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];
     }
 }