javascript-algorithms/src/algorithms/math/compute-power/README.md

Power(a,b)

This computes power of (a,b) eg: power(2,3) = 8 power(10,0) = 1

The algorithm uses divide and conquer approach to compute power. Currently the algorithm work for two positive integers X and Y Lets say there are two numbers X and Y. At each step of the algorithm:

1. if Y is even then power(X, Y/2) * power(X, Y/2) is computed
2. if Y is odd
   then X * power(X, Y/2) * power(X, Y/2) is computed

At each step since power(X,Y/2) is called twice, this is optimised by saving the result of power(X, Y/2) in a variable (lets say res). And then res is multiplied by self.

Illustration through example power (2,5)

• 2 * power(2,2) * power(2,2) power(2,2)
  • power(2,1) * power(2,1) power(2,1)
    • return 2

Going up the tree once the end values are computed power(2,1) = 2 power(2,2) = power(2,1) * power(2,1) = 2 * 2 = 4
power(2,5) = 2 * power(2,2) * power(2,2) = 2 * 4 * 4 = 32

Complexity relation: T(n) = T(n/2) + 1

Time complexity of the algorithm: O(logn)