Math & Geometry

Overview

Math & Geometry is a grab-bag of problems where the algorithmic insight is often a specific math identity or matrix trick rather than a general pattern. Common techniques:

• In-place matrix operations: rotate via transpose + reverse; spiral walking with boundary shrinking.
• Cycle detection on digit sequences: Happy Number (Floyd’s tortoise and hare).
• Fast exponentiation: Pow(x, n) by squaring.
• Big-integer arithmetic on strings / grids: Multiply Strings, Plus One.
• Counting point configurations: Detect Squares.

Problems

1. 48. Rotate Image (Medium)
2. 54. Spiral Matrix (Medium)
3. 73. Set Matrix Zeroes (Medium)
4. 202. Happy Number (Easy)
5. 66. Plus One (Easy)
6. 50. Pow(x, n) (Medium)
7. 43. Multiply Strings (Medium)
8. 2013. Detect Squares (Medium)

Key patterns unlocked here

• Transpose + row-reverse: Rotate Image.
• Boundary-shrinking traversal: Spiral Matrix.
• Using first row/column as markers: Set Matrix Zeroes ($O(1)$ space).
• Floyd’s on numeric sequence: Happy Number.
• Digit-by-digit carry: Plus One.
• Exponentiation by squaring: Pow(x, n).
• Schoolbook multiplication on digit arrays: Multiply Strings.
• Point counting with hash map: Detect Squares.