Given a set of points with integer coordinates xi, yi, i = 1...N, your program must find all the squares having each of four vertices in one of these points.
Input
Input file contains integer N followed by N pairs of integers xi yi.
Constraints
-104 ≤ xi, yi ≤ 104, 1 ≤ N ≤ 2000. All points in the input are different.
Output
Output file must contain a single integer — number of squares found.
Sample Input
Sample input 1
4 0 0 4 3 -3 4 1 7
Sample input 2
9
1 1 1 2 1 3
2 1 2 2 2 3
3 1 3 2 3 3
Sample Output
Sample output 1
1
Sample output 2
6
Hint
Bold texts appearing in the sample sections are informative and do not form part of the actual data.
題意:
給你 n 個點,判斷存在多少個正方形.
思路:
枚舉兩個點 || 正方形的邊, 然後根據枚舉的兩個點算出未知的兩個點,然後在給出的點中查找這兩個點是否出現,如果出現則說明存在正方形,反之說明不存在.
查找的話可以使用hash 或者 map, 但是map 我沒有試過,不知道具體能不能行.
代碼:
#include<cstdio>
#include<cstring>
#include<cmath>
#include<iostream>
#include<algorithm>
using namespace std;
const int prime = 1999;
typedef class{
public:
int x,y;
}node;
typedef class Hash{//手動寫hash表
public:
int x, y;
Hash *next;
Hash(){
next = 0;
}
}Hash;
node a[2000+10];
Hash *has[prime];
void insert_hash(int pos){
//hash的對應法則,我們採用平方和
int k = (a[pos].x * a[pos].x + a[pos].y * a[pos].y) % prime + 1;
if(!has[k]){
Hash *tmp = new Hash;
tmp->x = a[pos].x;
tmp->y = a[pos].y;
has[k] = tmp;
}else {
Hash * tmp = has[k];//如果這個點出現過
while(tmp->next)
tmp = tmp->next;
tmp->next = new Hash;
tmp->next->x = a[pos].x;
tmp->next->y = a[pos].y;
}
}
bool Find(int x, int y){
int k = (x * x + y * y) % prime + 1;
if(!has[k]) return false;
Hash * tmp = has[k];
while(tmp){
if(tmp->x == x && tmp->y == y)
return true;
tmp = tmp->next;
}return false;
}
int main(){
int n;
while(scanf("%d", &n) != EOF && n){
memset(has,0, sizeof(has));
for(int i = 1; i <= n; ++i){
scanf("%d %d", &a[i].x, &a[i].y);
insert_hash(i);
}int num = 0;
for(int i = 1; i <= n; ++i)
for(int j = i+1; j <= n; ++j){
int x = a[j].x - a[i].x;//根據已知點算正方形未知點的座標
int y = a[j].y - a[i].y;
int x1 = y + a[i].x;
int y1 = a[i].y - x;
int x2 = y + a[j].x;
int y2 = a[j].y - x;
if(Find(x1,y1) && Find(x2,y2))
++num;
x1 = a[i].x - y;
y1 = a[i].y + x;
x2 = a[j].x - y;
y2 = a[j].y + x;
if (Find(x1,y1) && Find(x2,y2))
++num;
}printf("%d\n",num/4);//由於每個正方形被算了四次,所以除以4
}return 0;
}