SORTING ALGORITHMS

SELECTION SORT

Selection Sort(Cards Example)

Initial Configuration

(search all cards and find the largest)

Swap the two cards

As before, the swap is performed in three steps.

Sorted Unsorted

Among the remaining cardsthe king is the largest.

It will remain in place.

But the algorithm may performSome empty operations(ie., swap it with itself in place)

Sorted Unsorted

Among the remaining cardsthe queen is the largest.

It will remain in place.

But the algorithm may performSome empty operations(i.e., swap it with itself in place)

Sorted Unsorted

Among the remaining cardsthe Jack is the largest.

It will remain in place.

But the algorithm may performSome empty operations(i.e., swap it with itself in place)

As before, the swap is performed in three steps.

Sorted Unsorted

We are down to the last card.Because there is only one and Because we know that it is Smaller than all the restWe don’t need to do anything Else with it. This is why the Algorithm goes up to < N-1

Sorted

All cards are now sorted.

Selection Sort

[http://web.ics.purdue.edu/~cs154/lectures/lecture010.htm]

Example:SelectionSort

[http://web.ics.purdue.edu/~cs154/lectures/lecture010.htm]

Example: Selection Sort.c

// Selection Sort#include <stdlib.h>#define N 6int main() {

int a[N]= { 23, 78, 45, 8, 32, 56}; int i,j; // Sort the array using Selection Sort int minIndex; for(i=0; i < N-1; i++) { // find the minimum element in the unsorted part of the array minIndex=i; for(j=i+1; j < N; j++) if(a[j] < a[minIndex]) minIndex = j;

// Swap a[i] with the smallest element int temp = a[i]; a[i] = a[minIndex]; a[minIndex] = temp; } system("pause");

}

Time Complexity• Analysis of the worst case:

– Outer loop executes N-1 times (no exch rqd. for final element).– Inner loop executes N-i-1 comparisons. (N-1) + (N-2) + … + 2 + 1 = N*(N-1)/2 = O(N2)The worst case occurs if the array is already sorted in descending

order. Best Case = O (n^2) Average Case = O(n^2)

Selection sort is an inplace sorting algorithm. So its takes constant O(1) space.

Advantages– Easy to write– Can be done “in place”– Can be done on linked lists too (keep a tail

pointer)

Disadvantages– It is about N2 even in the best case for

comparisons.– So the running time (over all inputs) is

approximately O(N2).– The primary disadvantage of selection sort is

its poor efficiency when dealing with a huge list of items.