Trailing Zeroes (III)-;lightoj 1138

Trailing Zeroes (III)

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Time Limit:2 second (s)

Memory limit:32 MB

You task was 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! = 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	Output for Sample Input
3 1 2 5	Case 1:5 Case 2:10 Case 3:impossible

Problem Setter:jane ALAM Jan Test Instructions: If the factorial of a number has n 0, ask what the minimum number of numbers can be.

Title Description:

Suppose there is a number n, it has a Q 0 at the end of the factorial, and now gives Q, Q, what is the minimum?

Problem Solving Ideas:

Since the number at the end of the 0 equals min (the number of factors 2, the number of factor 5), and because 2<5, then assume that there is an infinite number of n,n=2^x=5^y, known x<<y.

So we can calculate the number of the 0 at the end of the factorial directly according to the number of factor 5. 1<=q<=10^8, so it can be solved with two points quickly.

Code:

1#include <iostream>2#include <cstdio>3#include <cstring>4 5 using namespacestd;6 7 Long LongSlove (Long LongN)8 {9     Long LongAns =0;Ten      while(n) One     { AAns + = n/5; -N/=5; -     } the     returnans; - } -  - intMain () + { -     intT, L =1; +  Ascanf"%d", &t); at      while(t--) -     { -         Long LongN; -scanf"%lld", &n); -         Long LongMid, Low =4, high =500000000; -  in          while(Low <=High )//two min Find Fast ~ -         { toMid = (Low+high)/2; +             Long Longnum =Slove (mid); -             if(Num >=N) theHigh = mid-1; *             Else $Low = mid+1;Panax Notoginseng         } -         if(Slove (low) = =N) theprintf"Case %d:%lld\n", l++, low); +         Else Aprintf"Case %d:impossible\n", l++); the     } +     return 0; -}

Trailing Zeroes (III)-;lightoj 1138