j, i - 1)) {
            cuts[i] = Math.Min(cuts[i], cuts[j] + 1);
        }
    }
}
Console.WriteLine(cuts[n]);

bool IsPalindrome(string str, int left, int right) {
    while (left < right) {
        if (str[left] != str[right]) return false;
        left++;
        right--;
    }
    return true;
}

medium

A. The outer loop should start from 0 instead of 1

B. The cuts array is not initialized for index n, causing incorrect values

C. The IsPalindrome function has incorrect loop conditions

D. The inner loop should run until j <= i instead of j < i

Solution

1. Step 1: Check cuts array initialization

   The loop initializes cuts from i=0 to i<n, missing index n, so cuts[n] remains 0 default, incorrect.

2. Step 2: Understand impact on DP calculation

   Without initializing cuts[n], Math.Min compares with 0, causing wrong minimum cuts result.

3. Final Answer:

   The cuts array is not initialized for index n, causing incorrect values -> Option B

4. Quick Check:

   Initialize cuts array fully to avoid wrong DP values [OK]

Hint: Initialize cuts array fully from 0 to n inclusive [OK]

Common Mistakes:

• Not initializing cuts[n] index
• Incorrect loop ranges in palindrome check
• Misunderstanding loop start indices

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

hard

A. 3

B. 4

C. 5

D. 6

Solution

1. Step 1: Understand the DP approach for complex string

   Use DP to check all substrings and update minimum cuts for partitions where substrings are palindromes.

2. Step 2: Apply known result or simulate DP

   For "ababbbabbababa", minimum cuts found by DP is 3, splitting into palindromic parts like "a|babbbab|b|ababa".

3. Final Answer:

   3 -> Option A

4. Quick Check:

   DP minimum cuts for complex palindrome partition = 3 [OK]

Hint: Use DP to find minimum cuts by checking all palindrome substrings [OK]

Common Mistakes:

• Guessing cuts without DP verification
• Miscounting palindrome partitions
• Assuming cuts equal to half string length