Structural Programming Course Content and Data Structures - PDF document

Structural Programming Course Content and Data Structures • Introduction • Vectors • Objects • Testing/Debugging Winter 2000 • Methods • Arrays • Tracing Programs • Searching CMPUT 102: Sorting • Object State • Files I/O • Sharing resources • Sorting Dr. Osmar R. Zaïane • Selection • Inheritance • Repetition • Recursion University of Alberta  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 1  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 2 2 Objectives of Lecture 23 Outline of Lecture 23 Sorting Sorting • The sorting problem • Introduce the problem of sorting collections; • Simple methods like bubble sort • Learn how to sort using a bubble sort • Selection sort example algorithm; • Selection sort code • Learn how to sort with the selection algorithm. • Complexity of selection sort  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 3  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 4 The Sort Problem Sorting Problem (con’t) • Given a container, with elements that can be • Given a container of n elements A[ 0 .. n-1 ] such compared, put it in increasing or decreasing that any elements x and y in the container A order. can be compared directly, either x<y, or x=y, or x>y. 0 1 2 3 4 5 6 7 8 9 25 50 10 95 75 30 70 55 60 80 • We want to permute the elements of A so that at the end A[ 0 ] ≤ A[ 1 ] ≤ … ≤ A[ n-1 ] (monotone non-decreasing), or A[ 0 ] ≥ A[ 1 ] ≥ … ≥ A[ n-1 ] 0 1 2 3 4 5 6 7 8 9 10 25 30 50 55 60 70 75 80 95 (monotone decreasing)  Dr. Osmar R. Zaïane, 2000  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 5 Structural Programming and Data Structures University of Alberta 6 1

The Order of Things Sorting • Numbers • There is often a need to put data in order. � -99 < -34< -6< 0 < 1 < 9 < 23 < 999 • Sorting is among the most basic and • Characters universal of computational problems. � A < B < C < D < E < F < …< X < Y < Z • There are hundreds of algorithms and � a < b < c < d < e < f < …< x < y < z variations on algorithms. � a < z < A < Z • Variety of sorting methods: internal vs. • Strings external, sorting in place vs. sorting with � “Abacus” < “Alpha” < “Hello” < “Memorization” auxiliary structures, etc. < “Memorize” < “Memory” < “Zebra”  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 7  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 8 One simple sorting method 35 18 22 97 61 10 Given a list: Outline of Lecture 23 Iterate over the collection and permute neighbours if necessary repeat iteration until no permutation possible. • The sorting problem 18 35 22 97 61 10 18 22 35 61 10 97 • Simple methods like bubble sort … • Selection sort example 18 22 35 97 61 10 18 22 35 10 61 97 • Selection sort code … • Complexity of selection sort 18 22 35 97 61 10 10 18 22 35 61 97 … 18 22 35 61 97 10 10 18 22 35 61 97 ...  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 9  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 10 The Bubble Sort 35 18 22 97 61 10 Given a list: public static void bubble_sort( int data[] ) { First pass of (compare and exchange) will send the largest to the last position. // Sort the given Array with selection sort method //(Ascending order) 35 18 22 97 61 10 18 22 35 61 10 97 ... … 18 35 22 97 61 10 int current, last; 18 22 35 10 61 97 ... 18 22 35 97 61 10 for ( last = data.length-1; last >=1; last--) 18 22 35 10 61 97 for ( current = 0; current < last; current++ ) ... 18 22 35 97 61 10 … if ( data[current] > data[current+1] ) this.exchange( data, current, current+1 ); 18 22 35 61 97 10 18 22 10 35 61 97 } … 10 18 22 35 61 97 18 22 35 61 10 97 ...  Dr. Osmar R. Zaïane, 2000  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 11 Structural Programming and Data Structures University of Alberta 12 2

Outline of Lecture 23 Selection Sort • The sorting problem • Look for the smallest element and exchange • Simple methods like bubble sort it with the element whose index is 0. • Selection sort example • Selection sort code 0 1 2 3 4 5 6 7 8 9 25 50 10 95 75 30 70 55 60 80 • Complexity of selection sort 0 1 2 3 4 5 6 7 8 9 10 50 25 95 75 30 70 55 60 80  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 13  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 14 Selection Sort (con’t) Selection Sort (con’t) • Look for the smallest element whose index • Look for the smallest element whose index is greater than or equal to 1 and exchange it is greater than or equal to 2 and exchange it with the element whose index is 1. with the element whose index is 2. 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 50 25 95 75 30 70 55 60 80 10 25 50 95 75 30 70 55 60 80 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 25 30 95 75 50 70 55 60 80 10 25 50 95 75 30 70 55 60 80  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 15  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 16 Selection Sort (con’t) Selection Sort (con’t) • Look for the smallest element whose index is greater than or equal to k and exchange it 0 1 2 3 4 5 6 7 8 9 with the element whose index is k (for k = 10 25 30 50 75 95 70 55 60 80 3, 4, …, n-1) 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 25 30 50 55 95 70 75 60 80 10 25 30 95 75 50 70 55 60 80 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 10 25 30 50 55 60 70 75 95 80 10 25 30 50 75 95 70 55 60 80  Dr. Osmar R. Zaïane, 2000  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 17 Structural Programming and Data Structures University of Alberta 18 3

Selection Sort (con’t) Outline of Lecture 23 • The sorting problem 0 1 2 3 4 5 6 7 8 9 10 25 30 50 55 60 70 75 95 80 • Simple methods like bubble sort • Selection sort example 0 1 2 3 4 5 6 7 8 9 • Selection sort code 10 25 30 50 55 60 70 75 95 80 • Complexity of selection sort 0 1 2 3 4 5 6 7 8 9 10 25 30 50 55 60 70 75 80 95  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 19  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 20 Selection Sort Algorithm Selection Sort Code INPUT : data: an array of int private void selectionSort(int anArray[]) { OUTPUT : data: sorted in ascending order // Sort the given Array with selection sort method (Ascending order) Method : int index; for ( first = 1; first < length - 1; first ++) { int smallIndex; find Smallest such that data[Smallest] is the for (index = 0; index < anArray.length - 1; index++) { smallest between data[first] and data[length-1]; smallIndex = this.getSmallest(anArray, index); permute Data[first] and Data[Smallest]; this.exchange(anArray, index, smallIndex); } } }  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 21  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 22 Code for method: getSmallest Code for method: exchange private int getSmallest(int anArray[], int start) { // Return the index of the smallest element private void exchange(int anArray[], int i, int j) { // of the given array whose index is greater // Exchange the elements of the array with // than or equal to the given start index. // the given two indexes. int smallestIndex; int index; int temp; smallestIndex = start; temp = anArray[i]; for (index = start + 1; index < anArray.length; index++) anArray[i] = anArray[j]; if (anArray[index] < anArray[smallestIndex]) anArray[j] = temp; smallestIndex = index; } return smallestIndex; }  Dr. Osmar R. Zaïane, 2000  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 23 Structural Programming and Data Structures University of Alberta 24 4

Complexity of Selection Sort Outline of Lecture 23 • How many comparison operations are required for a selection sort of an n -element container? • The sorting problem • The sort method executes getSmallest for the • Simple methods like bubble sort indexes: 0, 1, … n-2 . • Selection sort example • Each time getSmallest is executed for an index, it does: ( n - index) comparisons. • Selection sort code • The total number of comparisons is: • Complexity of selection sort ( n-0 ) + ( n-1 ) + … + ( n- ( n-2 )) = ( 1 + 2 + …+ n ) - 1 = n ( n + 1 ) - 1 ≈ n 2 for large n . 2 O( n 2 ) � Quadratic time complexity  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 25  Dr. Osmar R. Zaïane, 2000 Structural Programming and Data Structures University of Alberta 26 5