Leetcode: Partition Equal Subset Sum

Given a non-empty array containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.

Note:
Each of the array element will not exceed 100.
The array size will not exceed 200.
Example 1:

Input: [1, 5, 11, 5]

Output: true

Explanation: The array can be partitioned as [1, 5, 5] and [11].
Example 2:

Input: [1, 2, 3, 5]

Output: false

Explanation: The array cannot be partitioned into equal sum subsets.

Backpack problem: dp[i][j] means if the first i elements can sum up to value j

dp[i][j] = dp[i-1][j] || (j>=nums[i-1] && dp[i-1][j-nums[i-1]])

the result is if the half sum of the array can be summed up by elements in the array

public class Solution {
    public boolean canPartition(int[] nums) {
        if (nums.length == 0) return true;
        int volume = 0;
        for (int num : nums) {
            volume += num;
        }
        if (volume % 2 == 1) return false;
        volume /= 2;
        boolean[] dp = new boolean[volume+1];
        dp[0] = true;
        for (int i=1; i<=nums.length; i++) {
            for (int j=volume; j>=0; j--) {
                dp[j] = dp[j] || (j>=nums[i-1] && dp[j-nums[i-1]]);
            }
        }
        return dp[volume];
    }
}