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 precomputation, for every value of N!, the corresponding N is returned in constant time.



Below is the implementation of the above approach:

C++

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// 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;
}

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Java

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// 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

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Python3

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# 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

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C#

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// 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

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Output:

5
3

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Improved By : AnkitRai01, 29AjayKumar