GATE Overflow | Mock GATE | Test 1 | Question: 49

Question

The path length of a node is defined as the number of edges from root to that node. For a given full binary tree, the sum of path length of all leaf nodes is equal to $16$. The total number of internal nodes present is equal to $5$. What is the sum of path length of all internal nodes?

(Note: A full binary tree is a tree in which every node other than the leaves has 2 children)

Comments

Can confirm, in the test the options don't show.

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@pritishcBut it happened two times for me..

once while writing the exam and when i opened the exam for screen shot.. I thought it was a problem for everyone. Thanks for confirmation :)

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Can someone update with answer? and @Ruturaj Mohanty its still not showing options.

Answer 1

The answer is 5 as there are 3 Internal nodes according to this question out of which 2 internal node has path length 2 and 1 internal node has path length 1

Therefore, sum of path length = 2*2 +1 = 5.

Answer 2

In the question it isn't mentioned  if the tree is binary or complete. You can't draw a tree with internal path length 6 and 8 internal nodes. The internal path length should be at least 7(1 root node and 7 non-leaf, non-root node). Internal path length = 6 means there can be maximum 6 internal nodes with path length 1 from root, but internal nodes are mentioned 8. So, there has to be at least 7 nodes with path length 1 from root. Making internal path length 7!

Please verify!

Comments

I have updated the description to full binary tree.