【LeetCode】416. Partition Equal Subset Sum

Difficulty: Medium

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: trueExplanation: The array can be partitioned as [1, 5, 5] and [11].

Example 2:

Input: [1, 2, 3, 5]Output: falseExplanation: The array cannot be partitioned into equal sum subsets.

思路分析：

动态规划算法，f[i][j]表示前i个数能否取出和为j的方案

状态转移方程 f[i][j]=f[i-1][j] || f[i-1][ j-nums[i] ];

如果j从sum到nums[i]递减遍历，那么状态转移方程简写为 f[j]=f[j] || f[ j-nums[i] ];

时间复杂度为O(n*sum),sum为nums[i]所有元素之和

class Solution {public:    bool canPartition(vector<int>& nums) {bool f[10005];int sum,n;n=nums.size();sum=0;for(int i=0;i<n;i++){sum+=nums[i];}if(sum%2) return false;sum=sum/2;for(int i=1;i<=sum;i++)f[i]=false;f[0]=true;for(int i=0;i<n;i++)for(int j=sum;j>=nums[i];j--)f[j] = f[j] || f[j-nums[i] ];return f[sum];}};