{ "data": { "question": { "questionId": "3439", "questionFrontendId": "3203", "categoryTitle": "Algorithms", "boundTopicId": 2824508, "title": "Find Minimum Diameter After Merging Two Trees", "titleSlug": "find-minimum-diameter-after-merging-two-trees", "content": "
There exist two undirected trees with n
and m
nodes, numbered from 0
to n - 1
and from 0
to m - 1
, respectively. You are given two 2D integer arrays edges1
and edges2
of lengths n - 1
and m - 1
, respectively, where edges1[i] = [ai, bi]
indicates that there is an edge between nodes ai
and bi
in the first tree and edges2[i] = [ui, vi]
indicates that there is an edge between nodes ui
and vi
in the second tree.
You must connect one node from the first tree with another node from the second tree with an edge.
\n\nReturn the minimum possible diameter of the resulting tree.
\n\nThe diameter of a tree is the length of the longest path between any two nodes in the tree.
\n\n\n
Example 1:
Input: edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]
\n\nOutput: 3
\n\nExplanation:
\n\nWe can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.
\nExample 2:
\nInput: edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]
\n\nOutput: 5
\n\nExplanation:
\n\nWe can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.
\n\n
Constraints:
\n\n1 <= n, m <= 105
edges1.length == n - 1
edges2.length == m - 1
edges1[i].length == edges2[i].length == 2
edges1[i] = [ai, bi]
0 <= ai, bi < n
edges2[i] = [ui, vi]
0 <= ui, vi < m
edges1
and edges2
represent valid trees.给你两棵 无向 树,分别有 n
和 m
个节点,节点编号分别为 0
到 n - 1
和 0
到 m - 1
。给你两个二维整数数组 edges1
和 edges2
,长度分别为 n - 1
和 m - 1
,其中 edges1[i] = [ai, bi]
表示在第一棵树中节点 ai
和 bi
之间有一条边,edges2[i] = [ui, vi]
表示在第二棵树中节点 ui
和 vi
之间有一条边。
你必须在第一棵树和第二棵树中分别选一个节点,并用一条边连接它们。
\n\n请你返回添加边后得到的树中,最小直径 为多少。
\n\n一棵树的 直径 指的是树中任意两个节点之间的最长路径长度。
\n\n\n\n
示例 1:
输入:edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]
\n\n输出:3
\n\n解释:
\n\n将第一棵树中的节点 0 与第二棵树中的任意节点连接,得到一棵直径为 3 的树。
\n示例 2:
输入:edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]
\n\n输出:5
\n\n解释:
\n\n将第一棵树中的节点 0 和第二棵树中的节点 0 连接,可以得到一棵直径为 5 的树。
\n\n\n
提示:
\n\n1 <= n, m <= 105
edges1.length == n - 1
edges2.length == m - 1
edges1[i].length == edges2[i].length == 2
edges1[i] = [ai, bi]
0 <= ai, bi < n
edges2[i] = [ui, vi]
0 <= ui, vi < m
edges1
和 edges2
分别表示一棵合法的树。a
in tree1 with node b
in tree2. The diameter length of the resulting tree will be the largest of the following 3 values: \r\na
and that is completely within Tree 1 + The length of the longest path that starts at node b
and that is completely within Tree 2 + 1.a
and b
. Therefore, we need to pick a
and b
in such a way that minimizes value 3.",
"If we pick a
and b
optimally, they will be in the diameters of Tree 1 and Tree 2, respectively. Exactly which nodes of the diameter should we pick?",
"a
is the center of the diameter of tree 1, and b
is the center of the diameter of tree 2."
],
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