Nth Root via Binary Search | Dataford Interview Questions

Swiggy delivery and pricing services may need approximate roots when evaluating geometric scaling factors. Given a nonnegative number x and a positive integer n, compute the real value r such that r^n = x within an absolute error of 1e-7.

Implement the function using binary search. Do not use a built-in root, logarithm, or exponentiation function to directly calculate the answer.

Formal Specification

Input: A floating-point number x and a positive integer n.
Output: A floating-point approximation of x^(1/n).
The returned value is accepted when abs(result - x^(1/n)) <= 1e-7.
You may assume x >= 0 and n >= 1.

Constraints

0 <= x <= 10^18
1 <= n <= 100
The result must have absolute error at most 1e-7
Only nonnegative x values are provided

Function Signature

def nth_root(x, n):

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