Notes

Outline

COM1100 Fundamentals of Computer Science –Winter 2000 Lecture 18 02/24/00

Lecture today Array Search algorithm Linear Search Binary Search

Search algorithm A common requirement of many programs is to search a list (array) for a given element. Linear Search Binary Search

Linear Search In a linear search, which is also known as a sequential search, each item in the list is examined in the order in which it occurs in the list until the desired item is found or the end of the list is reached. Disadvantage and advantages: Р    Not efficient a    The algorithm is simple a    The list need not be in any particular order

Linear Search algorithm // function prototype int linearSearch(int list[], int size, int key); // function definition // this function returns the location of  key in the list // -1 is returned if the value is not found int linearSearch(int list[], int size, int key) { for (int i = 0; i < size; i++ ) { if (list[i] == key) return i; }   return -1; }

Linear Search // function call int grade[5] = {98, 87, 74, 65, 82}; int key; cout << "Enter the item you are searching for: "; cin >> key; cout << "The location is :" << linearSearch(grade,5,key)        << endl;

Binary Search In a binary search, the list must be in sorted order. The desired item is first compared to the element in the middle of the list (for lists with an even number of elements, either of the two middle elements can be used). Three possibilities present once the comparison is made: Case 1: the desired item may be equal to the middle element, Case 2: it may be greater than the middle element, Case 3: or it may be less than the middle element.

Binary Search In the first case, the search has been successful, and no further searches are required. In the second case, since the desired item is greater than the middle element, if it s found at all it must be in the upper part of the list. This means that the lower part of the list consisting of all elements from the list to the midpoint elements can be discards from any further search. In the third case, since the desired item is less than the middle element, if it s found at all it must be in the lower part of the list. This means that the upper part of the list consisting of all elements from the midpoint to the end of the list can be discards from any further search.

Binary search algorithm // function prototype int binarySearch(int list[], int size, int key); // function definition // this function returns the location of  key in the list // -1 is returned if the value is not found int binarySearch(int list[], int size, int key) { int left, right, middle; left = 0; right = size -1;  (refer to next slide)

Binary search algorithm – con’d while (left <= right) {   middle = (left + right) / 2; // find the middle element     // compare the desired element with the middle      if (key == list[middle]) { // if equal, return the position of the middle         return middle;     }     else if (key > list[middle]) { // if desired element is greater than the middle         left = middle + 1; // change the left pointer     }    else { // if desired element is less than the middle         right = middle -1; // change the right pointer     } } return -1; // if none of the element matches, return -1 }

Binary search algorithm – con’d // function call int list[] = {12, 23, 32, 45, 57, 68}; int key; cout << "Enter the item you are searching for: "; cin >> key; cout << "The location is :" << binarySearch(list, 6, key)  << endl;