Choose and divide UVA
Choose and divide UVA - 10375
The binomial coefficient C(m, n) is defined as C(m, n) = m! (m − n)! n!
Given four natural numbers p, q, r, and s, compute the the result of dividing C(p, q) by C(r, s).
Input
Input consists of a sequence of lines. Each line contains four non-negative integer numbers giving values for p, q, r, and s,
respectively, separated by a single space. All the numbers will be smaller than 10,000 with p ≥ q and r ≥ s.
Output
For each line of input, print a single line containing a real number with 5 digits of precision in the fraction, giving the number as described above.
You may assume the result is not greater than 100,000,000.
Sample Input
10 5 14 9
93 45 84 59
145 95 143 92
995 487 996 488
2000 1000 1999 999
9998 4999 9996 4998
Sample Output
0.12587
505606.46055
1.28223
0.48996
2.00000
3.99960
题解：刘汝佳p317
AC代码：
#include<iostream>
#include<cstring>
#include<cstdio>
#include<vector>
#include<cmath>
using namespace std;
const int maxn=10005;
int e[maxn];
int prime[maxn];
bool is_prime[maxn];
int cnt=0;
void sieve()
{
for(int i=0;i<maxn;i++)
is_prime[i]=true;
is_prime[0]=is_prime[1]=false;
for(int i=2;i<maxn;i++)
if(is_prime[i])
{
prime[cnt++]=i;
for(int j=2*i;j<maxn;j+=i)
is_prime[j]=false;
}
}
void add_integer(int n,int d)
{
for(int i=0;i<cnt;i++)
{
while(n%prime[i]==0)
{
n/=prime[i];
e[i]+=d;
}
if(n==1)
break;
}
}
void add_factorial(int n,int d)
{
for(int i=1;i<=n;i++)
{
add_integer(i,d);
}
}
int main()
{
int p,q,r,s;
sieve();
while(cin>>p>>q>>r>>s)
{
memset(e,0,sizeof(e));
add_factorial(p,1);
add_factorial(q,-1);
add_factorial(p-q,-1);
add_factorial(r,-1);
add_factorial(s,1);
add_factorial(r-s,1);
double ans=1;
for(int i=0;i<cnt;i++)
{
ans*=pow(prime[i],e[i]);
}
printf("%.5lf
",ans);
}
return 0;
}
今天也是元气满满的一天！good luck！