【LeetCode】验证4个点是否构成正方形

最新推荐文章于 2025-05-22 11:06:13 发布

zhonglao

最新推荐文章于 2025-05-22 11:06:13 发布

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本文链接：https://blog.youkuaiyun.com/zhonglao/article/details/85564620

该博客讨论了如何验证二维空间中的四个点是否可以构成一个正方形。根据给定的坐标，通过计算两两之间的距离来确定是否满足正方形的条件——四边等长且角度为90度。

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问题描述

Given the coordinates of four points in 2D space, return whether the four points could construct a square.

The coordinate (x,y) of a point is represented by an integer array with two integers.

Example:
Input: p1 = [0,0], p2 = [1,1], p3 = [1,0], p4 = [0,1]
Output: True

Note:
All the input integers are in the range [-10000, 10000].
A valid square has four equal sides with positive length and four equal angles (90-degree angles).
Input points have no order.

转至原题

解题思路

给点4个坐标点，要求判断是否能构成正方形。值得注意的是4个点不一定按顺序，可以计算两两之间的距离，如果是正方形，距离只有2个值

代码

class Solution {
public:
    int distance(vector<int>& p1, vector<int>& p2){
        return pow(p1[0]-p2[0],2)+pow(p1[1]-p2[1],2);
    }
    bool validSquare(vector<int>& p1, vector<int>& p2, vector<int>& p3, vector<int>& p4) {
        vector<vector<int>> points;
        points.push_back(p1);
        points.push_back(p2);
        points.push_back(p3);
        points.push_back(p4);
        vector<pair<int,int>> d_to_p1;
        d_to_p1.push_back(make_pair(distance(p1,p2),2-1));
        d_to_p1.push_back(make_pair(distance(p1,p3),3-1));
        d_to_p1.push_back(make_pair(distance(p1,p4),4-1));
        sort(d_to_p1.begin(),d_to_p1.end());
        if((d_to_p1[0].first!=d_to_p1[1].first)||(d_to_p1[2].first!=(d_to_p1[1].first+d_to_p1[0].first))||(d_to_p1[0].first==0))
            return false;
        int distance1=distance(points[d_to_p1[2].second],points[d_to_p1[1].second]);
        int distance2=distance(points[d_to_p1[2].second],points[d_to_p1[0].second]);
        if((distance1!=distance2)||(distance1!=d_to_p1[0].first))
            return false;
        return true;
    }
};