mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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209 lines
28 KiB
JSON
209 lines
28 KiB
JSON
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"title": "Find Building Where Alice and Bob Can Meet",
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"content": "<p>You are given a <strong>0-indexed</strong> array <code>heights</code> of positive integers, where <code>heights[i]</code> represents the height of the <code>i<sup>th</sup></code> building.</p>\n\n<p>If a person is in building <code>i</code>, they can move to any other building <code>j</code> if and only if <code>i < j</code> and <code>heights[i] < heights[j]</code>.</p>\n\n<p>You are also given another array <code>queries</code> where <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>. On the <code>i<sup>th</sup></code> query, Alice is in building <code>a<sub>i</sub></code> while Bob is in building <code>b<sub>i</sub></code>.</p>\n\n<p>Return <em>an array</em> <code>ans</code> <em>where</em> <code>ans[i]</code> <em>is <strong>the index of the leftmost building</strong> where Alice and Bob can meet on the</em> <code>i<sup>th</sup></code> <em>query</em>. <em>If Alice and Bob cannot move to a common building on query</em> <code>i</code>, <em>set</em> <code>ans[i]</code> <em>to</em> <code>-1</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]]\n<strong>Output:</strong> [2,5,-1,5,2]\n<strong>Explanation:</strong> In the first query, Alice and Bob can move to building 2 since heights[0] < heights[2] and heights[1] < heights[2]. \nIn the second query, Alice and Bob can move to building 5 since heights[0] < heights[5] and heights[3] < heights[5]. \nIn the third query, Alice cannot meet Bob since Alice cannot move to any other building.\nIn the fourth query, Alice and Bob can move to building 5 since heights[3] < heights[5] and heights[4] < heights[5].\nIn the fifth query, Alice and Bob are already in the same building. \nFor ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet.\nFor ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]]\n<strong>Output:</strong> [7,6,-1,4,6]\n<strong>Explanation:</strong> In the first query, Alice can directly move to Bob's building since heights[0] < heights[7].\nIn the second query, Alice and Bob can move to building 6 since heights[3] < heights[6] and heights[5] < heights[6].\nIn the third query, Alice cannot meet Bob since Bob cannot move to any other building.\nIn the fourth query, Alice and Bob can move to building 4 since heights[3] < heights[4] and heights[0] < heights[4].\nIn the fifth query, Alice can directly move to Bob's building since heights[1] < heights[6].\nFor ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet.\nFor ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet.\n\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= heights.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>1 <= heights[i] <= 10<sup>9</sup></code></li>\n\t<li><code>1 <= queries.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li>\n\t<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> <= heights.length - 1</code></li>\n</ul>\n",
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"translatedTitle": "找到 Alice 和 Bob 可以相遇的建筑",
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"translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的正整数数组 <code>heights</code> ，其中 <code>heights[i]</code> 表示第 <code>i</code> 栋建筑的高度。</p>\n\n<p>如果一个人在建筑 <code>i</code> ，且存在 <code>i < j</code> 的建筑 <code>j</code> 满足 <code>heights[i] < heights[j]</code> ，那么这个人可以移动到建筑 <code>j</code> 。</p>\n\n<p>给你另外一个数组 <code>queries</code> ，其中 <code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> 。第 <code>i</code> 个查询中，Alice 在建筑 <code>a<sub>i</sub></code> ，Bob 在建筑 <code>b<sub>i</sub></code><sub> </sub>。</p>\n\n<p>请你能返回一个数组 <code>ans</code> ，其中 <code>ans[i]</code> 是第 <code>i</code> 个查询中，Alice 和 Bob 可以相遇的 <strong>最左边的建筑</strong> 。如果对于查询 <code>i</code> ，Alice<em> </em>和<em> </em>Bob 不能相遇，令 <code>ans[i]</code> 为 <code>-1</code> 。</p>\n\n<p> </p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]]\n<b>输出：</b>[2,5,-1,5,2]\n<b>解释：</b>第一个查询中，Alice 和 Bob 可以移动到建筑 2 ，因为 heights[0] < heights[2] 且 heights[1] < heights[2] 。\n第二个查询中，Alice 和 Bob 可以移动到建筑 5 ，因为 heights[0] < heights[5] 且 heights[3] < heights[5] 。\n第三个查询中，Alice 无法与 Bob 相遇，因为 Alice 不能移动到任何其他建筑。\n第四个查询中，Alice 和 Bob 可以移动到建筑 5 ，因为 heights[3] < heights[5] 且 heights[4] < heights[5] 。\n第五个查询中，Alice 和 Bob 已经在同一栋建筑中。\n对于 ans[i] != -1 ，ans[i] 是 Alice 和 Bob 可以相遇的建筑中最左边建筑的下标。\n对于 ans[i] == -1 ，不存在 Alice 和 Bob 可以相遇的建筑。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]]\n<b>输出：</b>[7,6,-1,4,6]\n<strong>解释：</strong>第一个查询中，Alice 可以直接移动到 Bob 的建筑，因为 heights[0] < heights[7] 。\n第二个查询中，Alice 和 Bob 可以移动到建筑 6 ，因为 heights[3] < heights[6] 且 heights[5] < heights[6] 。\n第三个查询中，Alice 无法与 Bob 相遇，因为 Bob 不能移动到任何其他建筑。\n第四个查询中，Alice 和 Bob 可以移动到建筑 4 ，因为 heights[3] < heights[4] 且 heights[0] < heights[4] 。\n第五个查询中，Alice 可以直接移动到 Bob 的建筑，因为 heights[1] < heights[6] 。\n对于 ans[i] != -1 ，ans[i] 是 Alice 和 Bob 可以相遇的建筑中最左边建筑的下标。\n对于 ans[i] == -1 ，不存在 Alice 和 Bob 可以相遇的建筑。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= heights.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>1 <= heights[i] <= 10<sup>9</sup></code></li>\n\t<li><code>1 <= queries.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>queries[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li>\n\t<li><code>0 <= a<sub>i</sub>, b<sub>i</sub> <= heights.length - 1</code></li>\n</ul>\n",
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"For each query <code>[x, y]</code>, if <code>x > y</code>, swap <code>x</code> and <code>y</code>. Now, we can assume that <code>x <= y</code>.",
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"For each query <code>[x, y]</code>, if <code>x == y</code> or <code>heights[x] < heights[y]</code>, then the answer is <code>y</code> since <code>x ≤ y</code>.",
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"Otherwise, we need to find the smallest index <code>t</code> such that <code>y < t</code> and <code>heights[x] < heights[t]</code>. Note that <code>heights[y] <= heights[x]</code>, so <code>heights[x] < heights[t]</code> is a sufficient condition.",
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