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QUESTION

Given a number n. The task is to find the smallest number whose factorial contains at least n trailing zeroes.”,

“TESTCASE_1”: “6\n###—###SEPERATOR—###—\n25”, “TESTCASE_2”: “20\n###—###SEPERATOR—###—\n85”, “TESTCASE_3”: “14\n###—###SEPERATOR—###—\n60”, “TESTCASE_4”: “0\n###—###SEPERATOR—###—\n0”, “TESTCASE_5”: “0\n###—###SEPERATOR—###—\n0

``````// C++ program tofind smallest number whose
// factorial contains at least n trailing
// zeroes.
#include<bits/stdc++.h>
using namespace std;

// Return true if number's factorial contains
// at least n trailing zero else false.
bool check(int p, int n)
{
int temp = p, count = 0, f = 5;
while (f <= temp)
{
count += temp/f;
f = f*5;
}
return (count >= n);
}

// Return smallest number whose factorial
// contains at least n trailing zeroes
int findNum(int n)
{
// If n equal to 1, return 5.
// since 5! = 120.
if (n==1)
return 5;

// Initalising low and high for binary
// search.
int low = 0;
int high = 5*n;

// Binary Search.
while (low <high)
{
int mid = (low + high) >> 1;

// Checking if mid's factorial contains
// n trailing zeroes.
if (check(mid, n))
high = mid;
else
low = mid+1;
}

return low;
}

// driver code
int main()
{
int n;
cin>>n;
cout << findNum(n) ;
return 0;
}``````  