Array Indexing Simulation | mysimulator.uk

2D → 1D Layout

Columns (width) 8

Rows (height) 5

Binary Search (on memory strip)

Target index value 17

index = row·W + col (row-major)

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mid

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Comparisons

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How it works

A 2D array has no real shape in memory — it is a flat, contiguous 1D block, and every (row, col) pair is converted to a single offset by an indexing formula. In row-major layout (used by JavaScript, C, Python's NumPy default) that formula is index = row·W + col, so a whole row sits next to itself in memory. In column-major layout (Fortran, MATLAB, column-major NumPy) it flips to index = col·H + row. The upper grid highlights this: walking the grid left-to-right, top-to-bottom lights up the memory strip below it either sequentially (cheap, cache-friendly) or in long strides (expensive — each jump can miss the CPU cache entirely).

row-major:    index = row*W + col
column-major: index = col*H + row
binary search: mid = lo + ((hi - lo) >> 1)
               if strip[mid] == target: found
               elif strip[mid] < target: lo = mid + 1
               else: hi = mid - 1

Columns / Rows — the grid's dimensions W and H; the memory strip always holds exactly W·H cells, since the array's total size never depends on its shape.
Layout toggle — switches the index formula and replays the sweep, so you can compare which traversal order stays sequential in memory for the same grid.
Target / Step / Play — runs classic binary search over the strip (its values equal their own index, so it is sorted by construction); each step halves the search window using integer index arithmetic on lo/mid/hi.

Real-world relevance: row- vs column-major mismatches are a classic source of slow code — iterating a large matrix in the "wrong" order for its storage layout can be an order of magnitude slower purely from cache misses, and binary search's O(log n) index arithmetic is why sorted arrays outperform linear scans at scale.

Grid cell / memory cell Sweep cursor Binary search: lo–hi window Binary search: mid

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