Capstone: Transpose and Combined Algorithms

Part of: 2D Array

Bringing It Together The transpose of a grid swaps its rows and columns: the cell at (r, c) in the original moves to (c, r) in the result. A grid with R rows and C columns transposes into one with C rows and R columns. Transposition is the ultimate rows vs. columns exercise because it forces you to track both index orders at once. Sizing the Result Correctly - The result has dimensions [numCols][numRows], new int[grid[0].length][grid.length]. - The assignment is t[c][r] = grid[r][c]; swapping the indices is the whole trick. Combining Standard Algorithms Real problems chain the patterns from this unit: - Traverse in row-major order to read the grid. - Use per-row or per-column accumulators for statistics. - Apply search-and-position to locate values. - Restructure with a transpose when the orientation must change. The Mental Model Every 2D-array task reduces to three questions: which cells do I visit (all, one row, one column), in what order (row-major or column-wise), and what do I do at each cell (sum, count, compare, copy). Transpose ties these together, you read row-major but write column-major. Master this and you can tackle any grid free-response on the AP exam.

Challenge: Transpose the Grid