UVa 357 - Let Me Count The Ways 背包

Let Me Count The Ways

After making a purchase at a large department store, Mel's change was 17 cents. He received 1 dime, 1 nickel, and 2 pennies. Later that day, he was shopping at a convenience store. Again his change was 17 cents.
This time he received 2 nickels and 7 pennies. He began to wonder ' "How many stores can I shop in and receive 17 cents change in a different configuration of coins? After a suitable mental struggle, he decided the answer was 6. He then challenged you to consider
the general problem.

Write a program which will determine the number of different combinations of US coins (penny: 1c, nickel: 5c, dime: 10c, quarter: 25c, half-dollar: 50c) which may be used to produce a given amount of money.

Input

The input will consist of a set of numbers between 0 and 30000 inclusive, one per line in the input file.

Output

The output will consist of the appropriate statement from the selection below on a single line in the output file for each input value. The number m is the number your program computes, n is the
input value.

There are m ways to produce n cents change.
There is only 1 way to produce n cents change.

Sample input

17 
11
4

Sample output

There are 6 ways to produce 17 cents change. 
There are 4 ways to produce 11 cents change. 
There is only 1 way to produce 4 cents change.

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还是背包

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#include <iostream>
#include <cstdio>
#include <cstring>

using namespace std;

const int coins[6]={1,5,10,25,50};
long long f[51111];
int m;

int main()
{
    memset(f,0,sizeof(f));
    f[0]=1;
    for (int i=0;i<5;i++)
    {
        for (int j=0;j<=30000-coins[i];j++)
        {
            if (f[j]) f[j+coins[i]]+=f[j];
        }
    }
    while (~scanf("%d",&m))
    {
        if (f[m]==1)
        {
            printf("There is only 1 way to produce %d cents change.\n",m);
        }
        else
        {
            printf("There are %lld ways to produce %d cents change.\n",f[m],m);
        }
    }
    return 0;
}

Let Me Count The Ways

After making a purchase at a large department store, Mel's change was 17 cents. He received 1 dime, 1 nickel, and 2 pennies. Later that day, he was shopping at a convenience store. Again his change was 17 cents.
This time he received 2 nickels and 7 pennies. He began to wonder ' "How many stores can I shop in and receive 17 cents change in a different configuration of coins? After a suitable mental struggle, he decided the answer was 6. He then challenged you to consider
the general problem.

Write a program which will determine the number of different combinations of US coins (penny: 1c, nickel: 5c, dime: 10c, quarter: 25c, half-dollar: 50c) which may be used to produce a given amount of money.

Input

The input will consist of a set of numbers between 0 and 30000 inclusive, one per line in the input file.

Output

The output will consist of the appropriate statement from the selection below on a single line in the output file for each input value. The number m is the number your program computes, n is the
input value.

There are m ways to produce n cents change.
There is only 1 way to produce n cents change.

Sample input

17 
11
4

Sample output

There are 6 ways to produce 17 cents change. 
There are 4 ways to produce 11 cents change. 
There is only 1 way to produce 4 cents change.