Algorithm of searching

Question 1

Linear Searching vs Binary Searching

Answer 1

A simple approach is to do linear search.The time complexity of above algorithm is O(n). Another approach to perform the same task is using Binary Search.
The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(Log n)

Question 2

Interpolaton Search

Answer 2

The idea of formula is to return higher value of pos
// when element to be searched is closer to arr[hi]. And
// smaller value when closer to arr[lo]
pos = lo + [ (x-arr[lo])*(hi-lo) / (arr[hi]-arr[Lo]) ]

Question 3

Binary Search vs Interpolation Search

Answer 3

Interpolation search works better than Binary Search for a sorted and uniformly distributed array.
On average the interpolation search makes about log(log(n)) comparisons (if the elements are uniformly distributed), where n is the number of elements to be searched. In the worst case (for instance where the numerical values of the keys increase exponentially) it can make up to O(n) comparisons.

Question 4

Ternary Search

Answer 4

Ternary search is a divide and conquer algorithm that can be used to find an element in an array. It is similar to binary search where we divide the array into two parts but in this algorithm, we divide the given array into three parts and determine which has the key (searched element). We can divide the array into three parts by taking mid1 and mid2 which can be calculated as shown below. Initially, l and r will be equal to 0 and n-1 respectively, where n is the length of the array.
mid1 = l + (r-l)/3
mid2 = r – (r-l)/3
Time Complexity:

O(\log _{3} n)

, where n is the size of the array.