Codeforces Round #432 (Div. 2） B. Arpa and an exam about geometry（数学水题）_综合

Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a,?b,?c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Input

The only line contains six integers ax,?ay,?bx,?by,?cx,?cy (|ax|,?|ay|,?|bx|,?|by|,?|cx|,?|cy|?≤?109). It's guaranteed that the points are distinct.

Output

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

        Examples
       
          input
         
0 1 1 1 1 0

          output
         
Yes

          input
         
1 1 0 0 1000 1000

          output
         
No

Note

In the first sample test, rotate the page around (0.5,?0.5) by .

In the second sample test, you can't find any solution.

题解：

比赛还在进行但是我已经写不动了，10分钟过a题（太水不想写题解），20分钟过b题。。c题看不懂，d题不会做，e题。。。算了吧，虽然这题很水但还是水一发博客

题意：

给你3个点的坐标，问你是否能找到一个点，以该点为中心旋转一定的角度使得a与b重合，b与c重合

思路：

直接判断只要两个线段长度相同而且三个点不在同一直线上就行了

ps：

这题之前用double型40组数据出错估计是因为double精度不够，还有就是斜率不存在的时候会出问题，把数据类型改成long long，把斜率判等写成乘法就好了

暂时ac的代码：

#include<iostream>
#include<cstring>
#include<stdio.h>
#include<math.h>
#include<string>
#include<stdio.h>
#include<queue>
#include<stack>
#include<map>
#include<vector>
#include<deque>
#include<algorithm>
using namespace std;
#define INF 100861111
#define ll long long
#define eps 1e-7
#define maxn 20
int main()
{long long x1,y1,x2,y2,x3,y3,k1,k2,d1,d2;scanf("%lld%lld%lld%lld%lld%lld",&x1,&y1,&x2,&y2,&x3,&y3);d1=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);d2=(x2-x3)*(x2-x3)+(y2-y3)*(y2-y3);if(d1!=d2){printf("No\n");return 0;}if((x2-x3)*(y1-y2)==(x1-x2)*(y2-y3)){printf("No\n");}elseprintf("Yes\n");return 0;
}