10375 - Choose and divide
Time limit: 3.000 seconds
http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=115&page=show_problem&problem=1316
The binomial coefficient C(m,n) is defined as
m!
C(m,n) = --------
n!(m-n)!
Given four natural numbers p, q, r, and s, compute the the result of dividing C(p,q) by C(r,s).
The 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.
The 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
Output for Sample Input
0.12587
505606.46055
1.28223
0.48996
2.00000
3.99960
思路：不要被题目那个公式误导了~自己算一算几个组合数，比如C(100,4)，发现分子分母都是4个乘数，那就好办了，写一个for循环每次一除一乘就是。
完整代码：
/*0.022s*/
#include<cstdio>
#include<algorithm>
using namespace std;
int main()
{
int p, q, r, s,maxn,i;
double ans;
while (~scanf("%d%d%d%d", &p, &q, &r, &s))
{
q = max(q, p - q), s = max(s, r - s);
maxn = max(q, s);
ans = 1.0;
for (i = 1; i <= maxn; ++i)
{
if (i <= q) ans = ans / i * (p - q + i);
if (i <= s) ans = ans / (r - s + i) * i;
}
printf("%.5f\n", ans);
}
return 0;
}
作者署名：csdn博客 synapse7
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