416. Partition Equal Subset Sum

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本文探讨了如何解决一个非空正整数数组能否被划分为两个子集的问题，使得这两个子集元素之和相等。文章通过示例说明了算法的工作原理，并提供了一个具体的C++实现方案。

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.

class Solution {
public:
	bool canPartition(vector<int>& nums) {
		int sum = 0;
		int n = nums.size();
		for (int i = 0; i < n; ++i) {
			sum += nums[i];
		}
		if ((sum & 1) == 1) return false;
		sum = sum >> 1;
		vector<int> dp(sum + 1, 0);
		for (int i = 0; i < n; ++i) {  
            for (int j = sum; j >= 1; --j) {  
                if (j >= nums[i]) {  
                    dp[j] = max(dp[j], nums[i] + dp[j - nums[i]]);  
                }  
            }  
        } 
		return dp[sum] == sum;
	}
};