I went straight to XOR and they seemed okay with that direction, but then they asked me to also handle out-of-range values and duplicates explicitly and I fumbled a bit.
Use the array itself as a hash map by cyclically placing each element at its correct index (value equals index). After placement, verify that every element is in its correct position. This achieves O(n) time and O(1) extra space without sorting or hash sets.
Pro tip: Emphasize that the in-place cyclic sort approach modifies the input, so clarify whether the array can be mutated; if not, discuss the trade-off of using O(n) extra space or a different method. Also, mention that early termination during placement can optimize for non-permutations.
Confirm that the array can be modified in-place and discuss edge cases like n=0, n=1, duplicates, and out-of-range values.
Iterate through the array; for each index i, while the element at i is within [0, n-1] and not already at its correct position, swap it with the element at its target index.
After placement, check that for every index i, the element equals i. If any mismatch, it's not a permutation.
Argue that each element is swapped at most once, so total swaps are O(n), and no extra space is used beyond a few variables.
Mention that this modifies the input; if modification is not allowed, consider using the sign bit or other in-place marking techniques, but note they may not work for all cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Classic fast exponentiation, I've done this before.
Start by clarifying requirements and edge cases, then explain the binary exponentiation (exponentiation by squaring) algorithm that achieves O(log |exp|) time. Walk through handling negative exponents, zero base/exponent, and the overflow issue with the minimum 32-bit integer exponent, and finally discuss trade-offs and potential optimizations.
Pro tip: Mention that converting the exponent to a long or using unsigned arithmetic avoids overflow when negating INT_MIN, and note that iterative binary exponentiation is often preferred in production for its constant space and simplicity.
Ask about input types (integer vs floating-point base), expected output precision, and confirm that the exponent is a 32-bit signed integer. Identify edge cases: exp = 0, base = 0, negative exponents, and exp = INT_MIN.
Describe binary exponentiation (exponentiation by squaring): repeatedly square the base and halve the exponent, multiplying the result when the current exponent bit is 1. This yields O(log |exp|) time.
For negative exponents, compute the positive power and take the reciprocal. To avoid overflow when negating INT_MIN, convert the exponent to a 64-bit integer (e.g., long) or use unsigned arithmetic before negation.
Write clean code (iterative or recursive) with proper handling of edge cases. Test with cases like exp=0, base=0, negative exponents, and exp=INT_MIN to ensure correctness and no overflow.
Compare iterative vs recursive implementations (space vs readability), and mention potential optimizations like early termination for base 0 or 1, and handling floating-point precision if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.