CS 161Introduction to Programming

and Problem Solving

Chapter 22Sorting Methods

Herbert G. Mayer, PSUStatus 9/8/2014

Initial content copied verbatim fromECE 103 material by prof. Phillip Wong @ PSU

Syllabus Sorting Bubble Sort Sorting Algorithms Insertion Sort Pseudo Code

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Sorting is the process of arranging a collection of items in a specified order

Each sorting algorithm has its own unique advantages and disadvantages

Popular sorting algorithms:(computational time complexity – average case)

• Bubble sort O(n2)• Selection sort O(n2)• Insertion sort O(n2)• Shell sort O(nlog2n)

• Merge sortO(nlogn)

• Heap sortO(nlogn)

• Quick sortO(nlogn)

See: http://en.wikipedia.org/wiki/Sorting_algorithm

Sorting

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Bubble Sort

In a double nested loop across all elements: Look at all pairs of elements Pick the larger of the 2 in a pair And place the larger into the lower indexed array element, if

increasing order In the end the array is sorted in increasing (or non-

descending) order For decreasing order, reverse the logic

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Bubble Sort

#include <stdio.h>

#define LIMIT 12

int a[ LIMIT ] ={ 1, -1, 2, -2, 100, -100, 55, -55, 7, 77, 777, 7777 };

void print( char * msg ){ // print int i; printf( "%s array a{%d] = ", msg, LIMIT ); for( i = 0; i < LIMIT; i++ ) { printf( "%d ", a[ i ] ); } //end for printf( "\n" );} //end print

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Bubble Sort1: Remember Where to exchangevoid sort() // sort in non-descending order{ // sort int inner, outer, index, max, temp;

for( outer = 0; outer < LIMIT-1; outer++ ) { max = a[ outer ]; index = outer; for( inner = outer+1; inner < LIMIT; inner++ ) { if( a[ inner ] > max ) { // found larger index = inner; max = a[ inner ]; } //end if } //end for if( a[ outer ] < max ) { // then swap them out temp = a[ outer ]; a[ outer ] = max; a[ index ] = temp; } //end if } //end for} //end sort

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Bubble Sort2; Exchange (swap()) on the Flyvoid swap( int * a_ptr, int * b_ptr ) //sort non-descending{ // swap int temp = *a_ptr; // remember what a_ptr points to *a_ptr = *b_ptr; // overwrite it *b_ptr = temp; // completed the swap} //end swap void sort(){ // sort int inner, outer;

for( outer = 0; outer < LIMIT-1; outer++ ) { for( inner = outer+1; inner < LIMIT; inner++ ) { if( a[ inner ] > a[ outer ] ) {

// swap right away swap( & a[ inner ], & a[ outer ] ); } //end if } //end for } //end for} //end sort

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Insertion Sort (from Wikipedia article)

“Insertion sort is a sorting algorithm that is relatively efficient for small lists and mostly sorted lists.”

Elements from the list are taken one at a time and inserted in their correct position in a new sorted list.

Ai > Ai Ai …

Partially sorted Unsorted data

Ai Ai > Ai …

Partially sorted Unsorted data

Insert

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“… the new list and the remaining elements can share the array's space, but insertion is expensive, requiring shifting all following elements over by one”

Computational complexity:Worst case O(n2)

Best case O(n)

Average case O(n2)

Ascending insertion sort example from Wikipedia

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Pseudocode:

FUNCTION Insertion_Sort(array A) // zero index based array// Outer loop selects Ai from unsorted sideFOR i = 1 to size(A)-1

value = Ai

j = i-1// Inner loop shifts elements on partially sorted side to make room for Ai.

WHILE j >= 0 and Aj > valueAj+1 = Aj

j = j-1END WHILEAj+1 = value // Insert Ai in its place on partially sorted side

END FOREND FUNCTION

Ai

0 1 2 … i-1 i i+1 … Size-1

0 1 2 3 4 5 6 7

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Implementation for integer array:

void Insertion_Sort( int A[], int size ){ // Insertion_Sort

int value, i, j;for( i = 1; i <= size-1; i++ ) {

value = A[i];j = i-1;while( j >= 0 && A[j] > value ) {

A[j+1] = A[j];j = j-1;

} //end whileA[j+1] = value;

} //end for} //end Insertion_Sort