Partition Equal Subset Sum in DSA C# - Build from Scratch

Partition Equal Subset Sum

📖 Scenario: You are working on a budgeting app that helps users decide if they can split their expenses into two equal parts. To do this, you need to check if a list of expense amounts can be divided into two groups with the same total sum.

🎯 Goal: Build a program that checks if a given list of positive integers can be partitioned into two subsets with equal sum using the Partition Equal Subset Sum technique.

📋 What You'll Learn

Create an integer array called expenses with the exact values: 1, 5, 11, 5.

Create an integer variable called totalSum that stores the sum of all elements in expenses.

Implement a method called CanPartition that takes the expenses array and returns true if it can be partitioned into two subsets with equal sum, otherwise false.

Print the result of CanPartition(expenses).

💡 Why This Matters

🌍 Real World

Budgeting apps and financial tools often need to split expenses or resources evenly, which requires checking if equal partitions are possible.

💼 Career

Understanding partition problems and dynamic programming is useful for software engineers working on optimization, resource allocation, and algorithm design.

1

Create the expenses array

Create an integer array called expenses with the exact values 1, 5, 11, 5.

DSA C#

# Your code here

Hint

Use int[] expenses = {1, 5, 11, 5}; to create the array.

2

Calculate the total sum of expenses

Create an integer variable called totalSum that stores the sum of all elements in the expenses array.

DSA C#

int[] expenses = {1, 5, 11, 5};
// Your code here

Hint

Use a foreach loop to add each expense to totalSum.

3

Implement the CanPartition method

Implement a method called CanPartition that takes the integer array expenses and returns true if it can be partitioned into two subsets with equal sum, otherwise false. Use the totalSum variable inside the method to check if partitioning is possible.

DSA C#

int[] expenses = {1, 5, 11, 5};
int totalSum = 0;
foreach (int expense in expenses)
{
    totalSum += expense;
}

// Your code here

Hint

Use a boolean array dp to track possible sums up to target. Update it in reverse order for each number.

4

Print the partition result

Print the result of calling CanPartition(expenses).

DSA C#

int[] expenses = {1, 5, 11, 5};
int totalSum = 0;
foreach (int expense in expenses)
{
    totalSum += expense;
}

bool CanPartition(int[] nums)
{
    if (totalSum % 2 != 0) return false;
    int target = totalSum / 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];
}

// Your code here

Hint

Use Console.WriteLine(CanPartition(expenses)); to print the result.

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