poj1450

Gridland

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 8253 Accepted: 4181

Description

Background 

For years, computer scientists have been trying to find efficient solutions to different computing problems. For some of them efficient algorithms are already available, these are the "easy" problems like sorting, evaluating a polynomial or finding the shortest path in a graph. For the "hard" ones only exponential-time algorithms are known. The traveling-salesman problem belongs to this latter group. Given a set of N towns and roads between these towns, the problem is to compute the shortest path allowing a salesman to visit each of the towns once and only once and return to the starting point. 

Problem 

The president of Gridland has hired you to design a program that calculates the length of the shortest traveling-salesman tour for the towns in the country. In Gridland, there is one town at each of the points of a rectangular grid. Roads run from every town in the directions North, Northwest, West, Southwest, South, Southeast, East, and Northeast, provided that there is a neighbouring town in that direction. The distance between neighbouring towns in directions North-South or East-West is 1 unit. The length of the roads is measured by the Euclidean distance. For example, Figure 7 shows 2 * 3-Gridland, i.e., a rectangular grid of dimensions 2 by 3. In 2 * 3-Gridland, the shortest tour has length 6. 
 
Figure 7: A traveling-salesman tour in 2 ? 3-Gridland.

Input

The first line contains the number of scenarios. 

For each scenario, the grid dimensions m and n will be given as two integer numbers in a single line, separated by a single blank, satisfying 1 < m < 50 and 1 < n < 50.

Output

The output for each scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. In the next line, print the length of the shortest traveling-salesman tour rounded to two decimal digits. The output for every scenario ends with a blank line.

源代码

#include<iostream>
#include<math.h>
using namespace std;
int main()
{
int i,j,a,b,t;
float n;
cin>>t;
for (i=0;i<t;i++)
{
   cin>>a>>b;
        n=a*b;
        if(a%2==1 && b%2==1) 
{
             n+=sqrt(2.0)-1;
             printf("Scenario #%d:\n%.2f\n\n",i+1,n);
}
        else 
printf("Scenario #%d:\n%.2f\n\n",i+1,n);
}
    return 0;
}

本题找到规律，把公式写上去就行，自己在纸上画几个矩阵，再看它奇偶变化的规律，就很简单能发现，除了输出格式，其他应该都不是问题，算一道水题吧。