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

1 public class Solution {
2     public boolean canPartition(int[] nums) {
3         if (nums.length == 0) return true;
4         int volume = 0;
5         for (int num : nums) {
6             volume += num;
7         }
8         if (volume % 2 == 1) return false;
9         volume /= 2;
10         boolean[] dp = new boolean[volume+1];
11         dp[0] = true;
12         for (int i=1; i<=nums.length; i++) {
13             for (int j=volume; j>=0; j--) {
14                 dp[j] = dp[j] || (j>=nums[i-1] && dp[j-nums[i-1]]);
15             }
16         }
17         return dp[volume];
18     }
19 }