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I knew this was binary search pretty quickly, the monotonic property is obvious once you think about it.
Recognize that the answer lies between 1 and the maximum pile size, and that feasibility is monotonic: if speed k works, any larger speed also works. Use binary search on k, and for each candidate speed, compute the total hours required by summing ceil(pile/k) for all piles, checking if it's within the limit.
Pro tip: Mention that the lower bound can be tightened to ceil(total_items / max_hours) to reduce the search space, and always discuss integer overflow and edge cases like empty piles or hours less than number of piles.
Confirm that each hour you can process at most k items from one pile, and that you cannot split work across piles in the same hour. Ask about input size, value ranges, and whether k must be an integer.
For a given speed k, compute the total hours needed as sum(ceil(pile / k)). The speed is feasible if this sum is <= max_hours.
Explain that if speed k is feasible, any speed > k is also feasible. Therefore, binary search on the answer between 1 and max(piles).
Set low = 1 (or ceil(total/max_hours)) and high = max(piles). While low < high, compute mid, check feasibility, and adjust bounds accordingly. Return low.
Time complexity is O(n log(max(pile))), space O(1). Test cases: single pile, hours equal to number of piles, very large piles, and hours less than number of piles (impossible).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Classic problem but I kept second-guessing my index math.
Use a digit-by-digit multiplication approach, simulating the manual multiplication process with an array to store intermediate results. Iterate through each digit of the second number and multiply it with each digit of the first number, accumulating results with proper carry handling. Finally, convert the array to a string, removing leading zeros.
Pro tip: Clarify constraints upfront (e.g., maximum length, leading zeros) and discuss trade-offs between time and space complexity. Mention that you can optimize by using a single array and processing from right to left to avoid extra space.
Ask about input constraints (max length, leading zeros, empty strings) and expected output format. Confirm that built-in big integer conversion is not allowed.
Explain the schoolbook multiplication method: use an array of size m+n to store intermediate sums, iterate over digits from right to left, and handle carries.
Write code that converts characters to digits, performs nested loops, updates the result array, and manages carries. Ensure no built-in numeric conversion of the full strings.
Test with zeros, single-digit numbers, and large inputs. Discuss potential optimizations like using a single array or early termination for zeros.
State time complexity O(m*n) and space O(m+n). Mention alternative algorithms (e.g., Karatsuba) and when they might be beneficial.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.