mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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188 lines
18 KiB
JSON
188 lines
18 KiB
JSON
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"title": "Robot Bounded In Circle",
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"content": "<p>On an infinite plane, a robot initially stands at <code>(0, 0)</code> and faces north. Note that:</p>\n\n<ul>\n\t<li>The <strong>north direction</strong> is the positive direction of the y-axis.</li>\n\t<li>The <strong>south direction</strong> is the negative direction of the y-axis.</li>\n\t<li>The <strong>east direction</strong> is the positive direction of the x-axis.</li>\n\t<li>The <strong>west direction</strong> is the negative direction of the x-axis.</li>\n</ul>\n\n<p>The robot can receive one of three instructions:</p>\n\n<ul>\n\t<li><code>"G"</code>: go straight 1 unit.</li>\n\t<li><code>"L"</code>: turn 90 degrees to the left (i.e., anti-clockwise direction).</li>\n\t<li><code>"R"</code>: turn 90 degrees to the right (i.e., clockwise direction).</li>\n</ul>\n\n<p>The robot performs the <code>instructions</code> given in order, and repeats them forever.</p>\n\n<p>Return <code>true</code> if and only if there exists a circle in the plane such that the robot never leaves the circle.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> instructions = "GGLLGG"\n<strong>Output:</strong> true\n<strong>Explanation:</strong> The robot is initially at (0, 0) facing the north direction.\n"G": move one step. Position: (0, 1). Direction: North.\n"G": move one step. Position: (0, 2). Direction: North.\n"L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: West.\n"L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: South.\n"G": move one step. Position: (0, 1). Direction: South.\n"G": move one step. Position: (0, 0). Direction: South.\nRepeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (0, 2) --> (0, 1) --> (0, 0).\nBased on that, we return true.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> instructions = "GG"\n<strong>Output:</strong> false\n<strong>Explanation:</strong> The robot is initially at (0, 0) facing the north direction.\n"G": move one step. Position: (0, 1). Direction: North.\n"G": move one step. Position: (0, 2). Direction: North.\nRepeating the instructions, keeps advancing in the north direction and does not go into cycles.\nBased on that, we return false.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> instructions = "GL"\n<strong>Output:</strong> true\n<strong>Explanation:</strong> The robot is initially at (0, 0) facing the north direction.\n"G": move one step. Position: (0, 1). Direction: North.\n"L": turn 90 degrees anti-clockwise. Position: (0, 1). Direction: West.\n"G": move one step. Position: (-1, 1). Direction: West.\n"L": turn 90 degrees anti-clockwise. Position: (-1, 1). Direction: South.\n"G": move one step. Position: (-1, 0). Direction: South.\n"L": turn 90 degrees anti-clockwise. Position: (-1, 0). Direction: East.\n"G": move one step. Position: (0, 0). Direction: East.\n"L": turn 90 degrees anti-clockwise. Position: (0, 0). Direction: North.\nRepeating the instructions, the robot goes into the cycle: (0, 0) --> (0, 1) --> (-1, 1) --> (-1, 0) --> (0, 0).\nBased on that, we return true.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= instructions.length <= 100</code></li>\n\t<li><code>instructions[i]</code> is <code>'G'</code>, <code>'L'</code> or, <code>'R'</code>.</li>\n</ul>\n",
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"Calculate the final vector of how the robot travels after executing all instructions once - it consists of a change in position plus a change in direction.",
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"The robot stays in the circle if and only if (looking at the final vector) it changes direction (ie. doesn't stay pointing north), or it moves 0."
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