Advanced Binary Search Patterns

Question 1

When should you use Binary Search on Answer?

Accepted Answer

When feasibility of a value changes monotonically — Binary Search on Answer works when you can check "Is X achievable?" and the answer changes from NO to YES (or vice versa) monotonically as X increases.

Question 2

'Binary search on the answer' searches over…

Accepted Answer

Over the space of possible answer values, via monotonic feasibility — Instead of searching positions, you binary-search the candidate answer range, testing each midpoint with a feasibility predicate that is monotonic in the answer.

Question 3

For 'binary search on the answer' to be valid, the feasibility function feasible(x) must be…

Accepted Answer

Monotonic: once true, it stays true as x increases — Monotonicity guarantees a single false→true boundary, which binary search can locate. Without it, halving the answer range is unjustified.

Question 4

In 'Koko Eating Bananas' (min eating speed to finish in h hours), the search space is…

Accepted Answer

Eating speeds up to max(pile), checked via a feasibility function — As speed increases, hours-needed decreases monotonically, so binary-search speed for the smallest value satisfying hours ≤ h. Cost O(n log(maxPile)).

Question 5

'Split Array Largest Sum' / 'Capacity to Ship Packages in D Days' minimize the maximum subarray sum by…

Accepted Answer

Binary searching the candidate max-sum, using a feasibility check — The candidate answer (a capacity) is monotonic: larger cap ⇒ fewer parts. Binary-search the smallest cap whose greedy split uses ≤ k parts — O(n log(sum)).

Question 6

Searching a target in a ROTATED sorted array (no duplicates) is O(log n) because…

Accepted Answer

One half stays sorted, so you pick the right side — Comparing a[lo], a[mid], a[hi] reveals which side is sorted; check whether the target lies within that sorted side's range to choose the half — halving each step.

Question 7

Finding the median of two sorted arrays in O(log(min(m,n))) uses…

Accepted Answer

A binary search for the correct partition point — Binary search the split of the smaller array; the other split is forced by the median position. Adjust until maxLeft ≤ minRight on both sides — O(log(min(m,n))).

Question 8

The overall complexity of binary search on the answer with an O(C) feasibility check over a range R is…

Accepted Answer

Reducing it to a combined cost of O(C · log R) total — You perform O(log R) iterations, each running the O(C) feasibility check — O(C·log R). Choosing a tight range and cheap check matters.

Question 9

'Aggressive Cows' / 'Magnetic Force' (maximize the minimum gap) binary-searches the answer and uses feasible(d) =…

Accepted Answer

Placing all cows so every pair is at least d apart — Larger minimum-distance d is harder to satisfy (monotonic), so binary-search the largest d for which a greedy placement fits all cows — maximize-the-minimum pattern.

Question 10

For maximize-the-minimum problems, you search for the…

Accepted Answer

The largest value that remains feasible — Feasibility is true for small thresholds and false once too large; you want the boundary's largest true value. Minimize-the-maximum is the mirror image.

Advanced Binary Search Patterns

Binary search on the answer

Test your knowledge

When should you use Binary Search on Answer?

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Koko Eating Bananas

Example Cases

The short version

In more depth

Binary Search on Answer Space

When to reach for this

Interview Questions

References & Further Reading

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