Shell Sort and Selection Sort Algorithm

It is a highly efficient sorting algorithm and is based
on insertion sort algorithm.
Shell Sort
This algorithm avoids large shifts as in case of
insertion sort, if the smaller value is to the far right
and has to be moved to the far left.

Uses insertion sort on a widely spread elements,
sort them and then sorts the less widely spaced
elements. This spacing is termed as interval.
Shell Sort
This interval is calculated based on Knuth's formula
(h = h * 3 +1) where − h is interval with initial
value 1

This algorithm is quite efficient for medium-sized
data sets as its average and worst case complexity
are of Ο(n), where n is the number of items.
Shell Sort

THEOREM:
 Any sorting algorithm that only swaps adjacent
elements has average time no faster than
(O(n^{2})).
 The Shell sort (named for its inventor, Donald Shell)
is an early and interesting attempt to do this.
Shell Sort

 Insertion sort is fastest when;
a) The array is nearly sorted.
b) The array contains only small number of
data items
Shell Sort
 Makes use of intrinsic strength of Insertion sort.
THEOREM:

Shell Sort
 Shell sort works well because :
a) It always deals with a small number of
elements.
b) Elements are moved a long way through
array with each swap this leaves it more
nearly sorted.
THEOREM:

Shell Sort Best Case:
Shell Sort
• The best case in the shell sort is when the
array is already sorted in the right order.
• The number of comparisons is less.

Shell Sort Worst Case:
Shell Sort
• The running time of Shell sort depends on the
choice of increment sequence.
• Pairs of increments are not necessarily relatively
prime and smaller increments can have little
effect.

Shell Sort
Interval Sequence:
 The sequence h1,h2,h3….ht is a sequence of
increasing integer values which will be used as a
sequence (from right to left) of interval values.

• Any sequence will work as long as it is increasing
and h1=1.
Shell Sort
• For any interval value, we all have A[i] <=A[i + h].
• An array A for which this is true is hk sorted.
• An array which is hk and is then hk-1 sorted remains
as hk sorted.

 Implementation of Shell Sort
Shell Sort

Selection Sort
 It sorts an array by repeatedly finding the minimum
element (considering ascending order) from
unsorted part and putting it at the beginning.
 The algorithm maintains two sub-arrays in a given
array.
1) The sub-array which is already sorted.
2) Remaining sub-array which is unsorted.

Selection Sort
 It is conceptually the simplest sorting algorithm.
 It is unstable sort and at the same time it can be
also stable.
 It is unstable sort and at the same time it can be
also stable.

Selection Sort
 Idea of Selection Sort: Largest-to-Smallest
• The first element of the sorted array will be the
one with the largest value.
• Second will be the largest element of the rest of
the array.
• Third will be the largest element of the new rest of
the array (initial array without the two already
sorted elements).

Selection Sort
HOW DOES SELECTION SORT WORKS?
1ST:
Find the index of the largest element and exchange
the position with the element at the last index.

2nd:
Decrement the last index
When the array ends like this, the sorting stops.
Selection Sort

Selection Sort
Three procedures inside the selection sort:
1. Comparison, the times of comparison in a n value
array is (n(n-1))/2.
2. Value Assignment, the times of value assignment
is between 0 to 3(n-1).
3. Exchanging, the times need is between 0 to (n-1).

 Implementation of Selection Sort
Selection Sort

Shell Sort and Selection Sort Algorithm

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