[解题报告]369 - Combinations

 Combinations 

Computing the exact number of ways that N things can be taken M at a time can be a great challenge when Nand/or M become very large. Challenges are the stuff of contests. Therefore, you are to make just such a computation given the following:

 

 

GIVEN:

 

Compute the EXACT value of:

 

 

You may assume that the final value of C will fit in a 32-bit Pascal LongInt or a C long.

 

For the record, the exact value of 100! is:

 

     93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,
        468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,
        697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000

 

Input and Output

The input to this program will be one or more lines each containing zero or more leading spaces, a value forN, one or more spaces, and a value for M. The last line of the input file will contain a dummy N, M pair with both values equal to zero. Your program should terminate when this line is read.

 

The output from this program should be in the form:

 

 

N things taken M at a time is C exactly.

 

Sample Input

 

     100  6
      20  5
      18  6
       0  0

 

Sample Output

 

100 things taken 6 at a time is 1192052400 exactly.
20 things taken 5 at a time is 15504 exactly.
18 things taken 6 at a time is 18564 exactly.

 

 

 

 

略水，注意存储形式

#include<stdio.h>
long long int C(int n,int m)
{
    int i;
    long long int temp = 1;
    m=(n-m<m)?n-m:m;
    for(i=1;i<=m;i++)
    {
    temp*=n;
    temp/=i;
    n--;
    }
    return temp;
}
int main()
{
    int m,n;
    while(scanf("%d %d",&n,&m)&&n&&m)
    {
          printf("%d things taken %d at a time is %lld exactly.\n",n,m,C(n,m));
    }
  return 0;
}