416. 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.
 

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/partition-equal-subset-sum
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判断一个集合是否能分成两个子集，子集的和一样。

即能否找到一个子集的和是总合的1/2。

boolean dp[i]表示能不能找到和为i大小的子集。

class Solution {
    public boolean canPartition(int[] nums) {
        int target = 0;
        for (int i = 0; i < nums.length; i++) {
            target += nums[i];
        }
        if ((target & 1) == 1) {
            return false;
        }
        target = target / 2;
        boolean []dp = new boolean[target + 1];
        dp[0] = true;
        for (int j = 0; j < nums.length; j++) {
// 不能是从1到target，否则如果nums有1的话，会全为true
            for (int i = target; i >= nums[j]; i--) {
                    if (i >= nums[j]) {
                        if (dp[i - nums[j]]) {
                            dp[i] = true;
                        }
                    }
                }
        }
        return dp[target];
    }
}