Question 1:
It is known that the sequences of post-root traversal and mid-root traversal of a binary tree are: ACDBGIHFE and ABCDEFGHI, respectively,
Please draw this binary tree and write the sequence of its predecessors traversed
Root traversal sequence: EBADCFHGI
Problem solving ideas:
Let's find the root first
Back Root: Left and Right Root Middle Heel: Left Root Right
ACDB GIHF E ABCD E FGHI
We first look for the back root, this root must be behind this traversal, we can determine that E is the root
Then we find the position of E in the middle root traversal, so the left side of E is the left index node and the right side is the right index node
Now that the top number E is determined, then who is the root on the left exponent of E, and who is behind and who is the root: it is B
Then look at the root traversal, who is on the left of B and who is the left index: it is A; so:
Now only C and D are not drawn on the left index,
Fancy the root traversal to get: C and D are on the right side of B, look at the back root traversal and know that D is behind, so D is the root,
In the middle root traversal, C is to the left of D, so C is the left index of D;
So: take E as the left index of the root node to finish drawing
Next, look at the right index with E as the root node, first find the root node in the back root traversal, and who is behind who is the root node: it is F
Then find the F position in the middle root traversal, the left side of F is finished, so there is no left index, and then look at the right side: GHI
Go back to the post-root traversal to see GHI, and know that H is the root node, so:
Now only G and I are left unpainted, so go back to the middle root traversal and see that G is on the left of H and I is on the right of H, so:
If you want to know if the painting is correct, bring it into the question stem and see if his back root traversal and middle root traversal are correct.
Question two:
It is known that the sequence of pre-root traversal and mid-root traversal of a binary tree are: ABDGHCEFI and GDHBAECIF, respectively,
Please draw this binary tree and write the sequence of its post-root passes
The constructed binary tree is as follows
Post root traversal sequence: GHDBEIFCA
Problem- solving ideas:
first find the root
Tip root: Root left and right Middle root : Left root Right
A BDGH CEFI GDHB A ECIF
Look at the first root traversal and know that A is the root, and then find the position of A in the middle root traversal
So we know that GDHB is on the left of A and ECIF is on the right of A
Who is the root of GDHB? Back to the first root traversal, who is in front and who is the root, we know that it is B
Look at the middle root again, GDH is on the left of B, that is the left index of B
Who is the root of the GDH species? Look at the root, D is in front, then D is the root
Then go to the position of D in the middle root traversal, and know that the left is G and the right is H
Now that all left indices with A as the root node have been found, the right index is ECIF
Going back to the first root traversal, who is the root of the four who are in front, is C
Then go to the middle root traversal to find the position of C, E is on the left side of C (left index), IF is on the right side of C (right index)
Then IF who is the root? Go to the root traversal to find: F is first, F is the root
In the middle root traversal, I is to the left of F, so I is the left index of F