Finding a Value and Its Neighbors in a Grid

A 2D array is really an array of arrays, so there is no shortcut that lets you jump straight to a value. You sweep it the same way you'd read a page: row by row, and within each row, column by column. A nested loop handles this naturally, the outer loop walking down the rows and the inner loop walking across each row's columns. Once you find the target, you can break out of both loops immediately since there is no reason to keep checking cells you already know don't matter.

Once you have the row r and column c of a found cell, its orthogonal neighbors sit at four fixed offsets: one row up [r-1][c], one row down [r+1][c], one column left [r][c-1], and one column right [r][c+1]. These are the cells sharing an edge with it, not the diagonal ones. This is just arithmetic on the indices, no second search needed.

The complication shows up at the edges. A cell in row 0 has no row above it, and a cell in the last column has no column to its right, so blindly computing r-1 or c+1 can produce an index that doesn't exist in the array. Every neighbor-finding algorithm needs an if-check confirming the candidate row and column both fall between 0 and the array's last valid index before touching that cell. This bounds-checking habit carries straight into the next topics on traversing grids and recursive searches, where the same off-the-edge mistake is the usual bug.