Reshape the Matrix

Core idea: A 2D grid is secretly a 1D array laid down row by row. Number the cells 0, 1, 2, … in reading order — that's the flat index k. Then (row, col) and k are two views of the same thing: k = row·cols + col, and going back, row = k // cols, col = k % cols. Reshaping is just reading cells out at the old width and writing them back at the new width — no values change, only how you slice the stream.

1. The problem, in a fresh setting

You're handed a strip of photo thumbnails that a gallery exported as a grid: m rows of n images each, stored top-to-bottom, left-to-right. The print shop wants the same photos in the same order but laid out on a different page — r rows of c images. Nothing is added, removed, or reordered; the sequence is identical. You're only rewrapping the stream at a new line width.

That works only if the totals line up: an m × n grid holds m·n photos, and the new layout has room for exactly r·c. If m·n == r·c, refill the new grid in reading order. If they don't match, the reshape is impossible — hand back the original grid untouched.

The third row is the trap: 2·2 = 4 but 2·4 = 8. The cells can't fill a 2×4 grid, so we return the input as-is.