Which of the following is incorrect with respect to binary trees?OptionsLet T be a binary tree. For every k ≥ 0, there are no more than 2k nodes in level k Let T be a binary tree with λ levels. Then T has no more than 2λ – 1 nodesLet T be a binary tree with N nodes. Then the number of levels is at least ceil(log (N + 1))Let T be a binary tree with N nodes. Then the number of levels is at least floor(log (N + 1))
Question
Which of the following is incorrect with respect to binary trees?OptionsLet T be a binary tree. For every k ≥ 0, there are no more than 2k nodes in level k Let T be a binary tree with λ levels. Then T has no more than 2λ – 1 nodesLet T be a binary tree with N nodes. Then the number of levels is at least ceil(log (N + 1))Let T be a binary tree with N nodes. Then the number of levels is at least floor(log (N + 1))
Solution
The incorrect statement with respect to binary trees is: "Let T be a binary tree with λ levels. Then T has no more than 2λ – 1 nodes".
This is incorrect because a binary tree with λ levels can have up to 2^λ - 1 nodes. For example, a binary tree with 3 levels can have up to 2^3 - 1 = 7 nodes. The statement is incorrect because it suggests that the number of nodes is less than or equal to 2λ – 1, which is not always the case.
Similar Questions
Let T be a binary tree. The nodes in level k can be at most 2k, where k ≥ 0.Let T be a binary tree with λ levels. Then T has no more than 2^λ – 1 nodesLet T be a binary tree with N nodes. Then the number of levels is at least ceil(log (N + 1))Let T be a binary tree with N nodes. Then the number of levels is at least floor(log (N + 1))
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