Geometry Summary Resource

Geometry Summary Resource - aloalgo

A quick reference for geometry patterns in top interview problems.

Geometry problems are rare in typical interviews. The most common patterns are: K Closest Points (distance + heap), Rectangle Overlap (coordinate comparison), Valid Square (distance validation), and Rotate Image (matrix manipulation).

Concept	Formula	Use Case
Euclidean Distance	sqrt((x2-x1)² + (y2-y1)²)	Actual distance between points
Squared Distance	(x2-x1)² + (y2-y1)²	Comparing distances (faster)
Manhattan Distance	\|x2-x1\| + \|y2-y1\|	Grid movement (no diagonals)

Use squared distance with a max-heap of size K. Time: O(n log k).

Check if projections overlap on both axes. Easier to check no-overlap conditions and negate.

Calculate all 6 pairwise distances. Valid square has 4 equal sides, 2 equal diagonals, and diagonal² = 2 × side².

Rotate 90° clockwise = transpose + reverse each row. Time: O(n²), Space: O(1).

Avoid sqrt: Use squared distance when comparing distances
K Closest: Max-heap of size K beats sorting for large inputs
Rectangle overlap: Think in terms of "when do they NOT overlap"
Valid square: 6 distances = 4 sides + 2 diagonals
Matrix rotation: Clockwise = transpose + reverse rows

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Study plan All problems

Resources Cheat Sheet DSA Glossary

Geometry Summary

Key Formulas

K Closest Points to Origin

Rectangle Overlap

Valid Square

Rotate Image (Matrix Rotation)

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