已知下面的树，回答以下问题。

Given the tree below, answer the following questions.

如采用深度优先搜索，搜索的顺序是什么？ If depth-first search is used, what will be the order of the search?

选择
[選擇]
v1, v2, v3, v4, v5, v6
v1, v4, v2, v5, v6, v3
v1, v2, v4, v5, v3, v6
v4, v5, v2, v6, v3, v1

如采用广度优先搜索，搜索的顺序是什么？If breadth-first search is used, what will be the order of the search?

选择
[選擇]
v1, v2, v3, v4, v5, v6
v1, v4, v2, v5, v6, v3
v1, v2, v4, v5, v3, v6
v4, v5, v2, v6, v3, v1

Question

已知下面的树，回答以下问题。

Given the tree below, answer the following questions.

如采用深度优先搜索，搜索的顺序是什么？ If depth-first search is used, what will be the order of the search?

选择 
[選擇]
v1, v2, v3, v4, v5, v6
v1, v4, v2, v5, v6, v3
v1, v2, v4, v5, v3, v6
v4, v5, v2, v6, v3, v1

如采用广度优先搜索，搜索的顺序是什么？If breadth-first search is used, what will be the order of the search?

选择 
[選擇]
v1, v2, v3, v4, v5, v6
v1, v4, v2, v5, v6, v3
v1, v2, v4, v5, v3, v6
v4, v5, v2, v6, v3, v1

BlackTom AI · Accepted Answer

Depth-first search visits as deep as possible along each branch before backtracking, so with left-to-right child ordering the traversal is v1 → v2 → v4 → v5 → v3 → v6.

1) Relevant concepts:
- Depth-first search (DFS): follow a path to a leaf, then backtrack to explore other branches; typically implemented with a stack or recursion.
- Breadth-first search (BFS): level-order traversal using a queue; visit all nodes at depth d before nodes at depth d+1.

2) Step-by-step DFS reasoning (left child before right child):
- Start at root: visit v1.
- From v1 go to left child v2: visit v2.
- From v2 go to left child v4: visit v4. v4 is a leaf, so backtrack to v2.
- From v2 the next child is v5: visit v5. v5 is a leaf, backtrack to v2, then to v1.
- From v1 the next child is v3: visit v3.
- From v3 go to its child v6: visit v6. v6 is a leaf; traversal complete.
- DFS order collected: v1, v2, v4, v5, v3, v6.

(Intermediate “stack” view): push v1; push v2; push v4 (pop v4); back to v2 -> push v5 (pop v5); back to v1 -> push v3; push v6 (pop v6).

3) Step-by-step BFS reasoning:
- Level 0: visit v1.
- Level 1: visit v1’s children left-to-right: v2, v3.
- Level 2: visit children of v2 and v3 in queue order: v4, v5 (children of v2), then v6 (child of v3).
- BFS order: v1, v2, v3, v4, v5, v6.

4) Why the correct answers are correct:
- DFS rule forces full exploration down v2’s subtree (v4 then v5) before visiting the right subtree of v1 (v3 and v6), producing v1, v2, v4, v5, v3, v6.
- BFS rule forces level-order, yielding v1, then v2 and v3, then v4, v5, v6.

5) Why other options are incorrect (brief):
- Any DFS option that visits v3 or v6 before finishing v2’s subtree contradicts DFS left-to-right behavior (e.g., v1, v4, v2,... or starting at v4).
- Any BFS option that does not list v2 before v3 or mixes levels (e.g., v1, v4, v2, ...) breaks level-order sequencing.

Conclusion: The DFS order is v1, v2, v4, v5, v3, v6 and the BFS order is v1, v2, v3, v4, v5, v6, matching the provided answers.

类似问题

TTrave_Alg_3 Which one of the pseudocode given below is written for post-order traversal of a Binary Search Tree?

TTrave_2 Consider the post-order traversal of the following BST. Note that visiting the node is actually printing the node. Which node is printed 5th?

How does In-Order traversal work in a Binary Tree?

Which tree traversal method visits the nodes level by level starting from the root?

Visiting the left subtree, then the node, then the right subtree is called:

Provide the result of post-order traversal of the following Binary Search Tree (BST) as a sequence of nodes.

What is the sequence of ordering for the nodes of the following BST?

Question at position 19 Given a binary tree of height 3 with 5 nodes and the preorder traversal ABCDE Which nodes must be the rootCABDE

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