Matchsticks to Square问题及解法

问题描述：

Remember the story of Little Match Girl? By now, you know exactly what matchsticks the little match girl has, please find out a way you can make one square by using up all those matchsticks. You should not break any stick, but you can link them up, and each matchstick must be used exactly one time.

Your input will be several matchsticks the girl has, represented with their stick length. Your output will either be true or false, to represent whether you could make one square using all the matchsticks the little match girl has.

示例:

Input: [1,1,2,2,2]Output: trueExplanation: You can form a square with length 2, one side of the square came two sticks with length 1.

Input: [3,3,3,3,4]Output: falseExplanation: You cannot find a way to form a square with all the matchsticks.

问题分析：

本题与Partition to K Equal Sum Subsets类似，这里不多赘述。

过程详见代码：

class Solution {public:    bool makesquare(vector<int>& nums) {int sum = accumulate(nums.begin(), nums.end(), 0);sort(nums.begin(), nums.end(), [](int a, int b){return a > b; });if (sum % 4) return false;int t = sum / 4;vector<bool> dp(nums.size(), false);int res = 0;for (int i = 0; i < nums.size(); i++){if (!dp[i] && dfs(dp, nums, t, i, 0)) res++;}return res == 4;}bool dfs(vector<bool>& dp, vector<int>& nums, int target, int start, int sum){if (sum == target) {return true;}for (int i = start; i < nums.size(); i++){if (!dp[i]){dp[i] = true;bool b = dfs(dp, nums, target, i + 1, sum + nums[i]);if (!b) dp[i] = false;else return true;}}return false;}};