杭电1217

题目描述：

Arbitrage is the use of discrepancies in currency exchange rates to transform one unit of a currency into more than one unit of the same currency. For example, suppose that 1 US Dollar buys 0.5 British pound, 1 British pound buys 10.0 French francs, and 1 French franc buys 0.21 US dollar. Then, by converting currencies, a clever trader can start with 1 US dollar and buy 0.5 * 10.0 * 0.21 = 1.05 US dollars, making a profit of 5 percent.

Your job is to write a program that takes a list of currency exchange rates as input and then determines whether arbitrage is possible or not.

弗洛伊德算法，最短路径，AC代码：

using System;namespace a1{class Program{public const int M = 50;public static string[] countries = new string[M];public static double[][] relation = new double[M][];public static int find(string s, int n){  int mid = -1, high = n - 1, low = 0;  while (low <= high) {  mid = (low + high) / 2;  if (countries[mid] == s)return mid;else if (string.Compare(countries[mid], s) < 0)low = mid + 1;elsehigh = mid - 1;  }  return -1; }public static void Main(string[] args){int n, m, i, p, q, ce = 0;string a, b;  double t;  string str = string.Empty;while ((str = Console.ReadLine()) != null) {n = Convert.ToInt32(str);if (n == 0)break;ce++;  for (i = 0; i < n; i++) {relation[i] = new double[n];for (int j = 0; j < n; j++)relation[i][j] = 0;} for (i = 0; i < n; i++) {str = Console.ReadLine();countries[i] = str;relation[i][i] = 1;}  Array.Sort(countries,0,n);str = Console.ReadLine();m = Convert.ToInt32(str);for (i = 1; i <= m; i++) {  str = Console.ReadLine();string[] s = str.Split(' ');a = s[0];t = Convert.ToDouble(s[1]);b = s[2];p = find(a, n);  q = find(b, n);  relation[p][q] = t;  }  Console.ReadLine();for (i = 0; i < n; i++)for (p = 0; p < n; p++)for (q = 0; q < n; q++)if (relation[p][i] * relation[i][q] > relation[p][q])relation[p][q] = relation[p][i] * relation[i][q];  for (i = 0; i < n; i++)if (relation[i][i] > 1)break;  if (i >= n)Console.WriteLine("Case {0}: No", ce);elseConsole.WriteLine("Case {0}: Yes", ce);  }}}}