Virtual 1D index for 2D coordinates

Ashwini Gaddagi

Sep 29, 2025 — 1 min read

Understanding Virtual 1D index → 2D coordinates:

How does this formula work?
row = index / n
col = index % n

Mapping 1D to 2D

Imagine you have a bookshelf with 4 shelves (rows), and each shelf holds 3 books (columns).

Shelf 0: [Book0] [Book1] [Book2]
Shelf 1: [Book3] [Book4] [Book5]
Shelf 2: [Book6] [Book7] [Book8]
Shelf 3: [Book9] [Book10] [Book11]

If someone says "Give me book number 7", how do you find it?

Why Division (`/`) for Row?

Division tells you "How many COMPLETE rows can I fill?"

Book index = 7
Books per row = 3

How many complete rows before book 7?
7 / 3 = 2 (integer division)

This means: book 7 is in row 2 (the 3rd row)

Why Modulo (`%`) for Column?

Modulo tells you "What's the POSITION within the current row?"

Book index = 7
Books per row = 3

Position within the row?
7 % 3 = 1

This means: book 7 is at column 1 (the 2nd position in its row)

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