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Editorial Team
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Asked: 2026-05-25T03:16:27+00:00

The following text is snippet from algorithms book. We could draw the binary trees

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The following text is snippet from algorithms book.

We could draw the
binary trees using rectangular boxes that are customary for linked
lists, but trees are generally drawn as circles connected by lines
because they are actually graphs. We also do not explicitly draw NULL
links when referring to trees because every binary tree with N
nodes would require N+1 NULL links.

My question is what does author mean every binary tree with N nodes would require N+1 null links? how author came with N+1 number?

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1 Answer

  1. Editorial Team

    You could prove this by mathematical induction.

    Base case

    1 node has 2 NULL links – satisfies the property.

    Inductive step

    Now assume that all trees with n-1 nodes have n NULL links. Then we wish to show, that all trees with n nodes have n+1 NULL links.

    Take any tree with n nodes, and pick one of the leaves. Remove this leaf. We now have a tree with n NULL links, per our assumption. If we add the leaf again, we lose one NULL link, but gain two. Thus, we have n – 1 + 2 = n+1 NULL links on the tree with n nodes.

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