CMPT 102 Introduction to Scientific Computer Programming

CMPT 102Introduction to Scientific Computer Programming Applications of Arrays Sorting and Searching

Putting numbers into order • There are many approaches to taking an array of numbers and putting those numbers into ascending or descending order. • Insertion Sort (see lab 6) • Selection Sort • Bubble Sort • Quick Sort

Unsorted Array A[13] 95 23 3 3 5 86 7 75 12 19 12 46 16 37 7 32 19 75 46 23 23 19 32 95 37 16 37 46 86 12 75 5 7 86 16 5 32 95 3 A[0] A[0] A[0] A[1] A[1] A[1] A{2] A{2] A{2] A[3] A[3] A[3] A[4] A[4] A[4] A[5} A[5} A[5} A[6] A[6] A[6] A[7] A[7] A[7] A[8] A[8] A[8] A[9] A[9] A[9] A[10] A[10] A[10] A[11] A[11] A[11] A[12] A[12] A[12] Sorted Array A[13]: Descending order Sorted Array A[13]: Ascending order Ascending / Descending Order

Selection Sort • A method to transform the unsorted array into a sorted array. This example sorts into ascending order, sorting into descending order is a parallel process. • Apply a simple algorithm to an array of length M • Start with N=M • Consider the last N elements in the array, A[M-N] to A[M] • Find the element that contains the smallest value in the group of elements defined in (2). Record the index I at which this smallest value is found. Smallest = A[i] • Swap the smallest value with the (M-N)th element • A[M-N] swaped with A[i] the smallest element • Decrease N by 1 and return to step 2 (until N<0)

3 23 23 3 3 23 12 12 12 19 19 19 7 7 7 75 75 75 46 46 46 95 95 95 37 37 37 86 86 86 5 5 5 16 16 16 32 32 32 A[0] A[0] A[0] A[1] A[1] A[1] A{2] A{2] A{2] A[3] A[3] A[3] A[4] A[4] A[4] A[5} A[5} A[5} A[6] A[6] A[6] A[7] A[7] A[7] A[8] A[8] A[8] A[9] A[9] A[9] A[10] A[10] A[10] A[11] A[11] A[11] A[12] A[12] A[12] Iteration 1: N=M Smallest element is A[1], switch with A[M-N]=A[0] After Iteration 1: M=N Sample Selection Sort: 1 Unsorted Array A[13]

32 32 32 3 3 3 23 23 5 12 12 12 19 19 19 7 7 7 75 75 75 46 46 46 95 95 95 37 37 37 86 86 86 5 5 23 16 16 16 A[0] A[0] A[0] A[1] A[1] A[1] A{2] A{2] A{2] A[3] A[3] A[3] A[4] A[4] A[4] A[5} A[5} A[5} A[6] A[6] A[6] A[7] A[7] A[7] A[8] A[8] A[8] A[9] A[9] A[9] A[10] A[10] A[10] A[11] A[11] A[11] A[12] A[12] A[12] Iteration 2: N=M-1 Smallest element is A[10], switch with A[M-N]=A[1] After Iteration 2: N=M-1 Sample Selection Sort: 2

3 5 12 19 7 75 46 95 37 86 23 16 32 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Iteration 3: N=M-2 3 5 12 19 7 75 46 95 37 86 23 16 32 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Smallest element is A[4], switch with A[M-N]=A[2] After Iteration 3: N=M-2 3 5 7 19 12 75 46 95 37 86 23 16 32 A[12] A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] Sample Selection Sort: 3

3 5 7 19 12 75 46 95 37 86 23 16 32 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Iteration 4: N=M-3 3 5 7 19 12 75 46 95 37 86 23 16 32 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Smallest element is A[4], switch with A[M-N]=A[3] 3 5 7 12 19 75 46 95 37 86 23 16 32 A[12] A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] Sample Selection Sort: 4 After Iteration 4: N=M-3

3 5 7 12 19 75 46 95 37 86 23 16 32 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Iteration 5: N=M-4 3 5 7 12 19 75 46 95 37 86 23 16 32 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Smallest element is A[11], switch with A[M-N]=A[4] 3 5 7 12 16 75 46 95 37 86 23 19 32 A[12] A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] Sample Selection Sort: 5 After Iteration 5: N=M-4

3 5 7 12 16 19 23 32 37 86 46 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 5 7 12 16 19 23 32 37 86 46 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 5 7 12 16 19 23 32 37 86 46 75 95 A[12] A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] Sample Selection Sort: 9 Iteration 9: N=M-8 Smallest element is A[8], switch with A[M-N]=A[8] After Iteration 9: N=M-8

3 5 7 12 16 19 23 32 37 86 46 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] Iteration 10: N=M-9 3 5 7 12 16 19 23 32 37 86 46 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] Smallest element is A[10], switch with A[M-N]=A[9] After Iteration 10: N=M-9 3 5 7 12 16 19 23 32 37 46 86 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Sample Selection Sort: 10 A[12] A[12]

3 5 7 12 16 19 23 32 37 46 86 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Iteration 11: N=M-10 3 5 7 12 16 19 23 32 37 46 86 75 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Smallest element is A[11], switch with A[M-N]=A[10] After Iteration 11: N=M-10 3 5 7 12 16 19 23 32 37 46 75 86 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Sample Selection Sort: 11

3 5 7 12 16 19 23 32 37 46 75 86 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Iteration 12: N=M-10 3 5 7 12 16 19 23 32 37 46 75 86 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Smallest element is A[12], switch with A[M-N]=A[12] After Iteration 13: N=M-10 3 5 7 12 16 19 23 32 37 46 75 86 95 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Sample Selection Sort: 12

Selection sort function

Bubble Sort • A method to transform the unsorted array into a sorted array. This example sorts into ascending order, sorting into descending order is a parallel process. • Apply a simple algorithm to an array of length M • Start with N=0 • Consider the array elements A[0] to A[M-1-N] • For each I, 0 <= i <M-1-N • Compare A[i] and A[i+1] and put in order • A[M-1-N] now contains the largest number, it is in order • Increase N by 1 and return to step 2 (until N=M-1)

Sample Bubble Sort: 1 Iteration 1: N=M A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 23 3 12 19 7 75 46 95 37 86 5 16 32 Compare A[M-N] and A[M-N+I], put in order 3 23 12 19 7 75 46 95 37 86 5 16 32 Compare A[M-N+1] and A[M-N+2], put in order 3 12 23 19 7 75 46 95 37 86 5 16 32 Compare A[M-N+2] and A[M-N+3], put in order 3 12 19 23 7 75 46 95 37 86 5 16 32 Compare A[M-N+3] and A[M-N+4], put in order 3 12 19 7 23 75 46 95 37 86 5 16 32 Compare A[M-N+4] and A[M-N+5], put in order 3 12 19 7 23 75 46 95 37 86 5 16 32 Compare A[M-N+5] and A[M-N+6], put in order

Sample Bubble Sort: 2 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 12 19 7 23 46 75 95 37 86 5 16 32 Compare A[M-N+6] and A[M-N+7], put in order 3 12 19 7 23 46 75 95 37 86 5 16 32 Compare A[M-N+7] and A[M-N+8], put in order 3 12 19 7 23 46 75 37 95 86 5 16 32 Compare A[M-N+8] and A[M-N+9], put in order 3 12 19 7 23 46 75 37 86 95 5 16 32 Compare A[M-N+9] and A[M-N+10], put in order 3 12 19 7 23 46 75 37 86 5 95 16 32 Compare A[M-N+10] and A[M-N+11], put in order 3 12 19 7 23 46 75 37 86 5 16 95 32 Compare A[M-N+11] and A[M-N+12], put in order 3 12 19 7 23 46 75 37 86 5 16 32 95

Iteration 2: N=M-1 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 12 19 7 23 46 75 37 86 5 16 32 95 Compare A[M-N] and A[M-N+I], put in order 3 12 19 7 23 46 75 37 86 5 16 32 95 Compare A[M-N+1] and A[M-N+2], put in order 3 12 19 7 23 46 75 37 86 5 16 32 95 Compare A[M-N+2] and A[M-N+3], put in order 3 12 7 19 23 46 75 37 86 5 16 32 95 Compare A[M-N+3] and A[M-N+4], put in order 3 12 7 19 23 46 75 37 86 5 16 32 95 Compare A[M-N+4] and A[M-N+5], put in order 3 12 7 19 23 46 75 37 86 5 16 32 95 Compare A[M-N+5] and A[M-N+6], put in order Sample Bubble Sort: 3

Sample Bubble Sort: 4 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 12 7 19 23 46 75 37 86 5 16 32 95 Compare A[M-N+6] and A[M-N+7], put in order 3 12 7 19 23 46 37 75 86 5 16 32 95 Compare A[M-N+7] and A[M-N+8], put in order 3 12 7 19 23 46 37 75 86 5 16 32 95 Compare A[M-N+8] and A[M-N+9], put in order 3 12 7 19 23 46 37 75 5 86 16 32 95 Compare A[M-N+9] and A[M-N+10], put in order 3 12 7 19 23 46 37 75 5 16 86 32 95 Compare A[M-N+9] and A[M-N+10], put in order 3 12 7 19 23 46 37 75 5 16 32 86 95

Sample Bubble Sort: 5 Iteration 3: N=M-2 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 12 7 19 23 46 37 75 5 16 32 86 95 Compare A[M-N] and A[M-N+I], put in order 3 12 7 19 23 46 37 75 5 16 32 86 95 Compare A[M-N+1] and A[M-N+2], put in order 3 7 12 19 23 46 37 75 5 16 32 86 95 Compare A[M-N+2] and A[M-N+3], put in order 3 7 12 19 23 46 37 75 5 16 32 86 95 Compare A[M-N+3] and A[M-N+4], put in order 3 7 12 19 23 46 37 75 5 16 32 86 95 Compare A[M-N+4] and A[M-N+5], put in order 3 7 12 19 23 46 37 75 5 16 32 86 95 Compare A[M-N+5] and A[M-N+6], put in order

Sample Bubble Sort: 6 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 7 12 19 23 37 46 75 5 16 32 86 95 Compare A[M-N+6] and A[M-N+7], put in order 3 7 12 19 23 37 46 75 5 16 32 86 95 Compare A[M-N+7] and A[M-N+8], put in order 3 7 12 19 23 37 46 5 75 16 32 86 95 Compare A[M-N+8] and A[M-N+9], put in order 3 7 12 19 23 37 46 5 16 75 32 86 95 Compare A[M-N+9] and A[M-N+10], put in order 3 7 12 19 23 37 46 5 16 32 75 86 95

Sample Bubble Sort: 7 Iteration 4: N=M-3 No changes in first 6 comparisons then continue with A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 7 12 19 23 37 46 5 16 32 75 86 95 Compare A[M-N+6] and A[M-N+7], put in order 3 7 12 19 23 37 5 46 16 32 75 86 95 Compare A[M-N+7] and A[M-N+8], put in order 3 7 12 19 23 37 5 16 46 32 75 86 95 Compare A[M-N+8] and A[M-N+9], put in order 3 7 12 19 23 37 5 16 32 46 75 86 95

Sample Bubble Sort: 12 Iteration 9: N=M-8 No changes in first 3 comparisons then continue with A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 7 5 12 16 19 23 32 37 46 75 86 95 Compare A[M-N+1] and A[M-N+2], put in order 3 5 7 12 16 19 23 32 37 46 75 86 95 Compare A[M-N+2] and A[M-N+3], put in order 3 5 7 12 16 19 23 32 37 46 75 86 95 Compare A[M-N+3] and A[M-N+4], put in order 3 5 7 12 16 19 23 32 37 46 75 86 95 All numbers are in order: We are done

Bubble Sort Function void BubbleSort(int InArray[], int M, int N) { int end; int j; int k; int temp; int sorted=FALSE; end = N; while(!sorted) { sorted = TRUE; for( k=M; k<end; k++) { if(InArray[k] > InArray[k+1] ) { sorted = FALSE; temp = InArray[k]; InArray[k] = InArray[k+1]; InArray[k+1] = temp; } } end--; } }

A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 23 3 12 19 7 75 46 95 37 86 5 16 32 Pivot, middle element Less than pivot 46 32 3 12 19 7 75 23 95 37 86 5 16 Pivot First element larger than pivot Less than pivot 32 3 12 19 7 75 23 95 37 86 5 16 48 Pivot First element smaller than pivot Less than pivot More than pivot 48 3 12 19 7 32 23 95 37 86 5 16 75 Pivot Less than pivot More than pivot 48 3 12 19 7 32 23 95 37 86 5 16 75 Pivot First element larger than pivot Sample Quick Sort: 1

More than pivot Less than pivot 48 3 12 19 7 32 23 95 37 86 5 16 75 Pivot First element smaller than pivot Less than pivot More than pivot 95 48 3 12 19 7 32 23 16 37 86 5 75 Pivot Less than pivot More than pivot 48 3 12 19 7 32 23 16 37 86 5 95 75 Pivot First element larger than pivot More than pivot Less than pivot 75 48 3 12 19 7 32 23 16 37 86 5 95 Pivot First element smaller than pivot Less than pivot More than pivot 48 3 12 19 7 32 23 16 37 5 86 95 75 Pivot Sample Quick Sort: 2 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12]

Less than pivot More than pivot 48 3 12 19 7 32 23 16 37 5 86 95 75 Pivot First element larger than pivot Less than pivot More than pivot 48 3 12 19 7 32 23 16 37 5 86 95 75 Pivot First element smaller than pivot Less than pivot More than pivot 5 3 12 19 7 32 23 16 37 48 86 95 75 Pivot 5 3 12 19 7 32 23 16 37 48 86 95 75 Less than pivot 5 3 12 19 7 32 23 16 37 48 86 95 75 Pivot, middle element Sample Quick Sort: 3 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12]

A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Less than pivot 7 5 37 3 12 19 32 23 16 48 86 95 75 Pivot First element larger than pivot Less than pivot 7 3 12 19 5 32 23 16 37 48 86 95 75 Pivot First element smaller than pivot Less than pivot More than pivot 3 5 19 12 32 23 16 7 37 48 86 95 75 Pivot Less than pivot 7 3 5 19 12 32 16 37 23 48 86 95 75 Pivot First element larger than pivot Less than pivot 7 3 5 19 12 32 23 16 37 48 86 95 75 Pivot Sample Quick Sort: 4 First element smaller than pivot

A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Less than pivot More than pivot 5 19 3 7 12 32 23 16 37 48 86 95 75 Pivot 5 3 7 19 37 16 32 23 12 48 86 95 75 3 5 7 19 12 32 16 37 23 48 86 95 75 86 95 75 3 5 7 19 37 16 32 23 12 48 Pivot, middle element Pivot 19 12 86 95 75 3 5 7 37 32 23 48 16 First element larger than pivot Sample Quick Sort: 5

A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 3 5 7 16 37 19 32 23 12 48 86 95 75 Pivot First element smaller than pivot 86 95 75 3 5 7 16 12 19 32 23 37 48 Pivot 3 5 7 16 12 19 32 23 37 48 86 95 75 Pivot First element larger than pivot More than pivot Pivot 86 95 75 3 5 7 16 12 19 32 23 37 48 First element smaller than pivot More than pivot 12 16 86 95 75 3 5 7 19 32 23 48 37 Pivot Sample Quick Sort: 6

A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 86 95 75 3 5 7 12 16 19 32 23 37 48 86 95 75 3 5 7 12 16 19 32 23 37 48 Pivot Pivot 86 95 75 3 5 7 12 16 32 19 23 37 48 Pivot 86 95 75 3 5 7 12 16 32 19 23 37 48 First element larger than pivot 86 95 75 3 5 7 12 16 32 19 23 37 48 First element smaller than pivot Pivot First element smaller than pivot Sample Quick Sort: 7

A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] 86 95 75 3 5 7 12 16 23 19 37 48 32 Pivot 86 95 75 3 5 7 12 16 23 19 32 37 48 86 95 75 3 5 7 12 16 23 19 32 37 48 86 95 75 3 5 7 12 16 19 23 32 37 48 Pivot Pivot 75 86 3 5 7 12 16 19 23 32 37 48 95 Sample Quick Sort: 8

Sample Quick Sort: 9 A[0] A[1] A{2] A[3] A[4] A[5} A[6] A[7] A[8] A[9] A[10] A[11] A[12] Pivot 3 5 7 12 16 19 23 32 37 48 86 95 75 First element larger than pivot 3 5 7 12 16 19 23 32 37 48 86 75 95 Pivot 75 95 3 5 7 12 16 19 23 32 37 48 86 3 5 7 12 16 19 23 32 37 48 86 75 95 Pivot

Quicksort function: 1 void Quicksort( int InArray[], int loBound, int hiBound ) { int pivot; int loSwap; int hiSwap; int temp; /* Zero or one item to sort */ if (loBound >= hiBound) { return; } /* Two items to sort */ if (hiBound-loBound == 1) { if (InArray[loBound] > InArray[hiBound]) { temp = InArray[loBound]; InArray[loBound] = InArray[hiBound]; InArray[hiBound] = temp; } return; }

Quicksort function: 2 /* 3 or more items to sort */ pivot = InArray[(loBound+hiBound)/2]; InArray[(loBound+hiBound)/2] = InArray[loBound]; InArray[loBound] = pivot; loSwap = loBound + 1; hiSwap = hiBound;

Quicksort function: 3 do { while (loSwap <= hiSwap && InArray[loSwap] <= pivot) { loSwap++; } while (InArray[hiSwap] > pivot) { hiSwap--; } if (loSwap < hiSwap) { temp = InArray[loSwap]; InArray[loSwap] = InArray[hiSwap]; InArray[hiSwap] = temp; } } while (loSwap < hiSwap);

Quicksort function: 4 /* put pivot back in correct position */ InArray[loBound] = InArray[hiSwap]; InArray[hiSwap] = pivot; Quicksort(InArray, loBound, hiSwap-1); Quicksort(InArray, hiSwap+1, hiBound); }

CMPT 102 Introduction to Scientific Computer Programming