What is binary search on the answer?

Q: What is binary search on the answer?

# Binary Search on the Answer (Python) **Target Audience:** Learners who know basic binary search and want to apply it to optimisation problems. **Difficulty:** Medium **Language:** Python 3 > **How to read this doc:** Every idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the exact word an interviewer expects. All code is Python, and every output block was produced by actually running the programs (Python 3.13.16); nothing is quoted from memory. ## 1. Why This Even Matters — A Story First A bakery must deliver 10 trays of bread, in a fixed order, within 5 days, using one van that makes one trip a day. Vans come in every capacity from "one tray" upward; bigger vans cost more. What is the **smallest** capacity that still gets everything delivered in 5 days? You could try capacity 1, then 2, then 3, ... and stop at the first one that works. But notice something: if a capacity-15 van can do it, a capacity-16 van can certainly do it to

The problem

Question presented to candidate: "What does "binary search on the answer" mean? Show me how you would use it to find the minimum eating speed in the Koko bananas problem, and code it in Python."

What a strong answer should cover:

Searching the range of possible answers, not an array, with a yes/no feasible(x) check.
The requirement: the check is monotonic, with a one-sentence reason (faster speed never needs more hours).
Correct bounds (lo = 1, hi = max pile for Koko) and the right template: "first true" with hi = mid, or "last true" with a rounded-up midpoint.
Complexity O(n log M) for Koko, versus O(n × M) for trying every speed.
Python specifics: exact ceiling division with (p + k - 1) // k, and that big integers make overflow a non-issue (so the focus is on the template).
Recognises other instances: ship within D days, split array largest sum, maximise the minimum distance, integer square root.

Clarifying questions expected:

What are the limits on the pile sizes and the number of hours?
Is there always a valid answer (at least one hour per pile)?

Code / implementation expected: Yes — a Python feasible helper plus the binary search loop over the answer range.

binary-search
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Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

Stuck? Get a hint.

A short nudge toward the approach. It will not give the answer away.

Solution

Binary Search on the Answer (Python)

Target Audience: Learners who know basic binary search and want to apply it to optimisation problems. Difficulty: Medium Language: Python 3

How to read this doc: Every idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the exact word an interviewer expects. All code is Python, and every output block was produced by actually running the programs (Python 3.13.16); nothing is quoted from memory.

1. Why This Even Matters — A Story First

A bakery must deliver 10 trays of bread, in a fixed order, within 5 days, using one van that makes one trip a day. Vans come in every capacity from "one tray" upward; bigger vans cost more. What is the smallest capacity that still gets everything delivered in 5 days?

You could try capacity 1, then 2, then 3, ... and stop at the first one that w

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9 min read · 13 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonKoko eating bananas: binary vs linear search over speeds

Practice

PythonShip within D days and integer square root

Practice

PythonReal-valued answers: halving a fixed number of times

Practice

Discussion

Other approaches, follow-ups and how it went in real interviews.

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