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Use depth-first search (DFS) to simulate the movement of each ball from the top to the bottom, keeping track of the ball's column. If a ball encounters a 'V' shape or hits the wall, it gets stuck. This approach simulates the scenario for each ball individually.
Time Complexity: O(m * n), where m is the number of rows and n is the number of columns.
Space Complexity: O(n) for the result and recursion stack.
1class Solution:
2 def findBall(self, grid):
3 def dfs(row, col):
4 if row == len(grid):
5 return col
6 next_col = col + grid[row][col]
7 if next_col < 0 or next_col >= len(grid[0]) or grid[row][next_col] != grid[row][col]:
8 return -1
9 return dfs(row + 1, next_col)
10
11 return [dfs(0, col) for col in range(len(grid[0]))]For Python, a nested DFS function is used within the main function to explore the trajectory of each ball. The list comprehension gathers results from exploring each initial column, either obtaining the exit column or a stuck indication.
Utilize nested loops to simulate the motion of each ball iteratively instead of using recursion. It tracks each movement step-by-step across the grid, calculates next positions, transitions to subsequent rows, and monitors for blockages or exits.
Time Complexity: O(m * n), driven by iterating through all cells.
Space Complexity: O(n), where n stands for the result array requirement.
1Employing loops in Java helps simulate each ball's position across the grid step by step, determining the resultant landing column or identifying if blocked based on grid-defined movements, purely iteratively. This method maintains precision by direct checking.