out-of-boundary-paths

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python3

python

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golang

kotlin

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rust

ruby

dart

scala

elixir

erlang

racket

cangjie

bash

mysql

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postgresql

oraclesql

pythondata

Algorithms

There is an <code>m x n</code> grid with a ball. The ball is initially at the position <code>[startRow, startColumn]</code>. You are allowed to move the ball to one of the four adjacent cells in the grid (possibly out of the grid crossing the grid boundary). You can apply at most <code>maxMove</code> moves to the ball.

Given the five integers <code>m</code>, <code>n</code>, <code>maxMove</code>, <code>startRow</code>, <code>startColumn</code>, return the number of paths to move the ball out of the grid boundary. Since the answer can be very large, return it modulo <code>109 + 7</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_1.png" style="width: 500px; height: 296px;" />
<pre>
Input: m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0
Output: 6
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_2.png" style="width: 500px; height: 293px;" />
<pre>
Input: m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1
Output: 12
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>0 &lt;= maxMove &lt;= 50</code></li>
	<li><code>0 &lt;= startRow &lt; m</code></li>
	<li><code>0 &lt;= startColumn &lt; n</code></li>
</ul>

findPaths

Out of Boundary Paths

Knight Probability in Chessboard

knight-probability-in-chessboard

骑士在棋盘上的概率

Execution of All Suffix Instructions Staying in a Grid

execution-of-all-suffix-instructions-staying-in-a-grid

执行所有后缀指令

Dynamic Programming

给你一个大小为 <code>m x n</code> 的网格和一个球。球的起始坐标为 <code>[startRow, startColumn]</code> 。你可以将球移到在四个方向上相邻的单元格内（可以穿过网格边界到达网格之外）。你 最多 可以移动 <code>maxMove</code> 次球。

给你五个整数 <code>m</code>、<code>n</code>、<code>maxMove</code>、<code>startRow</code> 以及 <code>startColumn</code> ，找出并返回可以将球移出边界的路径数量。因为答案可能非常大，返回对 <code>109 + 7</code> 取余 后的结果。

&nbsp;

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_1.png" style="width: 500px; height: 296px;" />
<pre>
输入：m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0
输出：6
</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_2.png" style="width: 500px; height: 293px;" />
<pre>
输入：m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1
输出：12
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>0 &lt;= maxMove &lt;= 50</code></li>
	<li><code>0 &lt;= startRow &lt; m</code></li>
	<li><code>0 &lt;= startColumn &lt; n</code></li>
</ul>