Mr Kotiyana - Java Interview Questions

Binary search is one of the fundamental algorithms in computer science. In order to explore it, well first build up a theoretical backbone, then use that to implement the algorithm properly and avoid those nasty off-by-one errors everyones been talking about. Finding a value in a sorted sequence
In its simplest form, binary search is used to quickly find a value in a sorted sequence (consider a sequence an ordinary array for now).

Well call the sought value the target value for clarity. Binary search maintains a contiguous subsequence of the starting sequence where the target value is surely located. This is called the search space . The search space is initially the entire sequence. At each step, the algorithm compares the median value in the search space to the target value. Based on the comparison and because the sequence is sorted, it can then eliminate half of the search space.

By doing this repeatedly, it will eventually be left with a search space consisting of a single element, the target value. For example, consider the following sequence of integers sorted in ascending order and say we are looking for the number 55:

We are interested in the location of the target value in the sequence so we will represent the search space as indices into the sequence. Initially, the search space contains indices 1 through 11. Since the search space is really an interval, it suffices to store just two numbers, the low and high indices. As described above, we now choose the median value, which is the value at index 6 (the midpoint between 1 and 11): this value is 41 and it is smaller than the target value. From this we conclude not only that the element at index 6 is not the target value, but also that no element at indices between 1 and 5 can be the target value, because all elements at these indices are smaller than 41, which is smaller than the target value.

This brings the search space down to indices 7 through 11:

Proceeding in a similar fashion, we chop off the second half of the search space and are left with: Depending on how we choose the median of an even number of elements we will either find 55 in the next step or chop off 68 to get a search space of only one element. Either way, we conclude that the index where the target value is located is 7. If the target value was not present in the sequence, binary search would empty the search space entirely. This condition is easy to check and handle. Here is some code to go with the description: binary_search(A, target): lo = 1, hi = size(A) while lo <= hi: mid = lo + (hi-lo)/2 if A[mid] == target: return mid else if A[mid] < target: lo = mid+1 else: hi = mid-1 // target was not found Complexity :
Since each comparison binary search uses halves the search space, we can assert and easily prove that binary search will never use more than (in big-oh notation) O (log N ) comparisons to find the target value. The logarithm is an awfully slowly growing function.

In case youre not aware of just how efficient binary search is, consider looking up a name in a phone book containing a million names. Binary search lets you systematically find any given name using at most 21 comparisons. If you could manage a list containing all the people in the world sorted by name, you could find any person in less than 35 steps. Program : Java implementation of recursive Binary Search class BinarySearch { // Returns index of x if it is present in arr[l..r], else // return -1 int binarySearch(int arr[], int l, int r, int x) { if (r>=l) { int mid = l + (r - l)/2; // If the element is present at the middle itself if (arr[mid] == x) return mid; // If element is smaller than mid, then it can only // be present in left subarray if (arr[mid] > x) return binarySearch(arr, l, mid-1, x); // Else the element can only be present in right // subarray return binarySearch(arr, mid+1, r, x); } // We reach here when element is not present in array return -1; } public static void main(String args[]) { BinarySearch ob = new BinarySearch(); int arr[] = {2,3,4,10,40}; int n = arr.length; int x = 10; int result = ob.binarySearch(arr,0,n-1,x); if (result == -1) System.out.println("Element not present"); else System.out.println("Element found at index "+result); } } Output: Element is present at index 3 Program: Iterative implementation of Binary Search class BinarySearch { // Returns index of x if it is present in arr[], else // return -1 int binarySearch(int arr[], int x) { int l = 0, r = arr.length - 1; while (l <= r) { int m = l + (r-l)/2; // Check if x is present at mid if (arr[m] == x) return m; // If x greater, ignore left half if (arr[m] < x) l = m + 1; // If x is smaller, ignore right half else r = m - 1; } // if we reach here, then element was not present return -1; } public static void main(String args[]) { BinarySearch ob = new BinarySearch(); int arr[] = {2, 3, 4, 10, 40}; int n = arr.length; int x = 10; int result = ob.binarySearch(arr, x); if (result == -1) System.out.println("Element not present"); else System.out.println("Element found at index "+result); } } Output: Element is present at index 3 Bubble Sort Bubble sort algorithm is known as the simplest sorting algorithm. In bubble sort algorithm, array is traversed from first element to last element. Here, current element is compared with the next element.

If current element is greater than the next element, it is swapped.

Program: Bubble sort program in java public class BubbleSortExample { static void bubbleSort( int [] arr) { int n = arr.length; int temp = ; for ( int i= ; i < n; i++){ for ( int j= ; j < (n-i); j++){ if (arr[j- ] > arr[j]){ //swap elements temp = arr[j- ]; arr[j- ] = arr[j]; arr[j] = temp; } } } } public static void main(String[] args) { int arr[] ={ , , , , , , }; System.out.println( "Array Before Bubble Sort" ); for ( int i= ; i < arr.length; i++){ System.out.print(arr[i] + " " ); } System.out.println(); bubbleSort(arr); //sorting array elements using bubble sort System.out.println( "Array After Bubble Sort" ); for ( int i= ; i < arr.length; i++){ System.out.print(arr[i] + " " ); } } } Output: Array Before Bubble Sort 3 60 35 2 45 320 5 Array After Bubble Sort 2 3 5 35 45 60 320 Insertion sort Insertion sort is a simple sorting algorithm that works the way we sort playing cards in our hands. Algorithm
Step 1 If it is the first element, it is already sorted. return 1; Step 2 Pick next element Step 3 Compare with all elements in the sorted sub-list Step 4 Shift all the elements in the sorted sub-list that is greater than the value to be sorted Step 5 Insert the value Step 6 Repeat until list is sorted