Learning pathOriginal reference
Lesson 8 of 8

Prove the checker before searching

Connect greedy scans, capped arithmetic, and two-pointer counts to answer search.

Understand the idea

For nonnegative sequence partitioning, greedily extend each segment while its sum fits a capacity; starting a new segment only when necessary minimizes the number of segments for that capacity. For maximum minimum spacing, placing the next item at the earliest valid position leaves at least as much room for later placements.

Trace a small example

Partition [7, 2, 5, 10, 8] into at most two contiguous groups. Capacity 17 needs three groups, but 18 allows [7, 2, 5] and [10, 8]. For kth pair distance, sort first, count pairs with distance ≤ d using two pointers, and search the smallest d whose count reaches k.

Conditions and cost

The partition proof depends on nonnegative values. Count duplicate positions as distinct pairs. Saturate a count once it reaches the required threshold instead of overflowing. Include the O(n) checker and initial sorting in total complexity.

Pause & predict

What makes an answer search correct besides a correct binary-search loop?

Choose an answer
Try it yourself

Turn the idea into code

Place 3 items among sorted coordinates [1, 2, 4, 8, 9] to maximize the minimum gap.

Give me a hint

Try gaps 3 and 4 using the earliest possible placement.

Show the explained solution

Gap 3 works with 1, 4, 8. Gap 4 places 1 and 8 but cannot place a third, so the optimum is 3.

Your notes

Ready for the next idea?

Mark complete when you can explain it yourself.

From a problem to a programIdentify the input, output, and constraints, then translate a small plan into C++.Variables, types, and remembered valuesChoose a representation, initialize it, and understand what assignment really changes.Arithmetic without surprisesPredict division and remainder, widen before multiplication, and format decimal answers.Conditions and logical decisionsBuild exclusive categories, combine comparisons, and protect operations with short-circuit logic.Optional: other ways to chooseRecognize switch for exact choices and the conditional operator for choosing a value.For loops: make repetition preciseTrace initialization, condition, body, and update—and avoid an extra iteration.While, do-while, and stopping rulesChoose a loop from its stopping condition and read the exact input format.Break, continue, and early answersDistinguish leaving a loop from skipping one iteration, without losing required input.Five patterns worth understandingUse sums, counts, best-so-far candidates, products, and flags to process a stream.Nested loops: rows and columnsTranslate a shape into two loop roles and count the total work.Take a number apart, one digit at a timeUse remainder and division to process decimal digits, including zero.Multiple cases and a debugging mindsetCombine the patterns, isolate each case, and test the boundaries that can break your idea.Arrays: give every value a placeUnderstand indices, initialization, capacity, active length, and the first safe array loop.Scan, count, search, and compareDistinguish values from positions and preserve the exact tie rule a problem asks for.Change a sequence without losing itUpdate, copy, compare, reverse, and inspect neighbours using the correct bounds.Matrices: think in two coordinatesTraverse tables, total rows and columns, inspect diagonals, and protect grid neighbours.Characters become stringsSeparate characters from numbers, then safely inspect and edit managed text.Read the text the problem actually givesChoose words or full lines, preserve empty cases, and reset only the state that needs it.Scan text: count, filter, transformBuild a result from matching characters without losing leading zeros or skipping shifted text.Join, compare, and find textLearn content comparison, lexicographical order, substring counts, and the not-found sentinel.