ZJU1037-Gridland

Gridland

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Time Limit: 1 Second      Memory Limit: 32768 KB

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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 

思路：题目中一直强调旅行售货员问题，容易诱导去使用复杂的算法；而本题的城市位置特殊，边长也是特殊的，所以能够寻找简单的规律进行计算； 
当m或n为偶数时，最短路长度为mn;当m和n同时为奇数时，最短路再加0.41，因为要走一个斜边； 

代码：

#include <stdio.h>int main(){int T;scanf("%d",&T);for(int i=1;i<=T;i++){int N,M;scanf("%d%d",&M,&N);printf("Scenario #%d:\n",i);if(M%2&&N%2)    printf("%d.41\n\n",M*N);else        printf("%d.00\n\n",M*N);}return 0; }