leetcode-problemset/leetcode-cn/problem (English)/模拟行走机器人(English) [walking-robot-simulation].html

<p>A robot on an infinite XY-plane starts at point <code>(0, 0)</code> facing north. The robot can receive a sequence of these three possible types of <code>commands</code>:</p>

<ul>
	<li><code>-2</code>: Turn left <code>90</code> degrees.</li>
	<li><code>-1</code>: Turn right <code>90</code> degrees.</li>
	<li><code>1 &lt;= k &lt;= 9</code>: Move forward <code>k</code> units, one unit at a time.</li>
</ul>

<p>Some of the grid squares are <code>obstacles</code>. The <code>i<sup>th</sup></code> obstacle is at grid point <code>obstacles[i] = (x<sub>i</sub>, y<sub>i</sub>)</code>. If the robot runs into an obstacle, then it will instead stay in its current location and move on to the next command.</p>

<p>Return <em>the <strong>maximum Euclidean distance</strong> that the robot ever gets from the origin <strong>squared</strong> (i.e. if the distance is </em><code>5</code><em>, return </em><code>25</code><em>)</em>.</p>

<p><strong>Note:</strong></p>

<ul>
	<li>North means +Y direction.</li>
	<li>East means +X direction.</li>
	<li>South means -Y direction.</li>
	<li>West means -X direction.</li>
	<li>There can be obstacle in&nbsp;[0,0].</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> commands = [4,-1,3], obstacles = []
<strong>Output:</strong> 25
<strong>Explanation:</strong> The robot starts at (0, 0):
1. Move north 4 units to (0, 4).
2. Turn right.
3. Move east 3 units to (3, 4).
The furthest point the robot ever gets from the origin is (3, 4), which squared is 3<sup>2</sup> + 4<sup>2</sup> = 25 units away.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> commands = [4,-1,4,-2,4], obstacles = [[2,4]]
<strong>Output:</strong> 65
<strong>Explanation:</strong> The robot starts at (0, 0):
1. Move north 4 units to (0, 4).
2. Turn right.
3. Move east 1 unit and get blocked by the obstacle at (2, 4), robot is at (1, 4).
4. Turn left.
5. Move north 4 units to (1, 8).
The furthest point the robot ever gets from the origin is (1, 8), which squared is 1<sup>2</sup> + 8<sup>2</sup> = 65 units away.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> commands = [6,-1,-1,6], obstacles = []
<strong>Output:</strong> 36
<strong>Explanation:</strong> The robot starts at (0, 0):
1. Move north 6 units to (0, 6).
2. Turn right.
3. Turn right.
4. Move south 6 units to (0, 0).
The furthest point the robot ever gets from the origin is (0, 6), which squared is 6<sup>2</sup> = 36 units away.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= commands.length &lt;= 10<sup>4</sup></code></li>
	<li><code>commands[i]</code> is either <code>-2</code>, <code>-1</code>, or an integer in the range <code>[1, 9]</code>.</li>
	<li><code>0 &lt;= obstacles.length &lt;= 10<sup>4</sup></code></li>
	<li><code>-3 * 10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 3 * 10<sup>4</sup></code></li>
	<li>The answer is guaranteed to be less than <code>2<sup>31</sup></code>.</li>
</ul>