LeetCode416

EX416

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.

Example1:

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

Example2:

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

Solution:

  这是一个典型的背包问题，我们需要做的，就是当背包的容量刚好为nums中所有物品重量之和的一半时，是否可以刚好填满就行。  子问题为：对于物体i(i < nums.size())，当背包容量为j时(j <= sum/2)，是否存在能够刚好装满背包且包含物品i的组合。  dp[j] = dp[j] || dp[j-nums[i]];  nums[i]为物品i的重量

class Solution {public:    bool canPartition(vector<int>& nums) {        int len = nums.size(), sum = 0, half = 0;        for(int i = 0; i < len; i++) {            sum += nums[i];        }        //如果sum为奇数，return false        if (sum & 1)            return false;        half = sum/2;        vector<int> dp(half+1, 0);        dp[0] = 1;        for (int i = 0; i < len; i++) {            //单副本，未避免已经使用的物品对不同j产生影响，所以top to down            for (int j = half; j >= nums[i]; j--) {                dp[j] = dp[j] || dp[j-nums[i]];            }        }        return dp[half];    }};