Implement exponentiation and link tree neighbors
Overview
This question evaluates numerical algorithm implementation and in-place tree traversal skills, specifically fast exponentiation with careful edge-case and precision handling and iterative linking of next pointers in a perfect binary tree.
Solve two independent tasks.
Task A — Fast exponentiation: Implement fastExponent(x, n) that returns x raised to the integer power n, where x is a double and n is a 32-bit signed integer. Requirements: O(log |n|) time via exponentiation by squaring; O(
- extra space with an iterative approach; correctly handle negative exponents, n == Integer.MIN_VALUE, and edge cases such as x == 0 or x == ±1. Return a double; a relative error up to 1e-10 is acceptable.
Task B — Link neighbors in a perfect binary tree: Given the root of a perfect binary tree whose nodes have fields (val, left, right, next), set each node’s next pointer to its immediate right neighbor on the same level; if none, set it to null. Constraints: O(n) time, O(
- extra space, and do not use recursion. Afterward, each level should be traversable using next pointers starting from its leftmost node.