Find N from the value of N!

Given a number K which represents the factorial of a number N, the task is to find the value of N. 
Note: K < 10¹⁸
Examples:

Input: K = 120 
Output: 5 
Explanation:
5! = 1 * 2 * 3 * 4 * 5 = 120
Input: K = 6 
Output: 3 
Explanation:
3! = 1 * 2 * 3 = 6 

Approach: It is given that the value of N! is less than 10¹⁸. On observation, we can see that this is true only for N <= 18. Therefore we can precompute values of factorials from 1 to 18 and store it in a Hash Table or Map. After pre-computation, for every value of N!, the corresponding N is returned in constant time. 
Below is the implementation of the above approach: 

C++

// C++ program to find a number such that
// the factorial of that number is given

#include "bits/stdc++.h"
#define ll long long int
using namespace std;

// Map to precompute and store the
// factorials of the numbers
map<ll, ll> m;

// Function to precompute factorial
int precompute()
{

    ll fact = 1;
    for (ll i = 1; i <= 18; i++) {

        // Calculating the factorial for
        // each i and storing in a map
        fact = fact * i;
        m[fact] = i;
    }
}

// Driver code
int main()
{
    // Precomputing the factorials
    precompute();

    int K = 120;
    cout << m[K] << endl;

    K = 6;
    cout << m[K] << endl;

    return 0;
}

Java

// Java program to find a number such that
// the factorial of that number is given
import java.util.*;

class GFG{

// Map to precompute and store the
// factorials of the numbers
static Map<Integer, Integer> m = new HashMap<Integer, Integer>();

// Function to precompute factorial
static void precompute()
{

    int fact = 1;
    for (int i = 1; i <= 18; i++) {

        // Calculating the factorial for
        // each i and storing in a map
        fact = fact * i;
        m.put(fact, i);
    }
}

// Driver code
public static void main(String[] args)
{
    // Precomputing the factorials
    precompute();

    int K = 120;
    System.out.print(m.get(K) +"\n");

    K = 6;
    System.out.print(m.get(K) +"\n");

}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to find a number such that
# the factorial of that number is given

# Map to precompute and store the
# factorials of the numbers
m = {};

# Function to precompute factorial
def precompute() :

    fact = 1;
    for i in range(1, 19) :

        # Calculating the factorial for
        # each i and storing in a map
        fact = fact * i;
        m[fact] = i;

# Driver code
if __name__ == "__main__" :

    # Precomputing the factorials
    precompute();

    K = 120;
    print(m[K]);

    K = 6;
    print(m[K]) ;

# This code is contributed by AnkitRai01

C#

// C# program to find a number such that
// the factorial of that number is given
using System;
using System.Collections.Generic;

class GFG{

// Map to precompute and store the
// factorials of the numbers
static Dictionary<int, int> m = new Dictionary<int, int>();

// Function to precompute factorial
static void precompute()
{

    int fact = 1;
    for (int i = 1; i <= 18; i++) {

        // Calculating the factorial for
        // each i and storing in a map
        fact = fact * i;
        m.Add(fact, i);
    }
}

// Driver code
public static void Main(String[] args)
{
    // Precomputing the factorials
    precompute();

    int K = 120;
    Console.Write(m[K] +"\n");

    K = 6;
    Console.Write(m[K] +"\n");
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// Javascript implementation of the
// above approach

// Map to precompute and store the
// factorials of the numbers
var m = {};

// Function to precompute factorial
function precompute()
{

    var fact = 1;
    for (var i = 1; i <= 18; i++) {

        // Calculating the factorial for
        // each i and storing in a map
        fact = fact * i;
        m[fact] = i;
    }
}

// Driver code
precompute();
var K = 120;
document.write(m[K] + "<br>");

K = 6;
document.write(m[K]);


// This code is contributed by Shivanisingh
</script>

Output:

5
3

Time Complexity: O(1)
Auxiliary Space: O(1)

As constant extra space is used.