Find the next Factorial greater than N

Given a number N (≤ 10¹⁸), the task is to find the next factorial number greater than N.
Examples:

Input: N = 24 
Output: 120 
Explanation:
As 4! = 24. So the next number which factorial and greater than 24 is 5!, which is 120
Input: N = 150 
Output: 720 
Explanation:
As 5! = 120. So the next number which factorial and greater than 150 is 6!, which is 720. 

Approach:

1. Precompute the factorial of all number upto 20 in an array as 20! > 10¹⁸.
2. Traverse the factorial array and find the value which is just greater than N as the required next factorial number.

Below is the implementation of above approach: 

C++

// C++ implementation of the above approach

#include "bits/stdc++.h"
using namespace std;

// Array that stores the factorial
// till 20
long long fact[21];

// Function to pre-compute
// the factorial till 20
void preCompute()
{

    // Precomputing factorials
    fact[0] = 1;

    for (int i = 1; i < 18; i++)
        fact[i] = (fact[i - 1] * i);
}

// Function to return the next
// factorial number greater than N
void nextFactorial(int N)
{
    // Traverse the factorial array
    for (int i = 0; i < 21; i++) {

// Find the next just greater
// factorial than N
        if (N < fact[i]) {

            cout << fact[i];
            break;
        }
    }
}

// Driver Code
int main()
{
    // Function to precalculate
    // the factorial till 20
    preCompute();

    int N = 120;

    // Function call
    nextFactorial(N);

    return 0;
}

Java

// Java implementation of the above approach
class GFG {

// Array that stores the factorial
// till 20
final static int fact[] = new int[21];

    // Function to pre-compute
    // the factorial till 20
    static void preCompute()
    {

        // Precomputing factorials
        fact[0] = 1;

        for (int i = 1; i < 18; i++)
            fact[i] = (fact[i - 1] * i);
    }

    // Function to return the next
    // factorial number greater than N
    static void nextFactorial(int N)
    {
        // Traverse the factorial array
        for (int i = 0; i < 21; i++) {

            // Find the next just greater
            // factorial than N
            if (N < fact[i]) {

                System.out.println(fact[i]);
                break;
            }
        }
    }

    // Driver Code
    public static void main (String[] args)
    {
        // Function to precalculate
        // the factorial till 20
        preCompute();

        int N = 120;

        // Function call
        nextFactorial(N);
    }

}

// This code is contributed by AnkitRai01

Python3

# Python3 implementation of the above approach

# Array that stores the factorial
# till 20
fact = [0] * 21

# Function to pre-compute
# the factorial till 20
def preCompute():

    # Precomputing factorials
    fact[0] = 1

    for i in range(1, 18):
        fact[i] = (fact[i - 1] * i)

# Function to return the next
# factorial number greater than N
def nextFactorial(N):

    # Traverse the factorial array
    for i in range(21):

# Find the next just greater
# factorial than N
        if N < fact[i]:

            print(fact[i])
            break

# Driver Code
# Function to precalculate
# the factorial till 20
preCompute()

N = 120

# Function call
nextFactorial(N)

# This code is contributed by divyamohan123

C#

// C# implementation of the above approach
using System;

class GFG {

    // Array that stores the factorial
    // till 20
    static int []fact = new int[21];

    // Function to pre-compute
    // the factorial till 20
    static void preCompute()
    {

        // Precomputing factorials
        fact[0] = 1;

        for (int i = 1; i < 18; i++)
            fact[i] = (fact[i - 1] * i);
    }

    // Function to return the next
    // factorial number greater than N
    static void nextFactorial(int N)
    {
        // Traverse the factorial array
        for (int i = 0; i < 21; i++) {

            // Find the next just greater
            // factorial than N
            if (N < fact[i]) {

                Console.WriteLine(fact[i]);
                break;
            }
        }
    }

    // Driver Code
    public static void Main (string[] args)
    {
        // Function to precalculate
        // the factorial till 20
        preCompute();

        int N = 120;

        // Function call
        nextFactorial(N);
    }

}

// This code is contributed by AnkitRai01

Javascript

<script>
// Javascript implementation of the above approach

// Array that stores the factorial
// till 20
fact = Array(21).fill(0);

// Function to pre-compute
// the factorial till 20
function preCompute()
{

    // Precomputing factorials
    fact[0] = 1;

    for (var i = 1; i < 18; i++)
        fact[i] = (fact[i - 1] * i);
}

// Function to return the next
// factorial number greater than N
function nextFactorial(N)
{
    // Traverse the factorial array
    for (var i = 0; i < 21; i++) {

    // Find the next just greater
    // factorial than N
        if (N < fact[i]) {

            document.write(fact[i]);
            break;
        }
    }
}

// Driver Code

// Function to precalculate
// the factorial till 20
preCompute();
var N = 120;

// Function call
nextFactorial(N);

// This code is contributed by rutvik_56.
</script>

Output:

720

Time Complexity: O(21)

Auxiliary Space: O(21)