Out of Boundary Paths

Given an m x n grid, a starting cell, and a maximum number of moves, return the number of ways a ball can move out of the grid boundary using one step per move in the four cardinal directions. Pattern focus: Grid path counting. This is a counting DP over time and position.

Input Format

startRow and startCol are valid grid coordinates

Output Format

number of ways to exit the grid

Constraints

  • 1 <= m, n <= 50; 1 <= maxMove <= 50

Examples

Example 1:

Input:

m = 2
n = 2
maxMove = 2
startRow = 0
startCol = 0

Output:

6

Explanation:

There are 6 ways to leave the grid within 2 moves.

Example 2:

Input:

m = 1
n = 3
maxMove = 3
startRow = 0
startCol = 1

Output:

12

Explanation:

The ball can exit in 12 ways.

Example 3:

Input:

m = 3
n = 3
maxMove = 1
startRow = 1
startCol = 1

Output:

0

Explanation:

From the center, one move cannot leave the grid.

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Out of Boundary Paths - Dp Grid DSA Problem