How many nodes are there in a full complete binary tree of level 6?
a) 40 b) 31 c) 127 d) 128
A binary tree's level starts at 0, a full complete binary tree has 2^i nodes at level i. At level 0 there is 1 node, at level 1 there are 2 nodes and it goes on.
There are 2^0 + 2^1 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 = 2 ^ (6+1) - 1 = 2^7 - 1 = 127 nodes.
A level is also called the height of the binary tree. In a full complete binary tree of height 'h' there are 2^(h+1) - 1 nodes.
2^0+ 2^1+ 2^2 + 2^3+...................... +2^h = 2^(h+1) - 1
A full binary tree (sometimes proper binary tree or 2-tree) is a tree in which every node other than the leaves has two children. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes in the last level are filled in left to right order.
In a complete binary tree of height 2, there can be 4 minimum number of nodes and 7 maximum number of nodes.
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