Summing Rows and Columns of a Grid

A grid is just an array of arrays, rows nested inside an outer array. To sum one row, you walk across its columns adding each value into an accumulator. To get a separate total for every row, that accumulator has to start over at 0 each time you move to a new row. That means the reset line goes inside the outer loop, right before the inner loop starts, so each pass through a row begins collecting from scratch instead of carrying over what came before.

A grand total works differently: you want everything added together, so the accumulator resets once, before the outer loop even begins, and never resets again. Row sums and grand totals use the same nested-loop skeleton; the only difference is where the reset line sits. Column sums flip the structure: now the outer loop must step through columns and the inner loop through rows, because a column cuts across every row at the same index. Whichever direction you're summing becomes the outer loop, with its accumulator reset there, while the other direction becomes the inner loop doing the adding.

This topic is the natural follow-up to nested loop traversal of 2D arrays: once you can visit every element in the right order, summing rows and columns is just deciding when to zero out the accumulator. It sets up later work like finding row or column maximums and totals used in matrix-style problems, all of which depend on this same reset-placement logic.