binary trees
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I've read the following statement and I cannot understand something within it "In all binary trees, there are at most 2^i nodes at level i + 1" what I cannot understand is that tree's levels start at level 0, however, if we apply what is written in this statement there will be no level 0 at all as it says level i + 1 which mean 0 + 1 = level 1, 1 + 1 = level 2, etc. So is this statement wrong?!!! or I am missing something?!!!
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I've read the following statement and I cannot understand something within it "In all binary trees, there are at most 2^i nodes at level i + 1" what I cannot understand is that tree's levels start at level 0, however, if we apply what is written in this statement there will be no level 0 at all as it says level i + 1 which mean 0 + 1 = level 1, 1 + 1 = level 2, etc. So is this statement wrong?!!! or I am missing something?!!!
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I read it in 2 books "Data Structures Through C in Depth" and "Data Structures and Algorithms in C++, 4th Edition" and even the link you gave to me saying "The root of the tree, therefore, is at level 0" which means that tree's level starts at 0. So I am confused because those books also saying that tree's level starts at 0?!!!
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I read it in 2 books "Data Structures Through C in Depth" and "Data Structures and Algorithms in C++, 4th Edition" and even the link you gave to me saying "The root of the tree, therefore, is at level 0" which means that tree's level starts at 0. So I am confused because those books also saying that tree's level starts at 0?!!!
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Well, that's correct if you say 2N (instead of 2(N-1)) as maximum number of nodes at level N.
I know it is correct to say 2^N, however, to say for level N+1 is what makes me confused because tree's level starts at level 0 which mean that N = 0 so if we apply the above statement it will be 2^0 for level 0 + 1 which means 1 node for level number 1 I hope you get what I meant.
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Well, that's correct if you say 2N (instead of 2(N-1)) as maximum number of nodes at level N.
I know it is correct to say 2^N, however, to say for level N+1 is what makes me confused because tree's level starts at level 0 which mean that N = 0 so if we apply the above statement it will be 2^0 for level 0 + 1 which means 1 node for level number 1 I hope you get what I meant
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I know it is correct to say 2^N, however, to say for level N+1 is what makes me confused because tree's level starts at level 0 which mean that N = 0 so if we apply the above statement it will be 2^0 for level 0 + 1 which means 1 node for level number 1 I hope you get what I meant.
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\* Level 0 2^0 = 1 node / \\ / \\/ \
* * Level 1 2^1 = 2 nodes
/ \ / \
* * * * Level 2 2^2 = 4 nodesIt is
2Nfor levelN. If you find written2N-1then levels are numbered differently, starting from1(instead of0).Thanks for your reply :) I just get confused a little bit as some books state that level start at 0 and others state that level starts at 1. We need a unified solution between those authors :)
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Thanks for your reply :) I just get confused a little bit as some books state that level start at 0 and others state that level starts at 1. We need a unified solution between those authors :)
