Java/src/main/java/com/thealgorithms/searches/TernarySearch.java

package com.thealgorithms.searches;

import com.thealgorithms.devutils.searches.SearchAlgorithm;

/**
 * A ternary search algorithm is a technique in computer science for finding the
 * minimum or maximum of a unimodal function The algorithm determines either
 * that the minimum or maximum cannot be in the first third of the domain or
 * that it cannot be in the last third of the domain, then repeats on the
 * remaining third.
 *
 * <p>
 * Worst-case performance Θ(log3(N)) Best-case performance O(1) Average
 * performance Θ(log3(N)) Worst-case space complexity O(1)
 *
 * @author Podshivalov Nikita (https://github.com/nikitap492)
 * @see SearchAlgorithm
 * @see IterativeBinarySearch
 */
public class TernarySearch implements SearchAlgorithm {

    /**
     * @param arr The **Sorted** array in which we will search the element.
     * @param value The value that we want to search for.
     * @return The index of the element if found. Else returns -1.
     */
    @Override
    public <T extends Comparable<T>> int find(T[] arr, T value) {
        return ternarySearch(arr, value, 0, arr.length - 1);
    }

    /**
     * @param arr The **Sorted** array in which we will search the element.
     * @param key The value that we want to search for.
     * @param start The starting index from which we will start Searching.
     * @param end The ending index till which we will Search.
     * @return Returns the index of the Element if found. Else returns -1.
     */
    private <T extends Comparable<T>> int ternarySearch(T[] arr, T key, int start, int end) {
        if (start > end) {
            return -1;
        }
        /* First boundary: add 1/3 of length to start */
        int mid1 = start + (end - start) / 3;
        /* Second boundary: add 2/3 of length to start */
        int mid2 = start + 2 * (end - start) / 3;

        if (key.compareTo(arr[mid1]) == 0) {
            return mid1;
        } else if (key.compareTo(arr[mid2]) == 0) {
            return mid2;
        } /* Search the first (1/3) rd part of the array.*/ else if (key.compareTo(arr[mid1]) < 0) {
            return ternarySearch(arr, key, start, --mid1);
        } /* Search 3rd (1/3)rd part of the array */ else if (key.compareTo(arr[mid2]) > 0) {
            return ternarySearch(arr, key, ++mid2, end);
        } /* Search middle (1/3)rd part of the array */ else {
            return ternarySearch(arr, key, mid1, mid2);
        }
    }
}