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 intusing namespace std;// Map to precompute and store the// factorials of the numbersmap<ll, ll> m;// Function to precompute factorialint 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 codeint 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 givenimport java.util.*;class GFG{ // Map to precompute and store the// factorials of the numbersstatic Map<Integer, Integer> m = new HashMap<Integer, Integer>(); // Function to precompute factorialstatic 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 codepublic 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 givenusing System;using System.Collections.Generic;class GFG{ // Map to precompute and store the// factorials of the numbersstatic Dictionary<int, int> m = new Dictionary<int, int>(); // Function to precompute factorialstatic 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 codepublic 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 numbersvar m = {}; // Function to precompute factorialfunction 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 codeprecompute();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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