Posted by admin at April 2, 2020
You know your solution should return 1
when the number passed to the function is 0
or 1
. Also, the final value returned will be the product of all the numbers between 1 and the number (inclusive). If you initialize the value for the product to 1
, then think how you could start at the given number and continue decrementing this number until a specific value while multiplying the product by the number at each step.
Recursive Solution
This one starts easily since 0! = 1
, so you can go ahead and simply return 1
there.
We can use that as an if
in order to break the loop we’re going to create using a recursive function. It will check if the number you gave the function is 0 (which would be the end of your factorial chain). Functions “end” when they return anything. In fact, all functions without an explicit return
statement will return undefined
.
This is also why instead of having “finished”, a function is always said to “have returned”. And now this…
Understanding recursion
Recursion refers to a function repeating (calling) itself. In this case we are basically returning the given number (i.e. 5), multiplied by the function itself but this time the value passed to the num parameter is num-1
(which initially translates to 4). The very function is going to run inside itself interesting, eh?
Understanding the flow
The first returned value can be visualized better if you think about those parenthesis operations you did in secondary school where you do the math inside every parenthesis from inside out, bracket and square bracket until you get a final result (a total). This time it’s the same thing, look at the program flow:
During the first execution of the function:
[num = 5]
Is 5 equal to 1 or 0? No —> Oki doki, let’s continue…
Returns:
(5 _(second execution: 4 _(third execution: 3 _(fourth execution: 2 _fifth execution: 1))))
What it returns can be viewed as (5*(4*(3*(2*1))))
or just 5 * 4 * 3 * 2 * 1
, and the function will return the result of that operation: 120
. Now, let’s check what the rest of the executions do:
During the rest of the executions:
Second Execution:
num = 5-1 = 4 -> is num 0 or 1? No
–> return the multiplication between 4 and the next result when num is now 4-1.
Third Execution: num = 4 – 1 = 3 -> is num 0 or 1? No
–> return the multiplication between 3 and the next result when num is now 3-1.
Fourth Execution: num = 3-1 = 2 -> is num 0 or 1? No
–> return the multiplication between 2 and the next result when num is now 2-1.
Fifth Execution: num = 2-1 = 1 -> is num 0 or 1? Yep
–> return 1. And this is where the recursion stops because there are no more executions.
Solution 1
function factorialize(num) {
for (var product = 1; num > 0; num--) {
product *= num;
}
return product;
}
factorialize(5);
product
is initialized at one. For the case where the number is 0
, the for loop condition will be false, but since product
is initialized as 1
, it will have the correct value when the return
statement is executed.for
loop will decrement num
by one each iteration and recalculate product
down to the value 1
.Solution 2 (using Recursion)
function factorialize(num) {
if (num === 0) {
return 1;
}
return num * factorialize(num - 1);
}
factorialize(5);
Notice at the first line we have the terminal condition, i.e a condition to check the end of the recursion. If num == 0
, then we return 1, i.e. effectively ending the recursion and informing the stack to propagate this value to the upper levels. If we do not have this condition, the recursion would go on until the stack space gets consumed, thereby resulting in a Stack Overflow
Solution 3
function factorialize(num, factorial = 1) {
if (num == 0) {
return factorial;
} else {
return factorialize(num - 1, factorial * num);
}
}
factorialize(5);
Solution 4
function factorialize(num, factorial = 1) {
return num < 0 ? 1 : (
new Array(num)
.fill(undefined)
.reduce((product, val, index) => product * (index + 1), 1)
);
}
factorialize(5);
num
. And we filled all elements of the array as undefined
. In this case, we have to do this because empty arrays couldn’t reducible. You can fill the array as your wish by the way. This depends on your engineering sight completely.reduce
function’s accumulator is calling product
this is also our final value. We are multiplying our index value with the product to find factorial
value.
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