LeetCode 416: Partition Equal Subset Sum Solution

Master LeetCode problem 416 (Partition Equal Subset Sum), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

416. Partition Equal Subset Sum

Medium

Array Dynamic Programming

Problem Explanation

Explanation

To solve this problem, we can use dynamic programming. We need to find if there exists a subset of the given array whose sum is half of the total sum of the array. If such a subset exists, then it means the array can be partitioned into two subsets with equal sum.

We can create a 1D boolean array dp, where dp[i] represents whether it is possible to form a subset with sum i. We initialize dp[0] as true, since it is always possible to form a subset with sum 0. Then, for each element in the array, we update the dp array from right to left, marking all sums j as true if dp[j - nums[i]] is true.

Finally, we return dp[totalSum / 2], where totalSum is the sum of all elements in the array.

Time Complexity

The time complexity of this solution is O(n * sum), where n is the number of elements in the array and sum is the total sum of the array.

Space Complexity

The space complexity of this solution is O(sum), where sum is the total sum of the array.

Solution Code

class Solution {
    public boolean canPartition(int[] nums) {
        int totalSum = 0;
        for (int num : nums) {
            totalSum += num;
        }

        if (totalSum % 2 != 0) {
            return false;
        }

        int halfSum = totalSum / 2;
        boolean[] dp = new boolean[halfSum + 1];
        dp[0] = true;

        for (int num : nums) {
            for (int j = halfSum; j >= num; j--) {
                dp[j] = dp[j] || dp[j - num];
            }
        }

        return dp[halfSum];
    }
}

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