#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/math-fundamentals/exponents-roots/power-implementation

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░███████████████████████████████████████████████████████████████████████████████████

#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/math-fundamentals/exponents-roots/power-implementation

Repovive

Power - Implementation - Exponents & Roots | Math Fundamentals | Repovive

Repovive.

Math Fundamentals18 sections · 842 units13h total

Open in Course

Power - Implementation

Fast exponentiation

Here's the full solution using recursion:


function pow(x, n)
    if n = 0 then
        return 1
    if n < 0 then
        return 1 / pow(x, -n)
    if n is even then
        half := pow(x, n / 2)
        return half * half
    else
        return x * pow(x, n - 1)

The recursion depth is $O(\log n)$ because you halve $n$ at each step. Total time: $O(\log n)$ . Space: $O(\log n)$ for the call stack.