Three matrix algorithms, three walk orders – interactive animations
The article discusses three matrix algorithms and their respective walk orders for rotating a matrix. It explains the processes of rotating a matrix 90° clockwise, spiral traversal, and staircase search. Each method is accompanied by specific steps and common pitfalls to avoid during implementation.
- ▪The 90° clockwise rotation can be achieved by first transposing the matrix and then reversing each row.
- ▪Spiral traversal involves visiting every cell along the perimeter of a shrinking rectangle.
- ▪Staircase search is used when the matrix is monotone along both rows and columns, starting from a corner.
Opening excerpt (first ~120 words) tap to expand
/ library›matrixMatrix01 / The shared mechanismA matrix isn't a single sequence — it's a 2-D coordinate space where every cell is addressed by two indices that compose in specific ways. The job is finding the right walk order. Three classic sub-patterns: rotate by transpose-then-reverse, spiral by shrinking-boundary loops, and staircase search by walking from a corner where the answer is monotone in both directions.01Rotate in place02Spiral traversal03Staircase search02 / The one-sentence essenceA 90° clockwise rotation factors into transpose + reverse each row — two clean in-place passes whose composition is exactly the rotation, with no extra grid.animationcomplexity Problemrotate the matrix 90° clockwise, in placeM3×3?123456789Square matrix of size 3×3.
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Excerpt limited to ~120 words for fair-use compliance. The full article is at Algorhythm.