Start by clarifying the problem and edge cases, then propose a one-pass greedy algorithm that tracks the minimum price seen so far and computes the maximum profit at each step. Explain the algorithm clearly, walk through a small example, and analyze time and space complexity.
Pro tip: Mention that this is a classic problem with a known optimal solution, and relate it to real-world applications like trading or feature engineering for financial ML models, showing you understand the broader context.
Confirm that you can buy and sell only once, that you must buy before selling, and that you should return 0 if no profit is possible. Ask about edge cases like empty array or single element.
Briefly mention that a brute-force solution would check all pairs of buy and sell days, which is O(n^2) time. This shows you understand the naive solution before optimizing.
Describe maintaining two variables: min_price (the lowest price seen so far) and max_profit (the maximum profit found). Iterate through the array once, updating min_price and then max_profit.
Use a small array like [7,1,5,3,6,4] to demonstrate how the algorithm works step by step, showing how min_price and max_profit evolve.
State that time complexity is O(n) because of a single pass, and space complexity is O(1) since only two variables are used. Mention handling of decreasing prices (profit 0) and empty arrays.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Recognize that the minimum eating speed can be found using binary search on the answer space from 1 to max(piles). For a given speed, simulate the eating process by summing the hours needed for each pile (ceil(pile/speed)) and check if the total is within the time limit. Return the smallest speed that works.
Pro tip: Mention that the time complexity is O(n log m) where n is the number of piles and m is the maximum pile size, and emphasize that this is optimal because the feasibility check is monotonic. Also, note that using integer division with ceiling can be done efficiently as (pile + speed - 1) // speed.
Restate the problem to ensure understanding: given piles of bananas and h hours, find the minimum integer speed k such that the monkey can eat all bananas within h hours, eating from only one pile per hour.
For a given speed k, compute the total hours required as sum(ceil(pile/k) for pile in piles). If total hours <= h, then speed k is feasible.
The minimum possible speed is 1 (if h is large enough), and the maximum needed speed is max(piles) (if h equals the number of piles). Set low=1, high=max(piles).
While low < high, compute mid = (low + high) // 2. If feasible(mid), set high = mid; else set low = mid + 1. At the end, low is the minimum feasible speed.
Time complexity: O(n log m) where n is number of piles and m is max pile size. Space complexity: O(1). Handle edge cases: h < number of piles (impossible? but problem guarantees h >= piles.length), and large values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.