473. Matchsticks to Square-优快云博客

本文探讨了一个有趣的算法问题：如何利用给定的小火柴棒构建一个正方形。文章提供了两种解决方案，一种采用递归回溯的方法，另一种则通过寻找合适的子集来解决问题。这两种方法都考虑了所有可能的情况以确保能够正确地判断是否可以构建出正方形。

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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.

Example 1:

Input: [1,1,2,2,2]
Output: true

Explanation: You can form a square with length 2, one side of the square came two sticks with length 1.

Example 2:

Input: [3,3,3,3,4]
Output: false

Explanation: You cannot find a way to form a square with all the matchsticks.

Note:

The length sum of the given matchsticks is in the range of 0 to 10^9.
The length of the given matchstick array will not exceed 15.

class Solution {
private:
    bool generate(int i, std::vector<int> &nums, int target, int bucket[])
    {
        if(i>=nums.size())
        {
            return bucket[0] == target && bucket[1] == target
                    && bucket[2] == target && bucket[3] == target;
        }
        for(int j=0; j<4; j++)
        {
            if(bucket[j]+nums[i]>target)
                continue;
            bucket[j] += nums[i];
            if(generate(i+1, nums, target, bucket))
                return true;
            bucket[j] -= nums[i];
        }
        return false;
        
    }
public:
    bool makesquare(vector<int>& nums) {
        if(nums.size()<4)
            return false;
        int sum = 0;
        for(int i=0 ; i<nums.size(); i++)
        {
            sum += nums[i];
        }
        if(sum%4)
        {
            return false;
        }
        std::sort(nums.rbegin(), nums.rend());
        int bucket[4] = {0};
        return generate(0, nums, sum/4, bucket);
    }
};

class Solution {

public:
    bool makesquare(vector<int>& nums) {
        if(nums.size()<4)
            return false;
        int sum = 0;
        for(int i=0 ; i<nums.size(); i++)
        {
            sum += nums[i];
        }
        if(sum%4)
        {
            return false;
        }
        int target = sum/4;
        std::vector<int> ok_subset;
        std::vector<int> ok_half;
        int all = 1<<nums.size();
        for(int i=0; i<all; i++)
        {
            int sum = 0;
            for(int j=0; j<nums.size(); j++)
            {
                if(i&(1<<j))
                    sum+=nums[j];
            }
            if(sum == target)
                ok_subset.push_back(i);
        }
        
        for(int i=0; i<ok_subset.size(); i++)
            for(int j=i+1; j<ok_subset.size(); j++)
               if((ok_subset[i]&ok_subset[j]) == 0)
                   ok_half.push_back(ok_subset[i] | ok_subset[j]);
        
        for(int i=0; i<ok_half.size(); i++)
            for(int j=i+1; j<ok_half.size(); j++)
                if((ok_half[i] & ok_half[j]) == 0)
                    return true;
        return false;       
    }
};