Searching Arrays

COMP104 Array Sorting & Searching / Slide 2 Unordered Linear Search * Search an unordered array of integers for a value and save its index if the value is found. Otherwise, set index to -1. * Algorithm: Assume value not in array and set index = -1 Start with the first array element (index 0) WHILE(more elements in array){ If value found at current index, save index Try next element (increment index) }

COMP104 Array Sorting & Searching / Slide 3 Unordered Linear Search void main() { int A[8] = {10, 7, 9, 1, 17, 30, 5, 6}; int x, n, index; cout << "Enter search element: "; cin >> x; index = -1; for(n=0; n<8; n++) if(A[n]==x) index = n; if(index==-1) cout << "Not found!!" << endl; else cout << "Found at: " << index << endl; }

COMP104 Array Sorting & Searching / Slide 4 Ordered Linear Search * Search an ordered array of integers for a value and save its index if the value is found. Otherwise, set index to -1. * The key difference in design is that this array is ordered. * If we perform a linear search, and find that we have already passed where the element might be found, we can quit early.

COMP104 Array Sorting & Searching / Slide 5 Ordered Linear Search void main() { int A[8] = { 1, 5, 6, 7, 9, 10, 17, 30}; int x, n, index; cout << "Enter search element: "; cin >> x; index = -1; for(n=0; n<8 && A[n]<=x; n++) if(A[n] == x) index = n; if(index==-1) cout << "Not found!!" << endl; else cout << "Found at: " << index << endl; }

COMP104 Array Sorting & Searching / Slide 6 Binary Search * Search an ordered array of integers for a value and save its index if the value is found. Otherwise, set index to -1. * Binary search takes advantage of the sorting, to search the array efficiently.

COMP104 Array Sorting & Searching / Slide 7 Binary Search * Binary search is based on a divide-and- conquer strategy which works as follows: n Start by looking at the middle element of the array  1. If the value it holds is lower than the search element, eliminate the first half of the array.  2. If the value it holds is higher than the search element, eliminate the second half of the array. n Repeat this process until the element is found, or until the entire array is eliminated.

COMP104 Array Sorting & Searching / Slide 8 Binary Search void main() { int A[8] = {1, 5, 6, 7, 9, 10, 17, 30}; int x, lower, middle, upper; cout << "Enter search element: "; cin >> x; lower = 0; upper = 7;// array size - 1 middle = (lower + upper)/2; while(A[middle]!=x && lower<upper){ if(x<A[middle]) upper = middle - 1; else lower = middle + 1; middle = (lower + upper)/2; } if(A[middle]!=x) cout << "Not found!!" << endl; else cout << "Found at: " << middle << endl; }

Sorting Arrays

COMP104 Array Sorting & Searching / Slide 10 Sorting * To arrange a set of items in sequence. * About 25~50% of all computing power is used in sorting. * Possible reasons: n Many applications require sorting n Many applications perform sorting when they don't have to n Many applications use inefficient sorting algorithms

COMP104 Array Sorting & Searching / Slide 11 Sorting Applications * List of student ID names and numbers in a table (sorted by name) * List of scores before letter grade assignment (sorted by students' scores) * List of horses after a race (sorted by the finishing times) * To prepare an originally unsorted array for ordered binary searching

COMP104 Array Sorting & Searching / Slide 12 Some Sorting Methods * Selection sort * Bubble sort * Shell sort (a simple but faster sorting method) * Quick sort (a much faster sorting method for most applications)

COMP104 Array Sorting & Searching / Slide 13 Selection Sort * Selection sort performs sorting by repeatedly putting the largest element to the end of the unsorted part of the array until the whole array is sorted. * It is similar to the way that many people do their sorting.

COMP104 Array Sorting & Searching / Slide 14 Selection Sort * Algorithm 1. Define the unsorted part of the array as the entire array 2. While the unsorted part of the array has more than one element:  Find its largest element  Swap with last element  Reduce unsorted part of the array by 1

COMP104 Array Sorting & Searching / Slide 15 Selection Sort // Selection Sort of integers into ascending order int main(){ const int size = 9; int A[size] = { 10, 7, 9, 1, 9, 17, 30, 5, 6}; int i, rightmost, temp, max_index; for(rightmost=size-1; rightmost>0; rightmost--){ // find largest item max_index = 0; for(i=1; i<=rightmost; i++) if(A[i] > A[max_index]) max_index = i; // swap largest item with last item temp = A[max_index]; A[max_index] = A[rightmost]; A[rightmost] = temp; } cout << "The sorted array: "; for(i=0; i<size; i++) cout << A[i] << " "; cout << endl; return 0; }

COMP104 Array Sorting & Searching / Slide 16 Bubble Sort * Bubble sort examines the array from start to finish, comparing elements as it goes. * Any time it finds a larger element before a smaller element, it swaps the two. * In this way, the larger elements are passed towards the end. * The largest element of the array therefore "bubbles" to the end of the array. * It then repeats the process for the unsorted part of the array until the whole array is sorted.

COMP104 Array Sorting & Searching / Slide 17 Bubble Sort * Bubble sort works on the same general principle as shaking a soft drink bottle. * Right after shaking, the contents are a mixture of bubbles and soft drink, distributed randomly. * Because bubbles are lighter than the soft drink, they rise to the surface, displacing the soft drink downwards. * This is how bubble sort got its name, because the smaller elements "float" to the top, while the larger elements "sink" to the bottom.

COMP104 Array Sorting & Searching / Slide 18 Bubble Sort * Algorithm n Define the unsorted part of the array to be the entire array n While the unsorted part of the array has more than one element: 1. For every element in the unsorted part, swap with the next neighbor if it is larger than the neighbor 2. Reduce the unprocessed part of the array by 1

COMP104 Array Sorting & Searching / Slide 19 Bubble Sort // Bubble Sort of integers into ascending order int main(){ const int size = 9; int A[size] = { 10, 7, 9, 1, 9, 17, 30, 5, 6}; int i, rightmost, temp; for(rightmost=size-1; rightmost>0; rightmost--){ for(i=0; i<rightmost; i++){ if(A[i] > A[i+1] ){ // swap if greater temp = A[i]; A[i] = A[i+1]; A[i+1] = temp; } cout << "The sorted array: "; for(i=0; i<size; i++) cout << A[i] << " "; cout << endl; return 0; }