Solve Banana Speed and Interval Merge

During two technical phone screens for a new graduate software engineering role, the candidate was asked to solve two coding problems: minimum eating speed and merging overlapping intervals.

Constraints & Assumptions

• Provide clear algorithms, correctness reasoning, complexity, and edge cases.
• For minimum eating speed, each hour can be spent on only one pile.
• For interval merging, intervals overlap when the next start is less than or equal to the current merged end.
• Use sorted or binary-search approaches where appropriate.

Clarifying Questions to Ask

• Are piles and h always positive?
• Is h at least the number of piles?
• Are interval endpoints inclusive?
• Can intervals be empty or unsorted?

Part 1 - Minimum Eating Speed

Given piles and h, return the minimum integer speed k such that all piles can be eaten within h hours.

What This Part Should Cover

• Binary search on answer from 1 to max(piles).
• Feasibility function using sum of ceil(pile / k).
• Why feasibility is monotonic.
• Complexity and edge cases.

Part 2 - Merge Overlapping Intervals

Given intervals [start, end], merge all overlapping intervals and return non-overlapping intervals sorted by start.

What This Part Should Cover

• Sort by start.
• Maintain current merged interval.
• Extend on overlap, otherwise append and start a new interval.
• Complexity and edge cases.