Why is the int I in the first for loop in the heapsort start at (n/2-1)? why not 0?

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Why is the int i in the first for loop in the heapsort start at (n/2-1)? Why not 0?
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Posted 22-Mar-20 20:56pm

JacksonSteel

Updated 22-Mar-20 21:19pm

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OriginalGriff · Answer 1 · 2020-03-22T21:20:00

Think about it.
n is the number of elements in the collection to be sorted.
So what is (n / 2 - 1)?
Simple: it's a the midpoint of the collection, and the last node that could possibly have children, using i = 1 ... n inclusive rather than 0 ... n - 1 inclusive for the indexes. All the nodes from n / 2 + 1 to n are leaves.

Heap algorithms tend to use 1 ... n notation because it makes the calculation of child node indices cleaner. When using this notation the children of node x are at 2x and 2x + 1, and the parent of x is at x / 2. If you use 0 ... (n - 1) then the children of node x are at 2x + 1 and 2x + 2, and the parent of node x is at (x - 1) / 2.