My first instinct was brute force, nested loops, O(n²), and I actually said that out loud which I think was fine.
Start by clarifying the problem constraints and edge cases, then propose a brute-force solution and optimize it using a single pass with a running minimum. Discuss time and space complexity trade-offs and potential further optimizations like early termination or parallelization.
Pro tip: Demonstrate awareness of real-world data by mentioning that ticket prices can fluctuate and that the algorithm should handle large arrays efficiently, perhaps by discussing streaming or distributed computation if the dataset is huge.
Confirm that departure day must be strictly before return day, arrays are 1-indexed or 0-indexed, and that we need the minimum sum of outbound[i] + return[j] with i < j. Discuss edge cases like empty arrays or no valid pair.
Propose checking all valid pairs (i, j) with i < j, computing the sum, and tracking the minimum. This takes O(n^2) time and O(1) space.
Iterate through the arrays once, maintaining the minimum outbound price seen so far. For each day j, compute min_outbound + return[j] and update the global minimum. This reduces time to O(n) and space to O(1).
Explain that the optimized solution is optimal for a single machine, but if the arrays are extremely large, consider parallelizing by splitting the array and combining results, or using a streaming approach if data arrives sequentially.
Mention handling of missing data, negative prices (if allowed), and the possibility of multiple trips. Also, note that the algorithm can be adapted to find the actual days, not just the cost.
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Clarify the definition of a strobogrammatic number and the allowed digits (0, 1, 6, 8, 9). Then present a recursive construction that builds numbers from the outside in, handling the no-leading-zero constraint. Finally, analyze time and space complexity and discuss edge cases like k=0, k=1, and even/odd k.
Pro tip: Mention that this is a classic strobogrammatic number problem and that the same recursive pattern can be adapted to find the k-th such number or count them, showing you understand the underlying structure beyond just generating all.
Define what 'look identical after 180-degree rotation' means: digits must map to valid digits (0→0, 1→1, 6→9, 8→8, 9→6) and the number must not have leading zeros. Confirm that k-digit numbers cannot start with 0.
Observe that a k-digit strobogrammatic number can be formed by placing a valid pair of digits at the ends and recursively constructing the inner (k-2)-digit number. For odd k, the middle digit must be one of 0, 1, or 8.
Implement a recursive function that builds numbers from the outside in. At each step, choose a valid pair (or single middle digit for odd length), ensuring the first digit is not 0. Collect results when the desired length is reached.
Time complexity is O(5^{k/2}) since each pair has up to 5 choices. Space complexity is O(k) for recursion depth plus output storage. Handle edge cases: k=0 (return empty list or ['']), k=1 (return ['0','1','8']), and ensure no leading zeros for k>1.
Mention iterative BFS/DFS alternatives, or how to generate only the k-th number without generating all. Also note that the same logic applies to counting strobogrammatic numbers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.