Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Exponential Search
Exponential search is also known as doubling or galloping search. This mechanism is used to find the range where the search key may present. If L and U are the upper and lower bound of the list, then L and U both are the power of 2. For the last section, the U is the last position of the list. For that reason, it is known as exponential.
After finding the specific range, it uses the binary search technique to find the exact location of the search key.
The complexity of Exponential Search Technique
- Time Complexity: O(1) for the best case. O(log2 i) for average or worst case. Where i is the location where search key is present.
- Space Complexity: O(1)
Input and Output
Input: A sorted list of data: 10 13 15 26 28 50 56 88 94 127 159 356 480 567 689 699 780 850 956 995 The search key 780 Output: Item found at location: 16
Algorithm
binarySearch(array, start, end, key)
Input: An sorted array, start and end location, and the search key
Output − location of the key (if found), otherwise wrong location.
Begin if start <= end then mid := start + (end - start) /2 if array[mid] = key then return mid location if array[mid] > key then call binarySearch(array, mid+1, end, key) else when array[mid] < key then call binarySearch(array, start, mid-1, key) else return invalid location End
exponentialSearch(array, start, end, key)
Input: An sorted array, start and end location, and the search key
Output: location of the key (if found), otherwise wrong location.
Begin if (end – start) <= 0 then return invalid location i := 1 while i < (end - start) do if array[i] < key then i := i * 2 //increase i as power of 2 else terminate the loop done call binarySearch(array, i/2, i, key) End
Example
#include<iostream>
using namespace std;
int binarySearch(int array[], int start, int end, int key) {
if(start <= end) {
int mid = (start + (end - start) /2); //mid location of the list
if(array[mid] == key)
return mid;
if(array[mid] > key)
return binarySearch(array, start, mid-1, key);
return binarySearch(array, mid+1, end, key);
}
return -1;
}
int exponentialSearch(int array[], int start, int end, int key){
if((end - start) <= 0)
return -1;
int i = 1; // as 2^0 = 1
while(i < (end - start)){
if(array[i] < key)
i *= 2; //i will increase as power of 2
else
break; //when array[i] corsses the key element
}
return binarySearch(array, i/2, i, key); //search item in the smaller range
}
int main() {
int n, searchKey, loc;
cout << "Enter number of items: ";
cin >> n;
int arr[n]; //create an array of size n
cout << "Enter items: " << endl;
for(int i = 0; i< n; i++) {
cin >> arr[i];
}
cout << "Enter search key to search in the list: ";
cin >> searchKey;
if((loc = exponentialSearch(arr, 0, n, searchKey)) >= 0)
cout << "Item found at location: " << loc << endl;
else
cout << "Item is not found in the list." << endl;
}Output
Enter number of items: 20 Enter items: 10 13 15 26 28 50 56 88 94 127 159 356 480 567 689 699 780 850 956 995 Enter search key to search in the list: 780 Item found at location: 16
3K+ Views
