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Obvious algorithm on2 e d a c b f sweep line algorithm

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Unformatted text preview: y pair intersect? d e a c b f Line-segment intersection Given n line segments, does any pair intersect? Obvious algorithm: O(n2). e d a c b f Sweep-line algorithm • Sweep a vertical line from left to right (conceptually replacing x-coordinate with time). • Maintain dynamic set S of segments that intersect the sweep line, ordered (tentatively) by y-coordinate of intersection. • Order changes when • new segment is encountered, segment • existing segment finishes, or endpoints • two segments cross • Key event points are therefore segment endpoints. d aa acc abbb e d c b d c b e ed db bf e d a c b f e b d f b ee dd ff Sweep-line algorithm Process event points in order by sorting segment endpoints by x-coordinate and looping through: • For a left endpoint of segment s: • Add segment s to dynamic set S. • Check for intersection between s and its neighbors in S. • For a right endpoint of segment s: • Remove segment s from dynamic set S. • Check for intersection between the neighbors of s in S. Analysis Use red-black tree...
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