Question

Given the recursive bubble sort algorithm, analyze its time complexity in terms of Big O.

bubbleSort(A[], n)

{

// Base case

if (n == 1)

return;

// One pass of bubble sort. After

// this pass, the largest element

// is moved (or bubbled) to end.

for (i=0; i<n-1; i++)

if (A[i] > A[i+1])

swap(A[i], A[i+1]);

// Largest element is fixed,

// recur for remaining array

bubbleSort(A, n-1);

}

Answer #1

The true analysis of algorithm depends on the actual array because of the condition A[i] > A[i+1]

However, to determine the complexity in terms of Big O notation
i.e. upper bound, we consider the worst case which is the array
sorted in **descending order**.

(n-1 is added because of iterations from 0 to n-2)

With base case as and

Observing the pattern we find that,

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