Iterative function for pow(x, y)

Given two integers x and y, compute x^y efficiently. The approach should run in O(log y) time complexity and use O(1) auxiliary space.

Examples:

Input: x = 3, y = 19
Output: 1162261467
Explanation: 3¹⁹ = 1162261467

Input: x = 2, y = 5
Output: 32
Explanation: 2⁵ = 32

Binary Exponentiation - O(log y) Time and O(1) Space

Instead of multiplying x repeatedly y times, we use the binary representation of y to make the computation faster. Every number can be written as the sum of powers of 2, so we only need to consider those powers where the binary bit is 1.

We traverse through all the bits of y from LSB to MSB.

• If the current bit is 1, we multiply our answer with x.
• If the current bit is 0, we ignore it.
• At every step, we square x (to get the next power) and divide y by 2 to move to the next bit.

1162261467