3249. Count the Number of Good Nodes
Description
There is an undirected tree with n
nodes labeled from 0
to n - 1
, and rooted at node 0
. You are given a 2D integer array edges
of length n - 1
, where edges[i] = [ai, bi]
indicates that there is an edge between nodes ai
and bi
in the tree.
A node is good if all the subtrees rooted at its children have the same size.
Return the number of good nodes in the given tree.
A subtree of treeName
is a tree consisting of a node in treeName
and all of its descendants.
Example 1:
Input: edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]
Output: 7
Explanation:
All of the nodes of the given tree are good.
Example 2:
Input: edges = [[0,1],[1,2],[2,3],[3,4],[0,5],[1,6],[2,7],[3,8]]
Output: 6
Explanation:
There are 6 good nodes in the given tree. They are colored in the image above.
Example 3:
Constraints:
2 <= n <= 105
edges.length == n - 1
edges[i].length == 2
0 <= ai, bi < n
- The input is generated such that
edges
represents a valid tree.
Solutions
Solution 1: DFS
First, we construct the adjacency list $\textit{g}$ of the tree based on the given edges $\textit{edges}$, where $\textit{g}[a]$ represents all the neighboring nodes of node $a$.
Next, we design a function $\textit{dfs}(a, \textit{fa})$ to calculate the number of nodes in the subtree rooted at node $a$ and to accumulate the count of good nodes. Here, $\textit{fa}$ represents the parent node of node $a$.
The execution process of the function $\textit{dfs}(a, \textit{fa})$ is as follows:
- Initialize variables $\textit{pre} = -1$, $\textit{cnt} = 1$, $\textit{ok} = 1$, representing the number of nodes in a subtree of node $a$, the total number of nodes in all subtrees of node $a$, and whether node $a$ is a good node, respectively.
- Traverse all neighboring nodes $b$ of node $a$. If $b$ is not equal to $\textit{fa}$, recursively call $\textit{dfs}(b, a)$, with the return value being $\textit{cur}$, and add $\textit{cur}$ to $\textit{cnt}$. If $\textit{pre} < 0$, assign $\textit{cur}$ to $\textit{pre}$; otherwise, if $\textit{pre}$ is not equal to $\textit{cur}$, it means the number of nodes in different subtrees of node $a$ is different, and set $\textit{ok}$ to $0$.
- Finally, add $\textit{ok}$ to the answer and return $\textit{cnt}$.
In the main function, we call $\textit{dfs}(0, -1)$ and return the final answer.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Here, $n$ represents the number of nodes.
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