leetcode 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.

01背包问题，v = sum(nums[i])/2那么原问题可以转换为将n个物品装入容量为v的背包中能得到的最大值。如果最大值为v那么就返回true否则返回false

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int n = nums.size();
        int v = accumulate(nums.begin(), nums.end(), 0);
        if (v & 1) return false;
        v /= 2;
        vector<int> dp(v+1);
        // dp[i][j] = max(dp[i-1][j],dp[i-1][j-a[i]] + w[i]);
        for (int i = 0; i < n; ++i) {
            for (int j = v; j >= nums[i]; --j) {
                dp[j] = max(dp[j-nums[i]] + nums[i], dp[j]);
            }
        }
        cout << dp[v] <<endl;
        return (dp[v] == v);
    }
};