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$ curl repovive.com/roadmaps/math-fundamentals/logarithms/power-implementation-the-code

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Power - Implementation (The code) - Logarithms | Math Fundamentals | Repovive

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Math Fundamentals18 sections · 842 units13h total

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Power - Implementation (The code)

Recursive solution

Here's the recursive solution:


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

The base case is $n = 0$ , which returns $1$ . For negative $n$ , you flip $x$ to $1/x$ and make $n$ positive. Then you halve $n$ at each recursive step, giving $O(\log n)$ time and $O(\log n)$ space for the call stack.