The core squaring logic came to me pretty fast but I fumbled on the edge cases.
Start by clarifying the problem constraints and edge cases, then explain the iterative binary exponentiation algorithm using bit manipulation. Emphasize how handling negative exponents and the minimum 32-bit integer requires careful type casting and overflow prevention.
Pro tip: Mention that converting n to a 64-bit integer before negation avoids overflow when n is INT_MIN, and use a long long for the exponent to safely handle the negation.
Ask about input types (integer, float?), expected output precision, and constraints. Identify edge cases: n=0, x=0, negative n, and n = INT_MIN.
Describe how to repeatedly square the base and halve the exponent, multiplying the result when the current exponent bit is 1. This achieves O(log n) time.
For negative n, compute x^(-n) as 1/(x^n). To avoid overflow when n = INT_MIN, cast n to a 64-bit integer before negation.
Use double for the base and result to handle fractional values, and long long for the exponent to safely negate INT_MIN. Write clean, iterative code with a while loop.
Walk through examples: x=2, n=10; x=2, n=-2; x=0, n=0; x=1, n=INT_MIN. Confirm O(log n) time and O(1) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I knew the recursive version cold so having to go iterative without a queue tripped me up for a bit.
Use the already-established next pointers of the current level to traverse and set the next pointers of the next level. Start with the root, and for each level, iterate through nodes using next pointers, linking the children of adjacent nodes. This achieves O(1) space and no recursion.
Pro tip: Emphasize that the algorithm leverages the next pointers of the current level to avoid any additional data structures, and mention that it works because the tree is perfect, ensuring all nodes have both children.
Set a pointer to the root as the leftmost node of the current level.
While the current node exists, connect its left child's next to its right child, and if the current node has a next, connect its right child's next to the next node's left child.
Advance the current node to its next pointer.
After finishing the current level, set the level start to its left child and repeat until the level start is null.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.