Given a binary tree, if the node order of the first-order traversal is: KDCEFGHB, the middle-order traversal is: CDFEGHKB, then the result of the subsequent traversal is ()

Binary tree traversal

Title description

(Single choice) Given a binary tree, if the node order of the first-order traversal is: KDCEFGHB, the middle-order traversal is: CDFEGHKB, then the result of the subsequent traversal is ()

• [ ] A. CFHGEBDK
• [ ] B. CDFEGHBK
• [ ] C. FGHCDEBK
• [x] D. CFHGEDBK

Tree traversal rules: (remember by root position)

• First order: (root left and right) root first
• Middle order: (left root right) root middle
• Post sequence: (left and right root) root last

Ideas:

1. First determine the root node
2. In determining the left subtree and the right subtree
   2.1 Find the root of the left subtree from the left subtree, and go back to step 1
   2.2 Find the root of the right subtree from the right subtree, go back to step 1
3. Until the search is completed, build the tree

Detailed analysis:

The first traversal in pre-order must be the root of the tree, then K is the root;
Then the two sides of K in the middle-order traversal are the left subtree and the right subtree respectively;
The left subtree is CDFEGH and the right subtree is B

        K
CDFEGH     B

The first order traversal in the left subtree is that D is the first in DCEFGH, and all D is the root of the left subtree;

C is the left subtree, FEGH is the right subtree

      K
  D        B
C   FEGH

In the FEGH subtree, the pre-order traversal is EFGH, and all E is the root of the subtree

F is the left subtree, GH is the right subtree

      K
  D        B
C    E
   F   GH

In the GH subtree, GH is traversed first, so G is the root and H is the right subtree

      K
  D        B
C    E
   F   G
         H

So the subsequent traversal is:

C F H G E D B K