【LeetCode】416. Partition Equal Subset Sum

题目：
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.

分析：这道题是要我们判断一个数组是否可以分成和相等的两部分。这道题可以看成不重复的背包问题。先算出n个数的和sum，然后假设背包容量为sum/2.将每个数看成价值和大小都为数字的大小的物品，若n个物体能刚好填满整个背包，则表示该数组可以分成和相等的两部分。
若sum不是偶数，则不可能分成和相等的两部分，可直接返回false。
代码：

class Solution {public:    bool canPartition(vector<int>& nums) {        int sum = 0;        for(int i = 0;i<nums.size();i++)        sum+=nums[i];        if(sum%2!=0) return false;        int *dp;        dp = new int [sum/2+1];        for(int i = 0;i<=sum/2;i++)        {            if(i<nums[0]) dp[i] = 0;            else             dp[i] = nums[0];        }        for(int i = 1;i<nums.size();i++)        {            for(int j = sum/2;j>=nums[i];j--)            {                dp[j] =max(dp[j],dp[j-nums[i]]+nums[i]);            }        }        if(dp[sum/2] == sum/2)        return true;        else return false;    }};