Mid/SeniorDynamic Programming
Out of Boundary Paths
There is an m x n grid with a ball. The ball is initially at the position [startRow, startColumn]. You are allowed to move the ball to one of the four adjacent cells in the grid, possibly out of the grid by crossing the grid boundary. You can apply at most maxMove moves to the ball.
Given the five integers m, n, maxMove, startRow, and startColumn, return the number of paths to move the ball out of the grid boundary. Since the answer can be very large, return it modulo 10^9 + 7.
Example 1
Input
m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0Output
6There are 6 paths that move the ball out of the 2 x 2 grid using at most 2 moves from the top-left cell.
Example 2
Input
m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1Output
12There are 12 paths that move the ball out of the 1 x 3 grid using at most 3 moves from the middle cell.
Constraints
- 1 <= m, n <= 50
- 0 <= maxMove <= 50
- 0 <= startRow < m
- 0 <= startColumn < n