Find N from the value of N!

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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.

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