Set Intersection Size At Least Two

HardGreedygreedy

Solve this the way you would in the interview: out loud, on a timer, with an AI interviewer asking follow-ups while you code. You get a scored report at the end.

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Problem

You are given a list of closed integer intervals, intervals[i] = [start, end] with start < end, each representing the integers from start to end inclusive. Find a set of integers S such that **every** interval contains at least **two** elements of S. Return the minimum possible size of S. Aim for O(n log n) time.

Examples

Input: intervals = [[1,3],[3,7],[8,9]]
Output: 5
S = {2, 3, 4, 8, 9} works: [1,3] holds 2 and 3, [3,7] holds 3 and 4, [8,9] holds 8 and 9. Four numbers are not enough.
Input: intervals = [[1,3],[1,4],[2,5],[3,5]]
Output: 3
S = {2, 3, 4} puts two numbers in every interval.
Input: intervals = [[1,2],[2,3],[2,4],[4,5]]
Output: 5
S = {1, 2, 3, 4, 5} is needed; for instance [1,2] and [4,5] share nothing with each other.

Constraints

  • 1 <= intervals.length <= 3000
  • intervals[i].length == 2
  • 0 <= start < end <= 10^8

What the interviewer grades

A correct solution is one of five scores. The report also grades problem understanding (did you clarify inputs and edge cases before coding), problem solving, communication while you work, code quality, and testing. See a sample report, or read up on the pattern in the lessons.

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