Palindrome Partitioning DP Minimum Cuts in DSA Go - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

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

DSA Go

minCuts := make([]int, n)
for i := 0; i < n; i++ {
    minCuts[i] = [1]
}

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

Ai

Bn - 1

Cn

Di - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Initializing minCuts[i] with i or i-1 which is incorrect for the initial maximum cuts.

Using n instead of n-1 which is out of index range.

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

2fill in blank

medium

Complete the code to check if the substring s[j:i+1] is a palindrome using DP table.

DSA Go

if s[j] == s[i] && (i-j < 2 || dp[j+1][i-1] == [1]) {
    dp[j][i] = true
}

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

Afalse

BminCuts[i]

Cdp[j][i]

Dtrue

Attempts:

3 left

💡 Hint

Common Mistakes

Using false instead of true in the condition.

Checking dp[j][i] instead of dp[j+1][i-1].

A substring is palindrome if the characters at ends match and the inner substring is palindrome (dp[j+1][i-1] == true).

3fill in blank

hard

Fix the error in updating minimum cuts when substring s[j:i+1] is palindrome.

DSA Go

if j == 0 {
    minCuts[i] = 0
} else {
    minCuts[i] = min(minCuts[i], [1])
}

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

AminCuts[j-1] + 1

BminCuts[j] + 1

CminCuts[i-1] + 1

DminCuts[j] - 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using minCuts[j] instead of minCuts[j-1].

Subtracting 1 instead of adding 1.

We update minCuts[i] with minCuts[j-1] + 1 because we cut before index j.

4fill in blank

hard

Fill both blanks to complete the nested loops for DP palindrome partitioning.

DSA Go

for i := 0; i < n; i++ {
    for j := 0; j <= [1]; j++ {
        if s[j] == s[i] && (i-j < 2 || dp[j+1][i-1] == true) {
            dp[j][i] = true
            if j == 0 {
                minCuts[i] = 0
            } else {
                minCuts[i] = min(minCuts[i], minCuts[[2]] + 1)
            }
        }
    }
}

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

Ai

Bj

Cj-1

Di-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using j instead of i in inner loop condition.

Using j or i instead of j-1 for minCuts index.

Inner loop runs j from 0 to i. Update minCuts[i] using minCuts[j-1] + 1 for cut before j.

5fill in blank

hard

Fill all three blanks to complete the min function and return statement.

DSA Go

func min(a, b int) int {
    if a [1] b {
        return a
    }
    return [2]
}

return minCuts[[3]]

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

A<

B>

Cn-1

Db

Attempts:

3 left

💡 Hint

Common Mistakes

Using > instead of < in min function.

Returning a instead of b in else case.

Returning minCuts[i] instead of minCuts[n-1].

min returns smaller of a and b. Return minCuts[n-1] as minimum cuts for full string.

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