mediumTreesPattern: BFS
Minimum Tree Traversal Path Solution
Problem Statement
Given a tree represented as an adjacency list, find the minimum path that visits all nodes exactly once.
Examples
Example 1:
Input:adjacencyList = [[], [2, 3], [3, 4], []], root = 1
Output:minimum path: 1 -> 2 -> 3 -> 4
Explanation: The minimum path that visits all nodes exactly once in the given tree is 1 -> 2 -> 3 -> 4.
Example 2:
Input:adjacencyList = [[], [2, 3], [3, 4, 5], [4]], root = 1
Output:minimum path: 1 -> 2 -> 3 -> 4 -> 5
Explanation: The minimum path that visits all nodes exactly once in the given tree is 1 -> 2 -> 3 -> 4 -> 5.
Example 3:
Input:adjacencyList = [[], [2, 3], [3, 4], [5, 6]], root = 1
Output:minimum path: 1 -> 2 -> 3 -> 4 -> 5 -> 6
Explanation: The minimum path that visits all nodes exactly once in the given tree is 1 -> 2 -> 3 -> 4 -> 5 -> 6.
Constraints
- The tree is represented as an adjacency list.
- Each node in the tree represents a unique value.
- The tree is connected, meaning that all nodes are reachable from the root node.
- Duplicate nodes can exist in the tree.
- The tree can have multiple paths that visit all nodes exactly once.
Time: O(V + E) Space: O(V + E)
A more efficient approach is to use a Breadth-First Search (BFS) algorithm. Traverse the tree from the root node, keeping track of the nodes you have visited, and using a queue to store the nodes to be visited next.
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