Partition Equal Subset Sum in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the total sum of the array.

DSA C#

int totalSum = 0;
foreach (int num in nums) {
    totalSum [1]= num;
}

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

A-

B+

C*

D/

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' instead of '+' causes subtraction instead of addition.

Using '*' or '/' will not accumulate the sum correctly.

We add each number to totalSum to get the sum of all elements.

2fill in blank

medium

Complete the code to check if the total sum is odd and return false if so.

DSA C#

if (totalSum [1] 2 != 0) {
    return false;
}

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

A%

B/

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using '/' instead of '%' will perform division, not remainder check.

Using '*' or '+' will not correctly check oddness.

Using '%' checks the remainder when dividing by 2 to determine if the sum is odd.

3fill in blank

hard

Fix the error in the initialization of the boolean array for dynamic programming.

DSA C#

bool[] dp = new bool[[1] + 1];
dp[0] = true;

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

Anums.Sum()

Bnums.Length

CtotalSum / 2

DtotalSum

Attempts:

3 left

💡 Hint

Common Mistakes

Using totalSum or nums.Length causes array size to be too large or incorrect.

Using nums.Sum() is redundant and may cause confusion.

We only need to check sums up to half of totalSum for partitioning.

4fill in blank

hard

Fill both blanks to update the dp array correctly inside the loop.

DSA C#

for (int i = 0; i < nums.Length; i++) {
    for (int j = [1]; j >= [2]; j--) {
        dp[j] = dp[j] || dp[j - nums[i]];
    }
}

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

Atarget

B0

Cnums[i]

DtotalSum

Attempts:

3 left

💡 Hint

Common Mistakes

Looping forward causes incorrect dp updates.

Using wrong bounds causes index errors or logic errors.

We iterate j from target down to nums[i] to update dp correctly without overwriting needed values.

5fill in blank

hard

Fill all three blanks to complete the method that returns if partition is possible.

DSA C#

public bool CanPartition(int[] nums) {
    int totalSum = 0;
    foreach (int num in nums) {
        totalSum [1]= num;
    }
    if (totalSum [2] 2 != 0) return false;
    int target = totalSum / 2;
    bool[] dp = new bool[target + 1];
    dp[0] = true;
    for (int i = 0; i < nums.Length; i++) {
        for (int j = target; j >= nums[i]; j--) {
            dp[j] = dp[j] || dp[j - nums[i]];
        }
    }
    return dp[[3]];
}

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

A+

B%

Ctarget

DtotalSum

Attempts:

3 left

💡 Hint

Common Mistakes

Using '-' instead of '+' in sum accumulation.

Using '/' instead of '%' for odd check.

Returning dp[totalSum] instead of dp[target].

We add numbers to totalSum, check if totalSum % 2 != 0, and return dp[target] at the end.

Practice

1. What does the Partition Equal Subset Sum problem ask you to determine about a given array of integers?

easy

A. If the array is sorted in ascending order

B. If the array contains any duplicate elements

C. If the array contains only positive numbers

D. If the array can be split into two subsets with equal sums

Solution

1. Step 1: Understand the problem statement

   The problem asks whether the array can be divided into two parts where the sum of elements in both parts is the same.

2. Step 2: Clarify what is being checked

   It is not about duplicates, sorting, or positivity, but about equal sum partitioning.

3. Final Answer:

   If the array can be split into two subsets with equal sums -> Option D

4. Quick Check:

   Partition Equal Subset Sum = Split array into two equal sum subsets [OK]

Hint: Focus on splitting array into two equal sum parts [OK]

Common Mistakes:

• Confusing with checking duplicates
• Thinking about sorting order
• Assuming all numbers must be positive

2. Which of the following C# code snippets correctly initializes a boolean array named dp of size sum + 1 for the Partition Equal Subset Sum problem?

easy

A. bool[] dp = new bool[sum];

B. bool[] dp = new bool(sum + 1);

C. bool[] dp = new bool[sum + 1];

D. bool dp = new bool[sum + 1];

Solution

1. Step 1: Understand array initialization syntax in C#

   Arrays are initialized with square brackets and the size inside new[]. For size sum+1, use new bool[sum + 1].

2. Step 2: Check each option

   bool[] dp = new bool[sum]; misses +1, bool dp = new bool[sum + 1]; uses wrong type declaration, bool[] dp = new bool(sum + 1); uses parentheses which is invalid.

3. Final Answer:

   bool[] dp = new bool[sum + 1]; -> Option C

4. Quick Check:

   Correct C# array syntax = bool[] dp = new bool[sum + 1]; [OK]

Hint: Use square brackets and new keyword for arrays in C# [OK]

Common Mistakes:

• Forgetting +1 for array size
• Using parentheses instead of square brackets
• Declaring array as single bool variable

3. What will be the output of the following C# code snippet for the input array nums = new int[] {1, 5, 11, 5};?

bool CanPartition(int[] nums) {
    int sum = 0;
    foreach (int num in nums) sum += num;
    if (sum % 2 != 0) return false;
    int target = sum / 2;
    bool[] dp = new bool[target + 1];
    dp[0] = true;
    foreach (int num in nums) {
        for (int i = target; i >= num; i--) {
            dp[i] = dp[i] || dp[i - num];
        }
    }
    return dp[target];
}

Console.WriteLine(CanPartition(nums));

medium

A. true

B. false

C. Compile-time error

D. Runtime exception

Solution

1. Step 1: Calculate total sum and check parity

   Sum = 1+5+11+5 = 22, which is even, so continue.

2. Step 2: Use dynamic programming to check subset sum

   Target = 11. The dp array tracks if sum i is achievable. The code finds that subset {11} or {5,5,1} sums to 11, so dp[11] = true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   Sum even and subset sum found = true [OK]

Hint: Check if half sum subset exists using dp array [OK]

Common Mistakes:

• Not checking if sum is even
• Incorrect dp array update direction
• Returning false prematurely

4. Identify the bug in the following C# code snippet for Partition Equal Subset Sum and select the correct fix:

bool CanPartition(int[] nums) {
    int sum = 0;
    foreach (int num in nums) sum += num;
    if (sum % 2 != 0) return false;
    int target = sum / 2;
    bool[] dp = new bool[target];
    dp[0] = true;
    foreach (int num in nums) {
        for (int i = target; i >= num; i--) {
            dp[i] = dp[i] || dp[i - num];
        }
    }
    return dp[target];
}

medium

A. Initialize dp array with false values explicitly

B. Change dp array size to target + 1

C. Change loop to iterate from 0 to target

D. Remove the dp[0] = true assignment

Solution

1. Step 1: Check dp array size and indexing

   dp array is declared with size target, but dp[target] is accessed, causing out-of-range error.

2. Step 2: Fix array size to include target index

   Change dp size to target + 1 to safely access dp[target].

3. Final Answer:

   Change dp array size to target + 1 -> Option B

4. Quick Check:

   Array size must cover all indices used [OK]

Hint: Array size must be one more than max index accessed [OK]

Common Mistakes:

• Ignoring array index out of range
• Changing loop direction unnecessarily
• Removing dp[0] initialization

5. Given the array nums = new int[] {2, 2, 3, 5}, which of the following statements is true regarding the Partition Equal Subset Sum problem?

hard

A. The array cannot be partitioned into two subsets with equal sum

B. The array can be partitioned into two subsets with equal sum: {2,3} and {2,5}

C. The array can be partitioned into two subsets with equal sum: {2,2,3} and {5}

D. The array can be partitioned into two subsets with equal sum: {3,5} and {2,2}

Solution

1. Step 1: Calculate total sum of array elements

   Sum = 2 + 2 + 3 + 5 = 12, which is even, so partition might be possible.

2. Step 2: Check possible subsets for half sum (6)

   Half sum = 6. Possible subsets: {2,2,2} no (only two 2s), {3,3} no (only one 3), {5,1} no 1 missing. No subset sums to 6 exactly.

3. Step 3: Verify given options

   The array can be partitioned into two subsets with equal sum: {2,3} and {2,5} sums: {2,3}=5 and {2,5}=7 (not equal). The array can be partitioned into two subsets with equal sum: {2,2,3} and {5} sums: {2,2,3}=7 and {5}=5 (not equal). The array can be partitioned into two subsets with equal sum: {3,5} and {2,2} sums: {3,5}=8 and {2,2}=4 (not equal).

4. Final Answer:

   The array cannot be partitioned into two subsets with equal sum -> Option A

5. Quick Check:

   Sum even but no subset sums to half sum = false [OK]

Hint: Check if any subset sums exactly to half total sum [OK]

Common Mistakes:

• Assuming even sum means partition always possible
• Incorrectly summing subsets
• Ignoring subset element counts