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Squaring an Inequality

An array X of...

Question

An array X of n distinct integers is interpreted as a complete binary tree. The index of the first element of the array is 0.

If the root node is at level 0, the level of element X[i], i $\neq$ 0, is

A

⌈ l o g_{2} (i + 1) ⌉

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B

⌈ l o g_{2} (i + 1) ⌉

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C

⌊ l o g_{2} i ⌋

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D

⌈ l o g_{2} i ⌉

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Solution

The correct option is B $⌈ l o g_{2} (i + 1) ⌉$

Index of every node is shown in the box. Floor (log (i + 1)) draw the tree and realise that the last element at each level is the best choice to arrive at a conclusion.

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