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/**

* LinearSearch: search a sorted array by resursively dividing the array into half.

*

* Time complexity: O(Logn).

* Space complexity:

* - Recursively: O(Logn).

* - Iteratively: O(1).

*

* Every time, compare x with the middle element of the array.

* - If x matches with the middle element, return the mid index;

* - Else if x is greater than the mid element, go to right half of the array;

* - Otherwise, go to the left half.

*

*/

public class TernarySearch {

public static int searchRecursively(int arr[], int x) {

return ternarySearch(arr, 0, arr.length - 1, x);

}

public static int searchIteratively(int arr[], int x) {

return ternarySearch(arr, x);

}

// Recursively

public static int ternarySearch(int arr[], int l, int r, int x) {

if (r >= l) {

int mid1 = l + (r - l)/3;

int mid2 = mid1 + (r - l)/3;

if (arr[mid1] == x) return mid1;

if (arr[mid2] == x) return mid2;

if (arr[mid1] > x) return ternarySearch(arr, l, mid1-1, x);

if (arr[mid2] < x) return ternarySearch(arr, mid2+1, r, x);

return ternarySearch(arr, mid1+1, mid2-1, x);

}

return -1;

}

// Iteratively

public static int ternarySearch(int arr[], int x) {

int l = 0;

int r = arr.length - 1;

while (l <= r) {

int mid1 = l + (r - l)/3;

int mid2 = mid1 + (r - l)/3;

if (arr[mid1] == x) return mid1;

if (arr[mid2] == x) return mid2;

if (arr[mid1] > x) {

r = mid1 - 1;

continue;

}

if (arr[mid2] < x) {

l = mid2 + 1;

continue;

}

}

return -1;

}

public static void main(String[] args) {

int[] arr = {3, 5, 7, 10, 15, 20};

System.out.println(TernarySearch.searchIteratively(arr, 10));

System.out.println(TernarySearch.searchIteratively(arr, 1));

}

}