Neighbours and bounds

The cells next to (r, c) are found by adding offsets. The 4 direct neighbours are:

for dr, dc in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
    nr = r + dr
    nc = c + dc

For 8 neighbours add the diagonals: loop dr and dc over -1, 0, 1 and skip (0, 0). Always say which one the problem means.

At an edge, some neighbours do not exist. Check before you index:

if 0 <= nr < rows and 0 <= nc < cols:

Python will not warn you about -1: grid[-1] is the last row, so a missing check on the low side silently reads the wrong cell. A missing check on the high side raises IndexError.

Watch the visual: the first candidate is outside and gets rejected.

See it run

grid = [[1, 2], [3, 4]]
r = 0
c = 0
for dr, dc in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
    nr = r + dr
    nc = c + dc
    if 0 <= nr < 2 and 0 <= nc < 2:
        print(grid[nr][nc])

We list the neighbours of the corner cell (0, 0).

Practice neighbours and bounds

Exercise 1

A map is a list of equal-length strings: "." is open ground and "#" is rock. A walker stands on open ground at row row, column col (row 0 is the top, column 0 is the left). The string moves holds the letters U (row − 1), D (row + 1), L (column − 1) and R (column + 1).

Return [row, col], the walker's position after all moves.

Rules:

Moves are made in order, one letter at a time.
A move that would leave the map or step onto rock is skipped: the walker stays where it is, and the next letter is still used.
moves may be empty.

Constraints: map up to 50×50; moves up to 1000 letters.

Example: solution(["..#", "..."], 0, 0, "RRDR") returns [1, 2]: R to (0,1); R is rock, skipped; D to (1,1); R to (1,2).

Exercise 2

A seed tray is a grid of 0 (empty cell) and 1 (a seedling is growing there).

Return how many empty cells have at least one seedling directly above, below, left or right of them.

Rules:

Only the 4 direct neighbours count; diagonal cells are not neighbours.
Cells outside the tray do not exist.
Cells that hold a seedling are never counted.

Constraints: 1 ≤ rows, columns ≤ 100.

Example: solution([[1, 0], [0, 0]]) returns 2: the cells right of and below the seedling count; the bottom-right cell only touches the seedling diagonally.

Exercise 3

A crowd map is a grid of whole numbers: crowd[r][c] is how many people stand on that square. For every square, count how many of its surrounding squares hold strictly fewer people than the square itself.

Return a new grid of the same size holding those counts.

Rules:

Surrounding means up to 8 squares: above, below, left, right and the 4 diagonals.
Squares outside the map do not exist, so edge and corner squares have fewer neighbours.
Equal counts are not fewer.
Do not change crowd.

Constraints: 1 ≤ rows, columns ≤ 100; 0 ≤ people ≤ 1000.

Example: solution([[3, 1], [2, 3]]) returns [[2, 0], [1, 2]]. The top-left 3 has neighbours 1, 2 and 3, and two of them are smaller.

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Practice

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