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What does "constant proportionality" mean in simple words?

English Language & Usage Asked by M K on December 5, 2020

I read this sentence from algorithm book:

The reason is that any split of constant proportionality yields a recursion tree of depth O(lg n).

What does mean by "constant proportionality" in a simple words?

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One Answer

For a quicksort, the "Big O" is the same, n lg n whether the binary tree is balanced or not. While n lg n makes sense if the tree is perfectly symmetrical, it also appears if the tree is highly asymmetrical (in the text, 99:1), as long as there is a constant proportion of asymmetricality (that is, all subtrees are 99:1).

Correct answer by rajah9 on December 5, 2020

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