ZOJ 1450 Girdland

本文介绍了一种解决Gridland旅行商问题的方法,该问题是计算在一个矩形网格中,从一个点出发访问所有点并返回起点的最短路径长度。文章提供了一个简单的公式来计算最短路径长度,并附带了实现这一算法的C++代码。

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Time Limit: 1000MS Memory Limit: 10000KB 64bit IO Format: %I64d & %I64u

 Status

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.

Sample Input

2
2 2
2 3

Sample Output

Scenario #1:
4.00

Scenario #2:
6.00

Source

Northwestern Europe 2001

 

规律题:

详细介绍请见

http://blog.youkuaiyun.com/manio/article/details/604254

 

#include<stdio.h>
int main (void)
{
    int t,a,b;
    double sum;
    scanf("%d",&t);
    for(int i=0;i<t;i++)
    {
        scanf("%d%d",&a,&b);
        if(a*b%2==1)
        {
            sum=a*b+0.41;
            printf("Scenario #%d:\n%.2lf\n\n",i+1,sum);
        }
        else
        {
            sum=a*b;
            printf("Scenario #%d:\n%.2lf\n\n",i+1,sum);
        }
    }
    return 0;
}

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