Q. Explain the insertion sort with a proper algorithm. What is the complication of insertion sort in the worst case?                                                                                                                              

Ans:

Insertion  Sort technique: One  of  the  easiest sorting algorithms is  the  insertion  sort.

Insertion sort comprises of n - 1 passes. For pass p = 2 through n, insertion sort assures that the elements in the positions 1 through p are in sorted order. Insertion sort makes use of the fact those elements in positions 1 through p - 1 are already known in the sorted order.

Void insertion_sort( input_type a[ ], unsigned int n )

{

unsigned int j, p;

input_type tmp;

a[0] = MIN_DATA;        /* sentinel */

for( p=2; p <= n; p++ )

{

tmp = a[p];

for( j = p; tmp < a[j-1]; j-- )

a[j] = a[j-1];

a[j] = tmp;

}

}

Because of the nested loops present, each of which can take n iterations, insertion sort is O(n2). Furthermore, this bound is tight, because input in reverse order can actually obtain this bound. A precise calculation shows that the test at line 4 can be executed at most of the p times for each value of p. By summing over all p gives a total of (n(n-1))/2 = O(n2).