mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-11 02:58:13 +08:00
187 lines
28 KiB
JSON
187 lines
28 KiB
JSON
{
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"question": {
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"questionId": "1000147",
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"questionFrontendId": "LCP 27",
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"categoryTitle": "Algorithms",
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"boundTopicId": 401338,
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"title": "黑盒光线反射",
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"titleSlug": "IQvJ9i",
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"translatedTitle": "黑盒光线反射",
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"translatedContent": "秋日市集上有个奇怪的黑盒，黑盒的主视图为 n\\*m 的矩形。从黑盒的主视图来看，黑盒的上面和下面各均匀分布有 m 个小孔，黑盒的左面和右面各均匀分布有 n 个小孔。黑盒左上角小孔序号为 0，按顺时针编号，总共有 2*(m+n) 个小孔。每个小孔均可以打开或者关闭，初始时，所有小孔均处于关闭状态。每个小孔上的盖子均为镜面材质。例如一个 2\\*3 的黑盒主视图与其小孔分布如图所示:\n\n{:height=\"200px\"}\n\n店长告诉小扣，这里是「几何学的快问快答」，店长可能有两种操作：\n\n- `open(int index, int direction)` - 若小孔处于关闭状态，则打开小孔，照入光线；否则直接照入光线；\n- `close(int index)` - 关闭处于打开状态小孔，店长保证不会关闭已处于关闭状态的小孔；\n\n其中：\n- `index`： 表示小孔序号\n- `direction`：`1` 表示光线沿 $y=x$ 方向，`-1` 表示光线沿 $y=-x$ 方向。\n\n{:height=\"200px\"}\n\n\n当光线照至边界时：若边界上的小孔为开启状态，则光线会射出；否则，光线会在小孔之间进行反射。特别地：\n1. 若光线射向未打开的拐角（黑盒顶点），则光线会原路反射回去；\n2. 光线自拐角处的小孔照入时，只有一种入射方向（如自序号为 0 的小孔照入方向只能为 `-1`）\n\n{:height=\"200px\"}\n\n请帮助小扣判断并返回店长每次照入的光线从几号小孔射出。\n\n\n**示例 1：**\n>输入：\n>`[\"BlackBox\",\"open\",\"open\",\"open\",\"close\",\"open\"]`\n>`[[2,3],[6,-1],[4,-1],[0,-1],[6],[0,-1]]`\n>\n>输出：`[null,6,4,6,null,4]`\n>\n>解释：\n>BlackBox b = BlackBox(2,3); // 新建一个 2x3 的黑盒\n>b.open(6,-1) // 打开 6 号小孔，并沿 y=-x 方向照入光线，光线至 0 号小孔反射，从 6 号小孔射出\n>b.open(4,-1) // 打开 4 号小孔，并沿 y=-x 方向照入光线，光线轨迹为 4-2-8-2-4，从 4 号小孔射出\n>b.open(0,-1) // 打开 0 号小孔，并沿 y=-x 方向照入光线，由于 6 号小孔为开启状态，光线从 6 号小孔射出\n>b.close(6) // 关闭 6 号小孔\n>b.shoot(0,-1) // 从 0 号小孔沿 y=-x 方向照入光线，由于 6 号小孔为关闭状态，4 号小孔为开启状态，光线轨迹为 0-6-4，从 4 号小孔射出\n\n**示例 2：**\n>输入：\n>`[\"BlackBox\",\"open\",\"open\",\"open\",\"open\",\"close\",\"open\",\"close\",\"open\"]`\n>`[[3,3],[1,-1],[5,1],[11,-1],[11,1],[1],[11,1],[5],[11,-1]]`\n>\n>输出：`[null,1,1,5,1,null,5,null,11]`\n>\n>解释：\n>\n>{:height=\"300px\"}\n>\n>BlackBox b = BlackBox(3,3); // 新建一个 3x3 的黑盒\n>b.open(1,-1) // 打开 1 号小孔，并沿 y=-x 方向照入光线，光线轨迹为 1-5-7-11-1，从 1 号小孔射出\n>b.open(5,1) // 打开 5 号小孔，并沿 y=x 方向照入光线，光线轨迹为 5-7-11-1，从 1 号小孔射出\n>b.open(11,-1) // 打开 11 号小孔，并沿逆 y=-x 方向照入光线，光线轨迹为 11-7-5，从 5 号小孔射出\n>b.open(11,1) // 从 11 号小孔沿 y=x 方向照入光线，光线轨迹为 11-1，从 1 号小孔射出\n>b.close(1) // 关闭 1 号小孔\n>b.open(11,1) // 从 11 号小孔沿 y=x 方向照入光线，光线轨迹为 11-1-5，从 5 号小孔射出\n>b.close(5) // 关闭 5 号小孔\n>b.open(11,-1) // 从 11 号小孔沿 y=-x 方向照入光线，光线轨迹为 11-1-5-7-11，从 11 号小孔射出\n\n\n\n**提示：**\n- `1 <= n, m <= 10000`\n- `1 <= 操作次数 <= 10000`\n- `direction` 仅为 `1` 或 `-1`\n- `0 <= index < 2*(m+n)`\n",
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