Consider the following binary tree:

What is the order that nodes are visited during an in-order traversal of this tree? (give the answer as a string of letters with no separators, e.g. ABCDEFGHIJKLM)

Question

Consider the following binary tree:

What is the order that nodes are visited during an in-order traversal of this tree?  (give the answer as a string of letters with no separators, e.g. ABCDEFGHIJKLM)

BlackTom AI · Accepted Answer

Before diving into the traversal, I’ll restate what we’re analyzing: we need the in-order (left, root, right) visitation order for the given binary tree.

Option-independent setup: In-order traversal visits the left subtree first, then the current node, and finally the right subtree. Applying this repeatedly from the root yields the overall visitation sequence.

Step-by-step analysis of the left subtree of A (rooted at J):
- The left child of J is D, whose left child is E. Since E is a leaf, we visit E first, then D, and there is no right subtree for D. So the first part is E, D.
- After finishing the left subtree of J, we visit J itself.
- The right subtree of J is rooted at F. The left child of F is L (a leaf), so we visit L, then F, then the right child B. Thus the right subtree of J contributes L, F, B in that order.
- Putting the left and root and right parts together for the J subtree gives: E, D, J, L, F, B.

Now visiting the root A, we place A after the entire left subtree of A: E, D, J, L, F, B, A.

Step-by-step analysis of the right subtree of A (rooted at H):
- The left child of H is C. C has no left child and a right child I. For C, we first visit C, then the in-order traversal of I.
- I has left child K and right child M, both leaves. The in-order then is K, I, M for the I subtree. Therefore, the C subtree yields C, K, I, M.
- After finishing the left subtree of H, we visit H itself.
- The right subtree of H is G, a leaf, so G comes after H.
- Thus the entire right subtree of A contributes: C, K, I, M, H, G.

Combine both halves around the root A:
- Left of A: E, D, J, L, F, B
- Root: A
- Right of A: C, K, I, M, H, G

Full in-order visitation sequence: E D J L F B A C K I M H G

If you remove the spaces to produce a single string as requested, the in-order traversal should be: EDJLFBACKIMHG

Note: The provided answer string 'EDJLBAHCKIM' is missing letters F, G, and misorders certain elements relative to the tree structure. In a correct in-order traversal for this tree, F and G must appear in their respective positions, and the final sequence ends with G.

XLMC0202501 Topic 9 Quiz

Consider the following binary tree: What is the order that nodes are visited during an in-order traversal of this tree? (give the answer as a string of letters with no separators, e.g. ABCDEFGHIJKLM)

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