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Linear and Binary Search

Instructor: Mainak Chaudhurimainakc@cse.iitk.ac.in

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Linear searchclass LinearAndBinarySearch { public static void main (String arg[]) { int size = 20, key = 23; int array[] = new int[size];

Initialize (array, size); // not shown PrintArray (array, size); // not shown System.out.println (“Linear search result:

” + LinearSearch (array, key)); System.out.println (“Binary search

result: ” + BinarySearch (array, 0, size-1, key));

}

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Linear search public static int LinearSearch (int

array[], int key) { int i;

for (i=0;i<array.length;i++) { if (array[i] == key) { return i; } } return -1; }

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Binary search public static int BinarySearch (int array[],

int start, int end, int key) { // Pre-condition: array is sorted // Caution: binary search does not work // on unsorted arrays. int mid; if (start > end) return -1; if (start == end) { if (key == array[start]) return start; else return -1; } // continued in next slide

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Binary search mid = (start + end)/2; if (key == array[mid]) return mid; else if (key < array[mid]) { return BinarySearch (array, start, mid-1,

key); } else { return BinarySearch (array, mid+1, end,

key); } }} // end class

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Run time analysis• Linear search in the worst case

requires n comparisons• Binary search in the worst case

requires O(log n) comparisons– Solution to T(n) = T(n/2) + O(1)– Remember that binary search can be

applied to sorted arrays only