[LeetCode] (medium) 416. Partition Equal Subset Sum

https://leetcode.com/problems/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.

---

01背包：

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int total = accumulate(nums.begin(), nums.end(), 0);
        if(total&1) return false;
        
        int target = (total >> 1);
        
        vector<bool> bag(target+1, false);
        
        bag[0] = true;
        
        int last = 0;
        
        for(int cur : nums){
            for(int i = min(target, last+cur); i >= cur; --i){
                if(bag[i-cur]){
                    bag[i] = true;
                    last = max(last, i);
                }
            }
            if(bag[target]) return true;
        }
        
        return bag[target];
    }
};

DFS剪枝：

越早剪枝越好

class Solution {
public:
    
    int total;
    int found = false;
    
    bool canPartition(vector<int>& nums) {
        total = accumulate(nums.begin(), nums.end(), 0);
        if(total%2) return false;
        
        total >>= 1;
        
        sort(nums.begin(), nums.end(), std::greater<int>());
        
        return dfs(nums, 1, nums[0]);
    }
    
    bool dfs(vector<int>& nums, int cur, int num){
        if(num == total){
            return true;
        }
        if(cur >= nums.size() || num > total) return false;
        
        return dfs(nums, cur+1, num+nums[cur]) || dfs(nums, cur+1, num);
    }
};