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  • C

    You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail.

    Input

    Input starts with an integer T (≤ 10000), denoting the number of test cases.

    Each case contains an integer Q (1 ≤ Q ≤ 108) in a line.

    Output

    For each case, print the case number and N. If no solution is found then print 'impossible'.

    Sample Input

    3

    1

    2

    5

    Sample Output

    Case 1: 5

    Case 2: 10

    Case 3: impossible

     

    /*****

    思路:对0--5*x进行二分(别问我为什莫,自己好好想想)

    *****/

    AC:代码

    #include<cstdio>
    #include<iostream>
    #include<cstring>
    #include<algorithm>
    using namespace std;
    typedef long long ll;
    ll judge(ll mid,ll n){
    	ll s = 0;
    	while(mid>=5){
    		mid /= 5;
    		s += mid;  
    	}
    	if(s>=n) return 0;
    	else return 1;
    }
    int main()
    {
    	int t,ncase = 1;
    	cin>>t;
    	while(t--)
    	{
    		ll n;
    		scanf("%lld",&n);
    		ll low = 0,high = 5*n,mid;
    		for(int i = 0;i<300;i++){
    			mid = low + (high - low)/2;
    			if(judge(mid,n)) low = mid + 1;
    			else high = mid;
    		}
    		ll a = low,s = 0;
    		while(low>=5){
    			low /= 5;
    			s += low;
    		}
    		printf("Case %d: ",ncase++);
    		if(s == n){
    			printf("%lld
    ",a);
    		}
    		else printf("impossible
    ");
    	}
    	
    	return 0;
     } 


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  • 原文地址:https://www.cnblogs.com/Nlifea/p/11746044.html
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