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Ternary Search
Like the binary search, it also separates the lists into sub-lists. This procedure divides the list into three parts using two intermediate mid values. As the lists are divided into more subdivisions, so it reduces the time to search a key value.
The complexity of Ternary Search Technique
- Time Complexity: O(log3 n)
- Space Complexity: O(1)
Input and Output
Input: A sorted list of data: 12 25 48 52 67 79 88 93 The search key 52 Output: Item found at location: 3
Algorithm
ternarySearch(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 midFirst := start + (end - start) /3 midSecond := midFirst + (end - start) / 3 if array[midFirst] = key then return midFirst if array[midSecond] = key then return midSecond if key < array[midFirst] then call ternarySearch(array, start, midFirst-1, key) if key > array[midSecond] then call ternarySearch(array, midFirst+1, end, key) else call ternarySearch(array, midFirst+1, midSecond-1, key) else return invalid location End
Example
#include<iostream> using namespace std; int ternarySearch(int array[], int start, int end, int key) { if(start <= end) { int midFirst = (start + (end - start) /3); //mid of first and second block int midSecond = (midFirst + (end - start) /3); //mid of first and second block if(array[midFirst] == key) return midFirst; if(array[midSecond] == key) return midSecond; if(key < array[midFirst]) return ternarySearch(array, start, midFirst-1, key); if(key > array[midSecond]) return ternarySearch(array, midSecond+1, end, key); return ternarySearch(array, midFirst+1, midSecond-1, key); } return -1; } 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 = ternarySearch(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: 8 Enter items: 12 25 48 52 67 79 88 93 Enter search key to search in the list: 52 Item found at location: 3
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