If a|b and a|c then b = am and c = an for some integer m and n. Hence, b + c = a(m + n). Therefore, a|(b+c).

Null case does not exist in complexity Theory.

This happens when the pivot is the smallest (or the largest) element. Then one of the partitions is empty, and we repeat recursively the procedure for N-1 elements.

Fibonacci is f(n) = f(n-1) + f(n-2), f(0) = 0, f(1) = 1. Let g(n) = 2n. Now prove inductively that f(n) > = g(n).

By the Division algorithm 12 = 3(4) + 0. Where remainder is 12 mod 3.

2+3+4+….6n = (n2 + n – 2) / 2.

In worst case nth comparison are required to insert the nth element into correct position.

The selection sort begins with finding the least element in the list. This element is moved to front and then the least element among the remaining elements. Is found and put into the second position and so on.

The worst case complexity of quick sort is O(n2).

The Worst case occur in linear search algorithm when Item is the last element in the array or is not there at all.