where will the ball fall

Author: always-maap

1706.WhereWillTheBallFall.py

@@ -0,0 +1,66 @@
+"""
+1706. Where Will the Ball Fall
+Medium
+Array | Dynamic Programming | Depth-First Search | Matrix | Simulation
+---
+You have a 2-D grid of size m x n representing a box, and you have n balls. The box is open on the top and bottom sides.
+
+Each cell in the box has a diagonal board spanning two corners of the cell that
+ can redirect a ball to the right or to the left.
+
+A board that redirects the ball to the right spans the top-left corner to
+ the bottom-right corner and is represented in the grid as 1.
+A board that redirects the ball to the left spans the top-right corner to
+ the bottom-left corner and is represented in the grid as -1.
+We drop one ball at the top of each column of the box. Each ball can get stuck in the box or fall out of the bottom. 
+ A ball gets stuck if it hits a "V" shaped pattern between two boards or
+  if a board redirects the ball into either wall of the box.
+
+Return an array answer of size n where answer[i] is the column that the ball falls out of at
+ the bottom after dropping the ball from the ith column at the top, or -1 if the ball gets stuck in the box.
+
+Example 1:
+Input: grid = [[1,1,1,-1,-1],[1,1,1,-1,-1],[-1,-1,-1,1,1],[1,1,1,1,-1],[-1,-1,-1,-1,-1]]
+Output: [1,-1,-1,-1,-1]
+Explanation: This example is shown in the photo.
+Ball b0 is dropped at column 0 and falls out of the box at column 1.
+Ball b1 is dropped at column 1 and will get stuck in the box between column 2 and 3 and row 1.
+Ball b2 is dropped at column 2 and will get stuck on the box between column 2 and 3 and row 0.
+Ball b3 is dropped at column 3 and will get stuck on the box between column 2 and 3 and row 0.
+Ball b4 is dropped at column 4 and will get stuck on the box between column 2 and 3 and row 1.
+
+Example 2:
+Input: grid = [[-1]]
+Output: [-1]
+Explanation: The ball gets stuck against the left wall.
+
+Example 3:
+Input: grid = [[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1]]
+Output: [0,1,2,3,4,-1]
+
+Constraints:
+m == grid.length
+n == grid[i].length
+1 <= m, n <= 100
+grid[i][j] is 1 or -1.
+"""
+
+
+from typing import List
+
+
+# O(m * n) time | O(m * n) space
+class Solution:
+    def findBall(self, grid: List[List[int]]) -> List[int]:
+        def dfs(row, col, grid):
+            if row == len(grid):
+                return col
+            nextCol = col + grid[row][col]
+            if nextCol < 0 or nextCol > len(grid[0]) - 1 or grid[row][col] != grid[row][nextCol]:
+                return -1
+            return dfs(row + 1, nextCol, grid)
+
+        res = []
+        for i in range(len(grid[0])):
+            res.append(dfs(0, i, grid))
+        return res