{ "data": { "question": { "questionId": "3181", "questionFrontendId": "2940", "categoryTitle": "Algorithms", "boundTopicId": 2529067, "title": "Find Building Where Alice and Bob Can Meet", "titleSlug": "find-building-where-alice-and-bob-can-meet", "content": "
You are given a 0-indexed array heights of positive integers, where heights[i] represents the height of the ith building.
If a person is in building i, they can move to any other building j if and only if i < j and heights[i] < heights[j].
You are also given another array queries where queries[i] = [ai, bi]. On the ith query, Alice is in building ai while Bob is in building bi.
Return an array ans where ans[i] is the index of the leftmost building where Alice and Bob can meet on the ith query. If Alice and Bob cannot move to a common building on query i, set ans[i] to -1.
\n
Example 1:
\n\n\nInput: heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]]\nOutput: [2,5,-1,5,2]\nExplanation: 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\n\n
Example 2:
\n\n\nInput: heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]]\nOutput: [7,6,-1,4,6]\nExplanation: 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\n\n
\n
Constraints:
\n\n1 <= heights.length <= 5 * 1041 <= heights[i] <= 1091 <= queries.length <= 5 * 104queries[i] = [ai, bi]0 <= ai, bi <= heights.length - 1给你一个下标从 0 开始的正整数数组 heights ,其中 heights[i] 表示第 i 栋建筑的高度。
如果一个人在建筑 i ,且存在 i < j 的建筑 j 满足 heights[i] < heights[j] ,那么这个人可以移动到建筑 j 。
给你另外一个数组 queries ,其中 queries[i] = [ai, bi] 。第 i 个查询中,Alice 在建筑 ai ,Bob 在建筑 bi 。
请你能返回一个数组 ans ,其中 ans[i] 是第 i 个查询中,Alice 和 Bob 可以相遇的 最左边的建筑 。如果对于查询 i ,Alice 和 Bob 不能相遇,令 ans[i] 为 -1 。
\n\n
示例 1:
\n\n\n输入:heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]]\n输出:[2,5,-1,5,2]\n解释: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\n\n
示例 2:
\n\n\n输入:heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]]\n输出:[7,6,-1,4,6]\n解释: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\n\n
\n\n
提示:
\n\n1 <= heights.length <= 5 * 1041 <= heights[i] <= 1091 <= queries.length <= 5 * 104queries[i] = [ai, bi]0 <= ai, bi <= heights.length - 1[x, y], if x > y, swap x and y. Now, we can assume that x <= y.",
"For each query [x, y], if x == y or heights[x] < heights[y], then the answer is y since x ≤ y.",
"Otherwise, we need to find the smallest index t such that y < t and heights[x] < heights[t]. Note that heights[y] <= heights[x], so heights[x] < heights[t] is a sufficient condition.",
"To find index t for each query, sort the queries in descending order of y. Iterate over the queries while maintaining a monotonic stack which we can binary search over to find index t."
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