Power of Three

Given an integer num, write a method to determine if it is a power of 3.

The method will be called as follows:

console.log(powerOfThree(9));
// true

console.log(powerOfThree(7));
// false

Constraints

• The given would be a non zero positive integer in the range between 1 and 2147483647
• Expected space complexity : O(logn)
• Expected time complexity : O(1)

```js
function powerOfThree(num) {
  // Fill in this method
  return num;
}

```

In the expression 3^6 what does the ^6 stand for?

What is a loop in programming terminology?

In programming, the while-loop can be considered as a repeating _____ statement.

Identify the correct exponential expression for the integer 729.

In programming, the exponential value of a number cannot be determined without loops.

The easiest way to go about this is to think about how exponents work. When you see 3^6, you are multiplying 3 by 3 exactly 6 times.

With that said, we can simply reverse the direction: we can take the result, and continuously divide it by 3. If we eventually get to 1, we know that it's been divisible all along and is thus an exponent of 3.

Complexity of Final Solution

Since we are dividing by 3 for every iteration in the while loop, we find our answer after roughly log3(n) (base 3) iterations for O(logn) time complexity. We do not use any additional data structures, so we use O(1) constant space.

One Pager Cheat Sheet

• Write a method powerOfThree which determines if a given non zero positive integer num between 1 and 2147483647 is a power of 3, with an expected space complexity of O(logn) and an expected time complexity of O(1).
• The ^6 in 3^6 stands for the exponent calculated using the formula base^exponent = result.
• Loops are a useful control structure in programming used to repeat certain code multiple times, saving the developer time when dealing with large data sets or unknown iterations.
• The while-loop can be considered as a repeating IF-statement because it needs an initial evaluation of the condition before continuing to repeat a certain set of instructions as long as the condition is true.
• The number 729 can be expressed using exponential notation as 3^6, since it is the result of raising 3 to the 6th power.
• The exponential value of any number can be calculated without loops, simply by raising that number to the power of itself.
• We can solve this problem in O(logn) time complexity and O(1) space complexity by continuously dividing the number by 3.