### Explaining the binary tree

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##### Reference no: EM1318107

The left spine of the binary tree is a path starting at root and following only left-child pointers down to a leaf. State the expected number of nodes in left spine of an n-node treap.

a) What is the expected number of leaves in an n-node treap?

b) Prove that expected number of the proper descendants of any node in the treap is exactly equal to expected depth of that node.

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