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Lesson 3 of 8

Reuse progress across sorted sequences

Merge, sweep offline queries, and filter with forward-moving indices.

Understand the idea

When two inputs are sorted, compare their next unused items and advance the side you consume. A merge never needs to restart a pointer. For threshold queries, sort queries with their original indices and advance one array pointer as the thresholds increase.

Trace a small example

Merging [1, 4, 8] and [2, 4, 7] produces [1, 2, 4, 4, 7, 8]. For values [1, 3, 3, 8] and thresholds 3, 0, 5, an offline sweep answers 3, 0, 3 after restoring the original query order. Stable filtering instead uses a read index and a write index, preserving accepted items in order.

Conditions and cost

Merging costs O(n + m). An offline sweep costs O(n + q) after sorting, plus the sort costs. Sorting is inappropriate when the original adjacency matters, such as contiguous subarrays.

Pause & predict

What must accompany an offline query when queries are reordered?

Choose an answer
Try it yourself

Turn the idea into code

Count values ≤ each threshold 6, 2, 6 for the sorted array [2, 2, 5, 9].

Give me a hint

Equal queries can reuse the same pointer position.

Show the explained solution

The answers are 3, 2, 3. The pointer passes the two 2s, then 5, and never passes 9.

Your notes

Ready for the next idea?

Mark complete when you can explain it yourself.

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