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Problems

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Geometry

Geometry primitives

Cross product for orientation, segment intersection, convex hull.

Quiz (10) Spot the pattern
Notes
  • Cross product: cross(o, a, b) = (a.x - o.x)*(b.y - o.y) - (a.y - o.y)*(b.x - o.x). Positive means a left turn (counter-clockwise), 0 means collinear.
  • Segment intersection: use orientation tests plus a collinear/on-segment special case.
  • Convex hull (monotone chain): sort the points and build the lower and upper hulls, popping while the turn is not left. O(n log n).
  • Max points on a line: for each anchor point, count normalized slopes (dy/g, dx/g) with the sign fixed.

Gotchas: use integer arithmetic when possible, since floats and slopes cause precision bugs.

5 problems

Advanced & competitive

Geometry Cross products, orientation, polygons.

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