List all overlapping intervals efficiently

Question

Let T be a given interval tree (of size n) and i be an interval. Let k be the number of intervals in T that overlap i. I need to find an algorithm to list all of them in time O(min(n, k log n)).

There is only one interval `i`? If there is only one interval, a simple O(n) algo should work, what is the difficulty? — Pham Trung, Mar 14 '18 at 06:41

score 0 · Answer 1 · answered Mar 14 '18 at 08:34

Generally, you just need to traverse the tree and stop whenever you got k overlapping intervals.
Lets mark the range you are currently checking by t, then you will need to check t against i as follows.
The first interval is t and the second is your i.

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Add t and you can stop iterating.

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Add t and go both left and right.

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  |---|

Add t and go only left

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Add t and go only right

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Go left (without adding t)

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Go right (without adding t)

List all overlapping intervals efficiently

1 Answers1