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Partition Equal Subset Sum

Certification: Intermediate Level Accuracy: 0% Submissions: 0 Points: 15

Write a C program to determine if a given non-empty array can be partitioned into two subsets such that the sum of elements in both subsets is equal. This is essentially asking if there exists a subset of the array whose sum is equal to half of the total sum of all elements.

Example 1
    
  
  • Input: nums = [1, 5, 11, 5]
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  • Output: true
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  • Explanation: 
    • Total sum = 1 + 5 + 11 + 5 = 22. 
    • Half of total sum = 22/2 = 11. 
    • We can partition it into [1, 5, 5] and [11]. 
    • Both subsets have sum = 11, so partition is possible.
    •
Example 2
    
  
  • Input: nums = [1, 2, 3, 5]
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  • Output: false
    • 
  
  • Explanation: 
    • Total sum = 1 + 2 + 3 + 5 = 11. 
    • Half of total sum = 11/2 = 5.5 (not an integer). 
    • Since half sum is not an integer, equal partition is impossible. 
    • Therefore, the array cannot be partitioned into two equal subsets.
    •
Constraints
    
  
  • 1 ≤ nums.length ≤ 200
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  • 1 ≤ nums[i] ≤ 100
    • 
  
  • The sum of all elements will not exceed 20000
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  • Time Complexity: O(n * sum)
    • 
  
  • Space Complexity: O(sum)
    •
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Hint
Solution

Solution Hints

    
  
  • First calculate the total sum of all elements in the array
    • 
  
  • If the total sum is odd, return false immediately as equal partition is impossible
    • 
  
  • Use dynamic programming to check if a subset with sum equal to half of total sum exists
    • 
  
  • Create a boolean DP array where dp[i] represents if sum i is achievable
    • 
  
  • For each number, update the DP array by checking all possible sums
    • 
  
  • Return dp[target] where target is half of the total sum
    •

Steps to solve by this approach:

 Step 1: Calculate the total sum of all elements in the input array.
 Step 2: Check if the total sum is even; if odd, return false as equal partition is impossible.
 Step 3: Set target sum as half of the total sum.
 Step 4: Create a boolean DP array where dp[i] indicates if sum i is achievable using array elements.
 Step 5: Initialize dp[0] as true since sum 0 is always achievable with an empty subset.
 Step 6: For each element, update the DP array by checking all possible sums from target down to the element value.
 Step 7: Return dp[target] which indicates if the target sum (half of total) is achievable.

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