lc 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:

1. Each of the array element will not exceed 100.
2. 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.

DP Accepted

这其实是一个01背包问题，对于每一个数，我们可以选择放入和不放入，使dp[i][j]代表数组中前i个进行选择能否可以累计得到j。dp[0][0]为1，其余情况dp[i][j] = dp[i-1][j] || dp[i-1][j-nums[i]]，因为要么不选择，那么就为dp[i-1][j]，要么选择，那么就为dp[i-1][j-nums[i]]。

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum & 1) return false;
        int target = sum >> 1;
        vector<int> dp(target + 1, 0);
        dp[0] = 1;
        for (auto num : nums)
            for (int i = target; i >= num; i--)
                dp[i] = dp[i] || dp[i-num];
        return dp[target];
    }
};