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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of minimum cuts for palindrome partitioning

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

DSA Rust

fn min_cut(s: &str) -> i32 {
    let n = s.len();
    let chars: Vec<char> = s.chars().collect();
    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 0..=i {
            if chars[i] == chars[j] && (i - j < 2 || palindrome[j + 1][i - 1]) {
                palindrome[j][i] = true;
                dp[i + 1] = dp[i + 1].min(dp[j] + 1);
            }
        }
    }
    dp[n]
}

fn main() {
    let s = "aab";
    println!("{}", min_cut(s));
}

A 1

B 0

C 3

D 2

💡 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.

The DP array dp keeps track of minimum cuts needed up to each position.

🧠 Conceptual

intermediate

Understanding the DP state in palindrome partitioning

In the palindrome partitioning minimum cuts problem, what does the dp[i] array represent?

A The minimum cuts needed for substring s[i..end]

B The maximum palindrome length ending at index i

C The number of palindromes in substring s[0..i]

D The minimum cuts needed for substring s[0..i-1]

💡 Hint

Think about how dp is used to build the solution from the start of the string.

dp[i] stores the minimum cuts needed to partition the substring from the start up to index i-1 into palindromes.

🔧 Debug

advanced

Identify the error in palindrome partitioning DP code

What error will this Rust code produce when run?

DSA Rust

fn min_cut(s: &str) -> i32 {
    let n = s.len();
    let chars: Vec<char> = s.chars().collect();
    let mut dp = vec![0; n];
    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 0..=i {
            if chars[i] == chars[j] && (i - j < 2 || palindrome[j + 1][i - 1]) {
                palindrome[j][i] = true;
                dp[i + 1] = dp[i + 1].min(dp[j] + 1);
            }
        }
    }
    dp[n]
}

A Type mismatch error due to dp vector initialization

B No error, code runs correctly

C Index out of bounds panic at dp[i] = i as i32 - 1;

D Borrow checker error due to mutable and immutable borrow

💡 Hint

Check the size of dp vector and the indices used to access it.

The dp vector is initialized with size n, but the code accesses dp[i] for i in 0..=n, which causes an index out of bounds panic.

🚀 Application

advanced

Minimum cuts for palindrome partitioning of a complex string

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

A 1

B 2

C 3

D 0

💡 Hint

Try to find palindrome substrings that cover the string with few cuts.

One optimal partition is "a" | "bccb" | "c" with 2 cuts.

❓ Predict Output

expert

Output of DP array after processing string "racecar"

Given the following Rust code snippet for palindrome partitioning minimum cuts, what is the final dp array printed after processing the string "racecar"?

DSA Rust

fn min_cut_dp_array(s: &str) -> Vec<i32> {
    let n = s.len();
    let chars: Vec<char> = s.chars().collect();
    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 0..=i {
            if chars[i] == chars[j] && (i - j < 2 || palindrome[j + 1][i - 1]) {
                palindrome[j][i] = true;
                dp[i + 1] = dp[i + 1].min(dp[j] + 1);
            }
        }
    }
    dp
}

fn main() {
    let s = "racecar";
    let dp_array = min_cut_dp_array(s);
    println!("{:?}", dp_array);
}

A [ -1, 0, 1, 2, 3, 2, 1, 0 ]

B [ -1, 0, 1, 2, 3, 4, 5, 6 ]

C [ 0, 0, 1, 2, 3, 4, 5, 6 ]

D [ -1, 1, 2, 3, 4, 5, 6, 7 ]

💡 Hint

The string "racecar" is a palindrome, so minimum cuts at the end should be 0.

The dp array starts with dp[i] = i-1.

As palindrome substrings are found, dp values update to minimum cuts.

For "racecar", the entire string is palindrome, so dp[7] = 0.

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