The factorial of a number, denoted as n!, is the product of all integers between n and 1. n! = n x (n-1) x (n-2) … x1. The value of 0! is 1. You can calculate factorials using iteration and recursion.
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How to calculate factorials using iteration?
In iteration implementation, you assign the initial value of fact to be 1. This is default value for number 0 and 1. Then you use for loop iterate from 2 to the input number. Each time fact is updated to previous fact times the loop variable i. When it finishes, return fact.
Java
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//Iteration, Time O(n), Space O(1), n is input number public static int factorial(int num) { int fact = 1; for (int i = 2; i <= num; i++) fact *= i; return fact; } |
Javascript
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//Iteration, Time O(n), Space O(1), n is input number function factorial(num) { var fact = 1; for (let i = 2; i <= num; i++) fact *= i; return fact; } |
Python
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#Iteration, Time O(n), Space O(1), n is input number def factorial(num) : fact = 1 for i in range(2, num+1): fact *= i return fact |
Doodle
How to calculate factorials using recursion?
In recursion implementation, the function calls itself with input number minus 1. The base condition is when the input number is 0, function returns 1. Then the call stack returns. The recursion simplifies the problem conceptually, but is not as efficient as loop-based approach.
Java
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//Recursion, Time O(n), Space O(n) public static int factorialRec(int num) { if (num == 0) //base condition return 1; return num * factorialRec(num-1); } |
Javascript
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//Recursion, Time O(n), Space O(n) function factorialRec(num) { if (num == 0 ) //base condition return 1; return num * factorialRec(num-1); } |
Python
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#Recursion, Time O(n), Space O(n) def factorialRec(num) : if num == 0 : #base case return 1 return num * factorialRec(num-1); |
Doodle
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What are the methods to calculate factorials?
You can use both iteration and recursion.