poj 1252 Euro Efficiency-----BFS 遍历，记录最短路

Euro Efficiency

Time Limit:1000MS		Memory Limit:10000K
Total Submissions:2158		Accepted:965

Description

On January 1st 2002, The Netherlands, and several other European countries abandoned their national currency in favour of the Euro. This changed the ease of paying, and not just internationally.
A student buying a 68 guilder book before January 1st could pay for the book with one 50 guilder banknote and two 10 guilder banknotes, receiving two guilders in change. In short:50+10+10-1-1=68. Other ways of paying were: 50+25-5-1-1, or 100-25-5-1-1.Either way, there are always 5 units (banknotes or coins) involved in the payment process, and it
could not be done with less than 5 units.
Buying a 68 Euro book is easier these days: 50+20-2 = 68, so only 3 units are involved.This is no coincidence; in many other cases paying with euros is more efficient than paying with guilders. On average the Euro is more efficient. This has nothing to do, of course, with the value of the Euro, but with the units chosen. The units for guilders used to be: 1, 2.5, 5, 10, 25, 50,whereas the units for the Euro are: 1, 2, 5, 10, 20, 50.
For this problem we restrict ourselves to amounts up to 100 cents. The Euro has coins with values 1, 2, 5, 10, 20, 50 eurocents. In paying an arbitrary amount in the range [1, 100] eurocents, on average 2.96 coins are involved, either as payment or as change. The Euro series is not optimal in this sense. With coins 1, 24, 34, 39, 46, 50 an amount of 68 cents can be paid using two coins.The average number of coins involved in paying an amount in the range [1, 100] is 2.52.
Calculations with the latter series are more complex, however. That is, mental calculations.These calculations could easily be programmed in any mobile phone, which nearly everybody carries around nowadays. Preparing for the future, a committee of the European Central Bank is studying the efficiency of series of coins, to find the most efficient series for amounts up to 100 eurocents. They need your help.
Write a program that, given a series of coins, calculates the average and maximum number of coins needed to pay any amount up to and including 100 cents. You may assume that both parties involved have sufficient numbers of any coin at their disposal.

Input

The first line of the input contains the number of test cases. Each test case is described by 6 different positive integers on a single line: the values of the coins, in ascending order. The first number is always 1. The last number is less than 100.

Output

For each test case the output is a single line containing first the average and then the maximum number of coins involved in paying an amount in the range [1, 100]. These values are separated by a space. As in the example, the average should always contain two digits behind the decimal point. The maximum is always an integer.

Sample Input

3
1 2 5 10 20 50
1 24 34 39 46 50
1 2 3 7 19 72

Sample Output

2.96 5
2.52 3
2.80 4

题目大意： 有六种不同面值的钱， 组合成 1 ~100 的各种数额，求出平均需要的张数和最多的张数。

解题思路: 用BFS遍历所有 1 ~100 的值。 用一个vir数组记录 最小的步数。 具体见代码。 关于这题，最值得记住的教训就是 边界问题， 刚开始把入队的条件 记为 1~100 就错了， 必须考虑可能会超过边界， 简单理解就是可以暂时走到 负数，然后再走回来。

代码：

//Memory: 344 KB		Time: 0 MS
//Language: C++ (g++ 4.4.5)		Result: Accepted

#include<stdio.h>
#include<string.h>
void bfs(int n);
int q[320],vir[320];
int dir[12];
int main()
{
//	freopen("in.txt","r",stdin);
	int n,i,sum,max;
	double ave;
	while(scanf("%d",&n)!=EOF)
	{
		while(n--)
		{
		memset(vir,0,sizeof(vir));
		sum=0,max=0;
		for(i=0;i<6;i++)
		{
			scanf("%d",&dir[i]);
			dir[i+6]=-dir[i];
		}
		bfs(100);
 //   	for(i=101;i<=200;i++)
//	    printf("(%d)%d  ",i,vir[i]);
		for(i=101;i<=200;i++)
		{
			sum+=vir[i];
			if(vir[i]>max)
				max=vir[i];
		}
		ave=(double)sum/100.0;
		printf("%.2lf %d\n",ave,max);
		}
	}
	return 0;
}

void bfs(int n)
{
	int i;
	int rear=0,front=0;
	q[rear++]=100;
	vir[100]=0;
	while(front<rear)
	{
		for(i=0;i<12;i++)
		{
			int temp=q[front]+dir[i];
			if(temp>=1&&temp<=n+100&&vir[temp]==0)   //边界以后要多注意！！！
			{
				q[rear++]=temp;
				vir[temp]=vir[q[front]]+1;
			}
		}
		front++;
	}
}