Skip to content

solution4.md

Latest commit

 

History

History
46 lines (39 loc) · 1.52 KB

solution4.md

File metadata and controls

46 lines (39 loc) · 1.52 KB

Solution 4: Cellular Automaton (Game of Life)

Approach Explanation

To update in-place, we use temporary state codes:

  • 2: Cell was dead (0), now live (1).
  • -1: Cell was live (1), now dead (0). When counting neighbors, absolute value of -1 is 1, so the original state is preserved.

Step-by-Step Logic

  1. For each cell (i, j), count its 8 neighbors.
  2. In neighbor count, consider original state 1 if value is 1 or -1.
  3. Apply rules:
    • If cell == 1 and neighbors < 2 or > 3, set cell = -1.
    • If cell == 0 and neighbors == 3, set cell = 2.
  4. After marking all cells, iterate and replace 2 -> 1 and -1 -> 0.

Complexity

  • Time Complexity: O(M * N).
  • Space Complexity: O(1).

Code

def game_of_life(board):
    m, n = len(board), len(board[0])
    
    for i in range(m):
        for j in range(n):
            live_neighbors = 0
            for r in range(i - 1, i + 2):
                for c in range(j - 1, j + 2):
                    if r == i and c == j: continue
                    if 0 <= r < m and 0 <= c < n and abs(board[r][c]) == 1:
                        live_neighbors += 1
            
            if board[i][j] == 1 and (live_neighbors < 2 or live_neighbors > 3):
                board[i][j] = -1
            if board[i][j] == 0 and live_neighbors == 3:
                board[i][j] = 2
                
    for i in range(m):
        for j in range(n):
            if board[i][j] > 0:
                board[i][j] = 1
            else:
                board[i][j] = 0