Palindrome Partitioning DP Minimum Cuts in DSA Rust - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to initialize the DP array with maximum cuts possible for each position.

DSA Rust

let n = s.len();
let mut cuts = vec![[1]; n + 1];

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

An

B0

Cn - 1

Dusize::MAX

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing cuts with 0 causes incorrect minimum cuts calculation.

Using usize::MAX causes overflow in later calculations.

We initialize the cuts array with the maximum cuts possible, which is equal to the length of the string n. This represents the worst case where every character is cut separately.

2fill in blank

medium

Complete the code to mark the substring s[left..=right] as palindrome in the DP table.

DSA Rust

if s.as_bytes()[left] == s.as_bytes()[right] && (right - left < 2 || dp[left + 1][right - 1]) {
    dp[left][right] = [1];
}

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

Afalse

Bright - left == 1

Cleft == right

Dtrue

Attempts:

3 left

💡 Hint

Common Mistakes

Setting dp[left][right] to false prevents recognizing palindromes.

Using conditions like left == right instead of true.

We set dp[left][right] to true to indicate that the substring s[left..=right] is a palindrome.

3fill in blank

hard

Fix the error in updating the minimum cuts when a palindrome substring is found.

DSA Rust

if dp[j][i] {
    cuts[i + 1] = cuts[i + 1].min(cuts[[1]] + 1);
}

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Aj + 1

Bi

Cj

Di + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using cuts[j + 1] causes index out of bounds or wrong calculation.

Using cuts[i] or cuts[i + 1] inside min causes no update.

We use cuts[j] because cuts[j] represents the minimum cuts needed for substring s[0..j], so adding 1 cut after j gives cuts for s[0..i+1].

4fill in blank

hard

Fill both blanks to complete the nested loops iterating over substring indices.

DSA Rust

for [1] in 0..n {
    for [2] in 0..=i {
        // palindrome check and cuts update
    }
}

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Ai

Bj

Cn

Dleft

Attempts:

3 left

💡 Hint

Common Mistakes

Using same variable name for both loops causes errors.

Using n in inner loop causes out of range indices.

The outer loop variable is i iterating over substring end indices, and inner loop variable is j iterating over substring start indices.

5fill in blank

hard

Fill all three blanks to complete the palindrome partitioning minimum cuts function.

DSA Rust

fn min_cut(s: &str) -> usize {
    let n = s.len();
    let mut dp = vec![vec![false; n]; n];
    let mut cuts = vec![0; n + 1];
    for i in 0..=n {
        cuts[i] = [1];
    }
    for i in 0..n {
        for j in 0..=i {
            if s.as_bytes()[i] == s.as_bytes()[j] && (i - j < 2 || dp[j + 1][i - 1]) {
                dp[j][i] = [2];
                cuts[i + 1] = cuts[i + 1].min(cuts[[3]] + 1);
            }
        }
    }
    cuts[n] - 1
}

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

Ai

Bn

Cj

Dtrue

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing cuts with i causes wrong minimum cuts.

Setting dp[j][i] to false prevents palindrome recognition.

Using cuts[i] instead of cuts[j] in update causes errors.

Initialize cuts[i] with n (max cuts), mark dp[j][i] as true for palindrome, and update cuts[i+1] using cuts[j] + 1.

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 so that every piece after cutting 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: Minimum cuts split string into palindrome parts [OK]

Common Mistakes:

• Confusing minimum cuts with longest palindrome
• Thinking about total palindrome count instead of cuts
• Assuming maximum cuts is the goal

2. Which of the following Rust code snippets correctly initializes a 2D vector dp of size n x n with false values for palindrome checks?

easy

A. let dp = vec![vec![true; n]; n];

B. let dp = vec![false; n * n];

C. let dp = vec![vec![false; n * n]; 1];

D. let dp = vec![vec![false; n]; n];

Solution

1. Step 1: Understand 2D vector initialization in Rust

   To create an n by n 2D vector filled with false, use vec![vec![false; n]; n].

2. Step 2: Check each option

   let dp = vec![vec![false; n]; n]; correctly creates a 2D vector with n rows and n columns filled with false.

3. Final Answer:

   let dp = vec![vec![false; n]; n]; -> Option D

4. Quick Check:

   2D vector with false = vec![vec![false; n]; n] [OK]

Hint: Use vec![vec![false; n]; n] for 2D boolean vector [OK]

Common Mistakes:

• Using 1D vector instead of 2D
• Filling with true instead of false
• Incorrect dimensions in inner or outer vec

3. Given the Rust function below for minimum cuts, what is the output for input "aab"?

fn min_cut(s: &str) -> i32 {
    let n = s.len();
    let s_bytes = s.as_bytes();
    let mut dp = vec![0; n + 1];
    let mut palindrome = vec![vec![false; n]; n];
    for i in 0..=n {
        dp[i] = i as i32 - 1;
    }
    for i in 0..n {
        for j in i..n {
            if s_bytes[i] == s_bytes[j] && (j - i < 2 || palindrome[i + 1][j - 1]) {
                palindrome[i][j] = true;
                dp[j + 1] = dp[j + 1].min(dp[i] + 1);
            }
        }
    }
    dp[n]
}

println!("{}", min_cut("aab"));

medium

A. 3

B. 2

C. 1

D. 0

Solution

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

   Substrings: "a" (0,0), "aa" (0,1), "aab" (0,2), "a" (1,1), "ab" (1,2), "b" (2,2). "aa" and single letters are palindrome.

2. Step 2: Calculate dp array values

   dp[0] = -1, dp[1] = 0, dp[2] = 1, dp[3] = 2 initially. Updates: For "aa", dp[2] = min(dp[2], dp[0] + 1) = 0. For "b", dp[3] = min(dp[3], dp[2] + 1) = 1.

3. Final Answer:

   1 -> Option C

4. Quick Check:

   Minimum cuts for "aab" = 1 [OK]

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

Common Mistakes:

• Not initializing dp correctly
• Ignoring palindrome length 1 or 2 cases
• Off-by-one errors in dp indexing

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

fn min_cut(s: &str) -> i32 {
    let n = s.len();
    let s_bytes = s.as_bytes();
    let mut dp = vec![0; n + 1];
    let mut palindrome = vec![vec![false; n]; n];
    for i in 0..n {
        dp[i] = i as i32;
    }
    for i in 0..n {
        for j in i..n {
            if s_bytes[i] == s_bytes[j] && (j - i < 2 || palindrome[i + 1][j - 1]) {
                palindrome[i][j] = true;
                dp[j + 1] = dp[j + 1].min(dp[i] + 1);
            }
        }
    }
    dp[n]
}

medium

A. Palindrome check condition is incorrect

B. dp array initialization should start from -1 for dp[0]

C. Loop ranges for i and j are reversed

D. s_bytes should be converted to chars instead of bytes

Solution

1. Step 1: Check dp initialization

   dp[i] should be initialized as i - 1 to handle zero cuts correctly, but here dp[i] = i which is off by one.

2. Step 2: Understand impact of dp initialization

   Incorrect initialization causes wrong minimum cuts calculation because dp[0] should be -1 to represent no cuts before start.

3. Final Answer:

   dp array initialization should start from -1 for dp[0] -> Option B

4. Quick Check:

   dp[0] = -1 needed for correct minimum cuts [OK]

Hint: Initialize dp[0] = -1 for correct minimum cuts [OK]

Common Mistakes:

• Initializing dp with zeros or i instead of i-1
• Misunderstanding palindrome base cases
• Incorrect loop boundaries

5. You want to find the minimum cuts for the string "abccbaabccba" using the palindrome partitioning DP approach. Which of the following statements is TRUE about the expected minimum cuts and the DP process?

hard

A. The minimum cuts will be 0 because the entire string is a palindrome

B. The minimum cuts will be 1 because the string can be split into two palindromes

C. The minimum cuts will be 2 because the string contains two palindromic halves

D. The minimum cuts will be 3 because multiple small palindromes are needed

Solution

1. Step 1: Check if the entire string is palindrome

   "abccbaabccba" reads the same forwards and backwards, so it is a palindrome.

2. Step 2: Understand minimum cuts for a full palindrome

   If the whole string is palindrome, no cuts are needed, so minimum cuts = 0.

3. Final Answer:

   The minimum cuts will be 0 because the entire string is a palindrome -> Option A

4. Quick Check:

   Full palindrome means zero cuts [OK]

Hint: If whole string palindrome, minimum cuts = 0 [OK]

Common Mistakes:

• Assuming cuts needed even if full palindrome
• Splitting unnecessarily into halves
• Ignoring palindrome check for entire string