Parallelogram Counting
Time Limit: 5000MS | Memory Limit: 65536K | |
Total Submissions: 5605 | Accepted: 1885 |
Description
There are n distinct points in the plane, given by their integer coordinates. Find the number of parallelograms whose vertices lie on these points. In other words, find the number of 4-element subsets of these points that can be written as {A, B, C, D} such that AB || CD, and BC || AD. No four points are in a straight line.
Input
The first line of the input contains a single integer t (1 <= t <= 10), the number of test cases. It is followed by the input data for each test case.
The first line of each test case contains an integer n (1 <= n <= 1000). Each of the next n lines, contains 2 space-separated integers x and y (the coordinates of a point) with magnitude (absolute value) of no more than 1000000000.
The first line of each test case contains an integer n (1 <= n <= 1000). Each of the next n lines, contains 2 space-separated integers x and y (the coordinates of a point) with magnitude (absolute value) of no more than 1000000000.
Output
Output should contain t lines.
Line i contains an integer showing the number of the parallelograms as described above for test case i.
Line i contains an integer showing the number of the parallelograms as described above for test case i.
Sample Input
2 6 0 0 2 0 4 0 1 1 3 1 5 1 7 -2 -1 8 9 5 7 1 1 4 8 2 0 9 8
Sample Output
5 6
题目大意:给定n个点的坐标,问n个点能够组成多少个平行四边形。
#include <stdio.h> #include <iostream> #include <algorithm> #include <stdlib.h> using namespace std; typedef struct _point { int x; int y; }_Point; _Point p[1000100]; _Point temp[1010]; bool cmp(const _Point& point1, const _Point& point2) { if (point1.x == point2.x) { return point1.y > point2.y; } else { return point1.x > point2.x; } } int main() { int N; scanf("%d", &N); while(N--) { int n; scanf("%d", &n); int nCount = 0; for (int i = 0; i < n; i++) { scanf("%d%d", &temp[i].x, &temp[i].y); } for (int i = 0; i < n; i++) { for (int j = i + 1; j < n; j++) { p[nCount].x = temp[i].x + temp[j].x; p[nCount++].y = temp[i].y + temp[j].y; } } sort(p, p + nCount, cmp); int k = 1; int sum = 0; for (int i = 0; i < nCount; i++) { if (p[i].x == p[i + 1].x && p[i].y == p[i + 1].y) { k++; } else { sum += (k - 1) * k / 2; k = 1; } } printf("%d ", sum); } return 0; }