Searching Algorithm 5: Exponential Search

In this chapter we shall learn about below topics:

Exponential search is an improvement to binary search. We use this algorithm when we have large amount of data.

In exponential search algorithm we use binary search. But the difference is, we get the range of elements to search from and give that as input to binary search.

Initially we start with “1”. Then for each pass, we increase the gap 2 times every time.

Once we get our range, we give that range as input to binary search.

int exponential_search(arr[], int size, int key)
{
 
    int bound = 1;
    while (bound < size && arr[bound] < key) 
    {
    //for every pass, increase the gap 2 times.
        bound *= 2;
    }
 
    return binary_search(arr, key, bound/2, min(bound + 1, size));
}

Consider the array:
arr[] = {1, 2, 3, 4, 5, 6, 7, 8};
and the search key = 7;

Initially the bound value will be 1 for pass 1
Then the bound value will be 2 for pass 2
Then the bound value will be 4 for pass 3

Now we know the exact range of elements where our key element is present. 
Now we perform binary search on that range and return if we found the element or not.

#include<iostream>
#include <vector>
 
using namespace std;
 
 
void binarySearch(int arr[], int start, int end, int key) 
{ 
  if (end >= start) 
  { 
    int mid = start + (end - start)/2; 
 
    if (arr[mid] == key)
    {
      cout<<"Element found"<<endl;
      return; 
    }
 
    if (arr[mid] > key) 
      return binarySearch(arr, start, mid-1, key); 
 
    return binarySearch(arr, mid+1, end, key); 
  }
 
  cout<<"Element NOT found"<<endl;
  return; 
} 
 
 
 
void exponential_search(int arr[], int size, int key) 
{ 
  if (arr[0] == key)
  {
    cout<<"Element found"<<endl;
    return; 
  }
 
  int bound = 1; 
  while (bound < size && arr[bound] <= key)
  {
    cout<<"Bound = "<<bound<<endl;
    bound = bound*2; 
  }
 
  binarySearch(arr, bound/2,  min(bound + 1, size), key);
  return; 
} 
 
 
int main() 
{  
    int arr[] = {1, 2, 3, 4, 5, 6, 7, 8};
    int len = 8;
    int key = 7;
 
    exponential_search(arr, len, key);
 
    return 0; 
}

Element found

Time complexity is O(log i).