The factorial of an integer N, written N!, is the product of all the integers from 1 through N inclusive. The factorial quickly becomes very large: 13! is too large to store in a 32-bit integer on most computers, and 70! is too large for most floating-point variables. Your task is to find the rightmost non-zero digit of n!. For example, 5! = 1 * 2 * 3 * 4 * 5 = 120, so the rightmost non-zero digit of 5! is 2. Likewise, 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040, so the rightmost non-zero digit of 7! is 4.
PROGRAM NAME: fact4
INPUT FORMAT
A single positive integer N no larger than 4,220.SAMPLE INPUT (file fact4.in)
7
OUTPUT FORMAT
A single line containing but a single digit: the right most non-zero digit of N! .SAMPLE OUTPUT (file fact4.out)
4
把每个数分解质因数
因为2*5之后会产生一个零一直在右边,所以直接把2和5的个数同时减小,直到其中一个不存在(对答案无影响)
把所有质因数边乘边模
#include<cstdio>
#include<cstring>
#include<cmath>
#include<iostream>
#include<algorithm>
#define name "fact4"
using namespace std;
int n,ans=1;
int cnt[5000];
void fenjie(int x)
{
int i=2;
while (x!=0&&x!=1)
{
while (x%i==0)
{
cnt[i]++;
x/=i;
if (x==0) break;
}
i++;
}
}
int main()
{
freopen(name ".in","r",stdin);
freopen(name ".out","w",stdout);
cin>>n;
int i,j;
for (i=2;i<=n;i++)
fenjie(i);
cnt[2]-=cnt[5];cnt[5]=0;
for (i=2;i<=n;i++)
{
for (j=1;j<=cnt[i];j++)
ans=(ans*i)%10;
}
cout<<ans<<endl;
return 0;
}
/*
Executing...
Test 1: TEST OK [0.000 secs, 4196 KB]
Test 2: TEST OK [0.000 secs, 4196 KB]
Test 3: TEST OK [0.000 secs, 4196 KB]
Test 4: TEST OK [0.000 secs, 4196 KB]
Test 5: TEST OK [0.000 secs, 4196 KB]
Test 6: TEST OK [0.000 secs, 4196 KB]
Test 7: TEST OK [0.000 secs, 4196 KB]
Test 8: TEST OK [0.000 secs, 4196 KB]
Test 9: TEST OK [0.000 secs, 4196 KB]
Test 10: TEST OK [0.000 secs, 4196 KB]
All tests OK.
YOUR PROGRAM ('fact4') WORKED FIRST TIME! That's fantastic
-- and a rare thing. Please accept these special automated
congratulations.
*/