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97 lines
4.0 KiB
HTML
97 lines
4.0 KiB
HTML
<p>A robot on an infinite XY-plane starts at point <code>(0, 0)</code> facing north. The robot receives an array of integers <code>commands</code>, which represents a sequence of moves that it needs to execute. There are only three possible types of instructions the robot can receive:</p>
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<ul>
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<li><code>-2</code>: Turn left <code>90</code> degrees.</li>
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<li><code>-1</code>: Turn right <code>90</code> degrees.</li>
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<li><code>1 <= k <= 9</code>: Move forward <code>k</code> units, one unit at a time.</li>
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</ul>
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<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, it will stay in its current location (on the block adjacent to the obstacle) and move onto the next command.</p>
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<p>Return the <strong>maximum squared Euclidean distance</strong> that the robot reaches at any point in its path (i.e. if the distance is <code>5</code>, return <code>25</code>).</p>
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<p><strong>Note:</strong></p>
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<ul>
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<li>There can be an obstacle at <code>(0, 0)</code>. If this happens, the robot will ignore the obstacle until it has moved off the origin. However, it will be unable to return to <code>(0, 0)</code> due to the obstacle.</li>
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<li>North means +Y direction.</li>
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<li>East means +X direction.</li>
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<li>South means -Y direction.</li>
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<li>West means -X direction.</li>
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</ul>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">commands = [4,-1,3], obstacles = []</span></p>
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<p><strong>Output:</strong> <span class="example-io">25</span></p>
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<p><strong>Explanation: </strong></p>
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<p>The robot starts at <code>(0, 0)</code>:</p>
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<ol>
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<li>Move north 4 units to <code>(0, 4)</code>.</li>
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<li>Turn right.</li>
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<li>Move east 3 units to <code>(3, 4)</code>.</li>
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</ol>
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<p>The furthest point the robot ever gets from the origin is <code>(3, 4)</code>, which squared is <code>3<sup>2</sup> + 4<sup>2 </sup>= 25</code> units away.</p>
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</div>
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<p><strong class="example">Example 2:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">commands = [4,-1,4,-2,4], obstacles = [[2,4]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">65</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The robot starts at <code>(0, 0)</code>:</p>
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<ol>
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<li>Move north 4 units to <code>(0, 4)</code>.</li>
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<li>Turn right.</li>
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<li>Move east 1 unit and get blocked by the obstacle at <code>(2, 4)</code>, robot is at <code>(1, 4)</code>.</li>
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<li>Turn left.</li>
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<li>Move north 4 units to <code>(1, 8)</code>.</li>
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</ol>
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<p>The furthest point the robot ever gets from the origin is <code>(1, 8)</code>, which squared is <code>1<sup>2</sup> + 8<sup>2</sup> = 65</code> units away.</p>
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</div>
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<p><strong class="example">Example 3:</strong></p>
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<div class="example-block">
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<p><strong>Input:</strong> <span class="example-io">commands = [6,-1,-1,6], obstacles = [[0,0]]</span></p>
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<p><strong>Output:</strong> <span class="example-io">36</span></p>
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<p><strong>Explanation:</strong></p>
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<p>The robot starts at <code>(0, 0)</code>:</p>
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<ol>
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<li>Move north 6 units to <code>(0, 6)</code>.</li>
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<li>Turn right.</li>
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<li>Turn right.</li>
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<li>Move south 5 units and get blocked by the obstacle at <code>(0,0)</code>, robot is at <code>(0, 1)</code>.</li>
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</ol>
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<p>The furthest point the robot ever gets from the origin is <code>(0, 6)</code>, which squared is <code>6<sup>2</sup> = 36</code> units away.</p>
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</div>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= commands.length <= 10<sup>4</sup></code></li>
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<li><code>commands[i]</code> is either <code>-2</code>, <code>-1</code>, or an integer in the range <code>[1, 9]</code>.</li>
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<li><code>0 <= obstacles.length <= 10<sup>4</sup></code></li>
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<li><code>-3 * 10<sup>4</sup> <= x<sub>i</sub>, y<sub>i</sub> <= 3 * 10<sup>4</sup></code></li>
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<li>The answer is guaranteed to be less than <code>2<sup>31</sup></code>.</li>
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</ul>
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