hdu 1046 Gridland

Gridland

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 5137    Accepted Submission(s): 2342

Problem Description

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.

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.

 

 

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

 

 

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一道找规律的题，找到规律之后很简单。

 

题意：给定n*m的格点，问从一个角开始，遍历所有的点一次然后回到起点的最短距离。

 

附上代码：

 

#include <iostream>
#include <cstdio>
using namespace std;
int main()
{
    int m,k,n,j=1;
    double s;
    scanf("%d",&k);
    while(k--)
    {
        scanf("%d%d",&m,&n);
        if(m%2==0||n%2==0)
            s=m*n;     //若n是偶数，我们可以将m的最后一列留出来和n的最下面一行，为了回来，而剩余的段走S形完全遍历；m是偶数时同理，共n*m。
        else
            s=m*n+0.414;     //若都是奇数时，必须走一次斜线，才能变成上面的情况。共n*m-1+sqrt(2)。
        printf("Scenario #%d:\n",j);
        printf("%.2lf\n\n",s);
        j++;
    }
    return 0;
}