CODEWITHSUNDEEP
javascriptrecursion
MonuMan5
MonuMan5

Reputation: 373

Javascript Function that validates exponent equations

This is a hw assignment. The answer/output I want is correct. I just don't understand why. I want the output to be true if the power function matches the number I am checking against. I do get the answer true for these examples, but I don't understand how this recursive function is working.

In the else of this function, I am saying base * the function itself. what does that even represent? How can base * power(base, exponent - 1); even compute? Shouldn't it just run in a circle and then finally end? 

console.log(power(2,4) === 16);
console.log(power(2,3) === 8);
console.log(power(2,2) === 4);

var power = function(base, exponent) {
    if(exponent === 0) {
        return 1; 
    }
    else {
        return base * power(base, exponent - 1);
    }
};

Upvotes: 4

Views: 237

Answers (4)

newtonrd
newtonrd

Reputation: 2285

For the example of power(2,4), we have

  • 4 != 0 so else executes and it performs 2*power(2,3).
  • 3 != 0 so else executes and it performs 2*power(2,2).
  • 2 != 0 so else executes and it performs 2*power(2,1).
  • 1 != 0 so else executes and it performs 2*power(2,0).
  • Finally 0 == 0 so it returns 1 and it doesnt perform another recursive call.

So it goes back through the calls and comes to 2*power(2,0) which we know power(2,0) == 1. That returns as 2. Then it goes back to 2*power(2,1) and we know power(2,1) == 2 since [2*power(2,0)]. This returns as 4.

See the pattern? And so on until we get back to 2*power(2,3) ==16 since we have power(2,3) == 8 since [power(2,2) * power(2,1) * power(2,0) * 1]. Hope this helped!

Upvotes: 0

alex
alex

Reputation: 490423

The exponent is being reduced with each recursive call until it is equal to 0 where it will return a constant 1, and the function stops being recursive.

jsFiddle.

Also, if this wasn't homework, there is Math.pow() :)

Upvotes: 0

Hunter McMillen
Hunter McMillen

Reputation: 61520

The function power returns an integer, so when the function returns base * <some_integer> is a perfectly valid expression. The best way to trace these things is with a pen and paper:

call stack of power(2,4):

power(2, 4) = 2 * power(2, 3)
power(2, 3) = 2 * power(2, 2)
power(2, 2) = 2 * power(2, 1)
power(2, 1) = 2 * power(2, 0)
power(2, 0) = 1 <--base case

now all you have to do is substitute the values up the call stack

power(2, 4) = 2 * 8 = 16
power(2, 3) = 2 * 4 = 8
power(2, 2) = 2 * 2 = 4
power(2, 1) = 2 * 1 = 2

Upvotes: 5

Christian Mann
Christian Mann

Reputation: 8125

It might help to write the function using Javascript's syntactic sugar declaration style:

console.log(power(2,4) === 16);
console.log(power(2,3) === 8);
console.log(power(2,2) === 4);

function power(base, exponent) {
    if(exponent === 0) {
        return 1; 
    }
    else {
        return base * power(base, exponent - 1);
    }
};

If you want, you can also add the line

console.log("power("+base+", "+exponent+")");

at the head of the function, to watch the recursive call sequence.

Upvotes: 0

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