Squares

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Squares原题：

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Description

      A square is a 4-sided polygon whose sides have equal length and adjacent sides form 90-degree angles. It is also a polygon such that rotating about its centre by 90 degrees gives the same polygon. It is not the only polygon with the latter property, however, as a regular octagon also has this property.

      So we all know what a square looks like, but can we find all possible squares that can be formed from a set of stars in a night sky? To make the problem easier, we will assume that the night sky is a 2-dimensional plane, and each star is specified by its x and y coordinates.

Input

      The input consists of a number of test cases. Each test case starts with the integer n (1 <= n <= 1000) indicating the number of points to follow. Each of the next n lines specify the x and y coordinates (two integers) of each point. You may assume that the points are distinct and the magnitudes of the coordinates are less than 20000. The input is terminated when n = 0.

Output

      For each test case, print on a line the number of squares one can form from the given stars.

我的理解：

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      本题主要在搜索，找点，所以采用了hash表，并用链地址法解决冲突。

      注意，排序及条件判断解决重复计数。

 

AC代码：

// Squares: hash #include <iostream> #include <vector> #include <list> const int MAX_HASH = 10011; const int MAX_COUNT = 1001; struct point{ int x; int y; }; std::vector<point> resource(MAX_COUNT); int hashTable[MAX_HASH]; std::vector<int> hashChain(MAX_COUNT); int Hash(int x) { int h = x % MAX_HASH; if (h < 0) h += MAX_HASH; return h; } void Insert(point p) { int n = Hash(p.x * p.x + p.y * p.y); bool flag = false; for (int i = hashTable[n]; i != -1; i = hashChain[i]) { if (resource[i].x == p.x && resource[i].y == p.y) { flag = true; break; } } if (!flag) { resource.push_back(p); hashChain.push_back(hashTable[n]); hashTable[n] = resource.size() - 1; } } int Serch(point p) { int n = Hash(p.x * p.x + p.y * p.y); for (int i = hashTable[n]; i != -1; i = hashChain[i]) { if (resource[i].x == p.x && resource[i].y == p.y) return 1; } return 0; } bool op(const point& p1, const point& p2) { if (p1.x == p2.x) return p1.y < p2.y; else return p1.x < p2.x; } int main() { while (true) { memset(hashTable, -1, sizeof(hashTable)); resource.clear(); hashChain.clear(); int k(0), sum(0); std::cin >> k; if (k == 0) break; std::list<point> temp; for (int i = 0; i < k; ++i) { point p; std::cin >> p.x >> p.y; temp.push_back(p); } temp.sort(op); for (std::list<point>::iterator iter = temp.begin(); iter != temp.end(); iter++) Insert(*iter); for (int i = 0; i < k; ++i) { for (int j = i + 1; j < k; ++j) { if (resource[i].x <= resource[j].x && resource[i].y >= resource[j].y) { point p0, p1; p0.x = resource[i].x + resource[j].y - resource[i].y; p0.y = resource[i].y + resource[i].x - resource[j].x; p1.x = resource[j].x + resource[j].y - resource[i].y; p1.y = resource[j].y + resource[i].x - resource[j].x; if (!Serch(p0)) continue; if (!Serch(p1)) continue; sum++; } } } std::cout << sum << std::endl; } }

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