Transpose and rotate
To transpose a grid, swap rows and columns: the result's cell [c][r] is the original's [r][c]. An R-row, C-column grid becomes C rows by R columns.
To rotate a quarter turn clockwise, the old left column, read bottom to top, becomes the new top row: new[i][j] = old[R - 1 - j][i]. Four turns return the original, so use k % 4.
Both are easiest as new grids: build every row as a fresh list and leave the input alone. An in place rotation is only possible when the grid is square (R = C), because a non-square grid changes shape.
Two traps: [[0] * 3] * 2 makes two names for the same row, so changing one changes both. And rows are lists, so new = old or old[:] still shares the rows.
Watch the visual: the mirror has its own rows, so changing it leaves the original alone.
See it run
grid = [[1, 2, 3], [4, 5, 6]] mirror = [] for row in grid: mirror.append(row[::-1]) mirror[0][0] = 9 print(grid[0][0], mirror[0][0])
We build a mirrored copy, one reversed row at a time.
Practice transpose and rotate
Exercise 1
A seating chart lists the seats row by row: chart[r][c] is the name in row r (front row first), seat c (left seat first). The ushers want it listed by aisle instead: seat 0 of every row first, then seat 1 of every row, and so on.
Return a new grid out where out[c][r] is chart[r][c]. (This is the transpose: rows become columns.)
Rules:
- The chart is rectangular, with at least 1 row and 1 seat. With R rows and C seats, the result has C rows and R seats.
- Build and return a new grid;
chartis left unchanged.
Constraints: 1 ≤ R, C ≤ 100.
Example: solution([["Ann", "Bo"], ["Cy", "Di"], ["Ed", "Flo"]]) returns [["Ann", "Cy", "Ed"], ["Bo", "Di", "Flo"]].
Exercise 2
A ticker board is a grid of symbols. Row r (row 0 is the top) is rotated to the right by r × step cells: symbols pushed off the right end re-enter at the left, in the same order.
Return the rotated board as a new grid.
Rules:
stepmay be 0, negative (a negative amount rotates left) or larger than the row length; rotating by the row length changes nothing.- Row 0 is never moved. The board is rectangular with at least 1 row and 1 column.
- Do not change
board.
Constraints: 1 ≤ rows, columns ≤ 100; -1000 ≤ step ≤ 1000.
Example: solution([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 1) returns [[1, 2, 3], [6, 4, 5], [8, 9, 7]]: row 1 moves right by 1, row 2 by 2.
Exercise 3
A stage map is a rectangular grid. Return a new grid showing the map after it is turned k quarter-turns clockwise.
Rules:
- One clockwise quarter-turn of a grid with R rows and C columns gives a grid with C rows and R columns, where
new[i][j] = old[R − 1 − j][i]. The old left column, read bottom to top, becomes the new top row. kmay be 0 (return a copy of the map). Four turns bring the map back to the start.- Do not change the input grid.
Constraints: 1 ≤ R, C ≤ 100; 0 ≤ k ≤ 10^9. The performance test turns a small map many, many times.
Example: solution([[1, 2, 3], [4, 5, 6]], 1) returns [[4, 1], [5, 2], [6, 3]]. With k = 2 it returns [[6, 5, 4], [3, 2, 1]].
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Practice
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