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

Palindrome Partitioning DP Minimum Cuts

📖 Scenario: Imagine you have a word, and you want to cut it into pieces so that each piece is a palindrome. You want to make as few cuts as possible.This is useful in text processing, where you want to split words or sentences into palindromic parts for special effects or analysis.

🎯 Goal: Build a Rust program that finds the minimum number of cuts needed to split a given string into palindromic substrings using dynamic programming.

📋 What You'll Learn

Create a string variable with the exact value "abcbm"

Create a 2D vector called is_palindrome to store palindrome checks

Create a vector called min_cuts to store minimum cuts for each prefix

Use nested loops to fill is_palindrome for all substrings

Use a loop to compute min_cuts using the palindrome info

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 palindromic patterns are important.

💼 Career

Understanding dynamic programming and string manipulation is essential for software engineers working on algorithms, competitive programming, and technical interviews.

1

Create the input string

Create a string variable called s with the exact value "abcbm"

DSA Rust

# Create the string variable s with value "abcbm"
# Your code here

Hint

Use String::from("abcbm") to create the string.

2

Initialize palindrome table and min cuts vector

Create a 2D vector called is_palindrome of type Vec> with size s.len() by s.len(), initialized to false. Also create a vector called min_cuts of type Vec with size s.len(), initialized to 0.

DSA Rust

let s = String::from("abcbm");
# Create is_palindrome 2D vector and min_cuts vector
# Your code here

Hint

Use vec![vec![false; n]; n] for 2D boolean vector and vec![0; n] for min_cuts.

3

Fill palindrome table and compute minimum cuts

Use nested loops with variables end from 0 to n-1 and start from 0 to end. Inside, check if substring s[start..=end] is palindrome by comparing characters and using is_palindrome. Update is_palindrome[start][end] accordingly. Then, use a loop with variable i from 0 to n-1 to compute min_cuts[i] as the minimum cuts needed for substring s[0..=i] using the palindrome info.

DSA Rust

let s = String::from("abcbm");
let n = s.len();
let mut is_palindrome = vec![vec![false; n]; n];
let mut min_cuts = vec![0; n];

// Fill is_palindrome and compute min_cuts
// Your code here

Hint

Use chars vector for indexing characters. Check palindrome by comparing characters and inner substring palindrome status.

4

Print the minimum cuts needed

Print the value of min_cuts[n - 1] which is the minimum cuts needed for the entire string s.

DSA Rust

let s = String::from("abcbm");
let n = s.len();
let mut is_palindrome = vec![vec![false; n]; n];
let mut min_cuts = vec![0; n];

let chars: Vec = s.chars().collect();

for end in 0..n {
    let mut min_cut = end; // max cuts
    for start in 0..=end {
        if chars[start] == chars[end] && (end - start  min_cuts[start - 1] + 1 {
                min_cut = min_cuts[start - 1] + 1;
            }
        }
    }
    min_cuts[end] = min_cut;
}

// Print the minimum cuts for the entire string
# Your code here

Hint

Use println!("{}", min_cuts[n - 1]) to print the minimum cuts.

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