C++ Program to Find Factorial of a Number Using Dynamic Programming

The Factorial of a number N can be defined as the product of numbers from 1 to the number N. More formally factorial of n can be defined by function,

[Tex]f(n) = 1 \times 2 \times 3 \times… \ n[/Tex]

In this article, we will learn how to find the factorial of a number using dynamic programming in C++.

Example:

Input: n = 5 Output: Factorial = 120

Factorial of a Number Using Dynamic Programming in C++

To find the factorial of the number N using dynamic programming, we will first define an array of size (N + 1) and then define dp[0]=1 and dp[1]=1 . After that, we will fill the dp array by multiplying the current index by the value in dp array at previous index.

Approach

• Define an array named as dp.
• Declare dp[0]=1 abd dp[1]=1.
• Start a loop from 1 to N.
• In each iteration of the loop, do dp[i]=i*dp[i-1].
• The value at dp[N] will correspond to the factorial of number N.

C++ Program to Find the Factorial of a Number Using Dynamic Programming

C++

// CPP Program to illustrate how to Find the Factorial of a
// Number Using Dynamic Programming
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    // Number to find the factorial of
    int num = 5;

    // Vector to store factorials
    vector<long long> factorial(num + 1);

    // Base case
    factorial[0] = 1;

    // Calculate factorials
    for (int i = 1; i <= num; i++) {
        factorial[i] = i * factorial[i - 1];
    }

    // Print the factorial of the number
    cout << "Factorial of " << num
         << " is: " << factorial[num] << endl;

    return 0;
}

Output

Factorial of 5 is: 120

Time complexity: O(N)
Space complexity: O(N)

This method is efficient for large numbers or when the factorial function is called multiple times.