Palindrome Partitioning DP Minimum Cuts in DSA Go - 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 reads the same forwards and backwards. You want to make as few cuts as possible.This is useful in text processing, like splitting words into palindromic parts for fun puzzles or data compression.

🎯 Goal: Build a 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 a specific value

Create a 2D boolean slice to track palindromic substrings

Create a slice to store minimum cuts for each prefix

Use nested loops to fill the palindrome table

Use a loop to calculate minimum cuts using the palindrome table

Print the minimum cuts for the entire string

💡 Why This Matters

🌍 Real World

Palindrome partitioning helps in text analysis, DNA sequence analysis, and data compression where palindromic patterns are important.

💼 Career

Understanding dynamic programming and string manipulation is essential for software engineering roles involving algorithms and problem solving.

1

Create the input string

Create a string variable called s and set it to "aab".

DSA Go

# Create a string variable called s and set it to "aab"
# Your code here

Hint

Use s := "aab" to create the string variable.

2

Setup palindrome table and cuts slice

Create a 2D boolean slice called palindrome with size len(s) x len(s), and a slice of integers called cuts with size len(s).

DSA Go

package main

func main() {
    s := "aab"
    // Create a 2D boolean slice palindrome with size len(s) x len(s)
    // Create a slice of int cuts with size len(s)
    // Your code here
}

Hint

Use make([][]bool, n) for the 2D slice and make([]int, n) for the cuts slice.

3

Fill palindrome table and calculate minimum cuts

Use nested loops with variables end and start to fill palindrome. Then use a loop with variable i to fill cuts with minimum cuts needed. Use palindrome[start][end] to check palindromes and update cuts accordingly.

DSA Go

package main

func main() {
    s := "aab"
    n := len(s)
    palindrome := make([][]bool, n)
    for i := range palindrome {
        palindrome[i] = make([]bool, n)
    }
    cuts := make([]int, n)

    // Use nested loops with end and start to fill palindrome
    // Use a loop with i to fill cuts with minimum cuts
    // Your code here
}

Hint

Check palindrome by comparing characters and previous palindrome results. Update cuts with minimum values.

4

Print the minimum cuts for the string

Print the value of cuts[len(s)-1] which is the minimum cuts needed for the entire string.

DSA Go

package main

import "fmt"

func main() {
    s := "aab"
    n := len(s)
    palindrome := make([][]bool, n)
    for i := range palindrome {
        palindrome[i] = make([]bool, n)
    }
    cuts := make([]int, n)

    for end := 0; end < n; end++ {
        minCut := end
        for start := 0; start <= end; start++ {
            if s[start] == s[end] && (end-start < 2 || palindrome[start+1][end-1]) {
                palindrome[start][end] = true
                if start == 0 {
                    minCut = 0
                } else if cuts[start-1]+1 < minCut {
                    minCut = cuts[start-1] + 1
                }
            }
        }
        cuts[end] = minCut
    }

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

Hint

Use fmt.Println(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 maximum length of a palindrome substring in s

C. The total number of palindrome substrings in s

D. The longest palindrome substring 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: Differentiate from other palindrome problems

   It is not about longest palindrome or counting palindromes, but minimizing cuts for palindrome partitions.

3. Final Answer:

   The minimum number of cuts needed to partition s into palindromic substrings -> Option A

4. Quick Check:

   Minimum cuts = minimum partitions [OK]

Hint: Focus on cuts that split string into palindrome parts [OK]

Common Mistakes:

• Confusing minimum cuts with longest palindrome length
• Thinking problem counts palindrome substrings
• Assuming problem finds longest palindrome substring

2. Which of the following Go code snippets correctly initializes a 2D boolean slice isPalindrome for a string s of length n?

easy

A. isPalindrome := [][]bool{{false}}
for i := 0; i < n; i++ {
isPalindrome[i][i] = true
}

B. var isPalindrome [][]bool
isPalindrome = make([]bool, n*n)

C. isPalindrome := make([][]bool, n)
for i := range isPalindrome {
isPalindrome[i] = make([]bool, n)
}

D. isPalindrome := make([]bool, n)
for i := 0; i < n; i++ {
isPalindrome[i] = true
}

Solution

1. Step 1: Understand 2D slice initialization in Go

   To create a 2D slice, first allocate the outer slice, then allocate each inner slice separately.

2. Step 2: Check each option for correct 2D boolean slice creation

   isPalindrome := make([][]bool, n) for i := range isPalindrome { isPalindrome[i] = make([]bool, n) } correctly creates a slice of slices with length n and initializes each inner slice with length n.

3. Final Answer:

   isPalindrome := make([][]bool, n) for i := range isPalindrome { isPalindrome[i] = make([]bool, n) -> Option C

4. Quick Check:

   2D slice needs nested make calls [OK]

Hint: Use nested make calls for 2D slices in Go [OK]

Common Mistakes:

• Trying to create 2D slice with single make call
• Confusing slice of bool with slice of slices
• Not initializing inner slices before use

3. What is the output of the following Go code snippet that calculates minimum cuts for palindrome partitioning of s = "aab"?

func minCut(s string) int {
    n := len(s)
    isPalindrome := make([][]bool, n)
    for i := range isPalindrome {
        isPalindrome[i] = make([]bool, n)
    }
    for i := n - 1; i >= 0; i-- {
        for j := i; j < n; j++ {
            if s[i] == s[j] && (j - i < 2 || isPalindrome[i+1][j-1]) {
                isPalindrome[i][j] = true
            }
        }
    }
    cuts := make([]int, n)
    for i := 0; i < n; i++ {
        minCut := i
        for j := 0; j <= i; j++ {
            if isPalindrome[j][i] {
                if j == 0 {
                    minCut = 0
                } else if cuts[j-1]+1 < minCut {
                    minCut = cuts[j-1] + 1
                }
            }
        }
        cuts[i] = minCut
    }
    return cuts[n-1]
}

fmt.Println(minCut("aab"))

medium

A. 0

B. 1

C. 2

D. 3

Solution

1. Step 1: Identify palindromic substrings in "aab"

   "a", "a", "b" are palindromes; "aa" is palindrome; "aab" is not.

2. Step 2: Calculate minimum cuts using DP logic

   Minimum cuts needed: cut between "aa" and "b" -> 1 cut.

3. Final Answer:

   1 -> Option B

4. Quick Check:

   Minimum cuts for "aab" = 1 [OK]

Hint: Check palindrome substrings, then count cuts between them [OK]

Common Mistakes:

• Assuming no cuts needed for "aab"
• Counting cuts as number of palindrome substrings
• Misunderstanding DP array meaning

4. The following Go code attempts to compute minimum cuts for palindrome partitioning but has a bug. What is the error?

func minCut(s string) int {
    n := len(s)
    isPalindrome := make([][]bool, n)
    for i := range isPalindrome {
        isPalindrome[i] = make([]bool, n)
    }
    for i := 0; i < n; i++ {
        for j := i; j < n; j++ {
            if s[i] == s[j] && (j - i < 2 || isPalindrome[i+1][j-1]) {
                isPalindrome[i][j] = true
            }
        }
    }
    cuts := make([]int, n)
    for i := 0; i < n; i++ {
        cuts[i] = i
        for j := 0; j <= i; j++ {
            if isPalindrome[j][i] {
                if j == 0 {
                    cuts[i] = 0
                } else if cuts[j-1]+1 < cuts[i] {
                    cuts[i] = cuts[j-1] + 1
                }
            }
        }
    }
    return cuts[n-1]
}

medium

A. The function returns cuts[0] instead of cuts[n-1]

B. The cuts array is not initialized with correct default values

C. The condition s[i] == s[j] is incorrect for palindrome check

D. The palindrome check loop should run from i = n-1 down to 0, not 0 to n-1

Solution

1. Step 1: Analyze palindrome DP filling order

   Palindrome DP requires filling from end to start (i from n-1 down to 0) to use isPalindrome[i+1][j-1] correctly.

2. Step 2: Identify impact of incorrect loop order

   Looping i from 0 to n-1 causes isPalindrome[i+1][j-1] to be uninitialized or incorrect, leading to wrong results.

3. Final Answer:

   The palindrome check loop should run from i = n-1 down to 0, not 0 to n-1 -> Option D

4. Quick Check:

   Fill palindrome DP bottom-up from right [OK]

Hint: Fill palindrome DP from right to left for correct subproblems [OK]

Common Mistakes:

• Filling palindrome DP from left to right
• Ignoring dependency on isPalindrome[i+1][j-1]
• Incorrect initialization of 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. 6

C. 5

D. 3

Solution

1. Step 1: Understand the string and palindrome partitions

   The string "ababbbabbababa" can be partitioned into palindromes with minimum cuts by checking all substrings using DP.

2. Step 2: Apply DP minimum cuts algorithm

   Using the palindrome DP table and cuts array, the minimum cuts calculated for this string is 4.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Minimum cuts for "ababbbabbababa" = 4 [OK]

Hint: Use DP palindrome table and cuts array to find minimum cuts [OK]

Common Mistakes:

• Underestimating cuts by ignoring some palindrome partitions
• Overcounting cuts by splitting unnecessarily
• Not using DP to optimize palindrome checks