Тернарный поиск

Опубликовано: 14 Января, 2022

Тернарный поиск - это алгоритм «разделяй и властвуй», который можно использовать для поиска элемента в массиве. Это похоже на двоичный поиск, когда мы делим массив на две части, но в этом алгоритме мы делим данный массив на три части и определяем, в какой из них есть ключ (искомый элемент). Мы можем разделить массив на три части, взяв mid1 и mid2, которые можно вычислить, как показано ниже. Первоначально l и r будут равны 0 и n-1 соответственно, где n - длина массива.

mid1 = l + (r-l)/3 
mid2 = r – (r-l)/3 

Примечание. Для выполнения троичного поиска в массиве необходимо выполнить сортировку.

Шаги для выполнения троичного поиска:

  1. Сначала мы сравниваем ключ с элементом mid1. Если найдено равное, мы возвращаем mid1.
  2. Если нет, то мы сравниваем ключ с элементом mid2. Если найдено равное, мы возвращаем mid2.
  3. Если нет, то мы проверяем, меньше ли ключ, чем элемент mid1. Если да, то вернемся к первой части.
  4. Если нет, то мы проверяем, больше ли ключ, чем элемент mid2. Если да, то вернемся к третьей части.
  5. Если нет, то возвращаемся ко второй (средней) части.

Пример:

Recursive Implementation of Ternary Search 

C++

// C++ program to illustrate
// recursive approach to ternary search
#include <bits/stdc++.h>
using namespace std;
 
// Function to perform Ternary Search
int ternarySearch(int l, int r, int key, int ar[])
{
    if (r >= l) {
 
        // Find the mid1 and mid2
        int mid1 = l + (r - l) / 3;
        int mid2 = r - (r - l) / 3;
 
        // Check if key is present at any mid
        if (ar[mid1] == key) {
            return mid1;
        }
        if (ar[mid2] == key) {
            return mid2;
        }
 
        // Since key is not present at mid,
        // check in which region it is present
        // then repeat the Search operation
        // in that region
        if (key < ar[mid1]) {
 
            // The key lies in between l and mid1
            return ternarySearch(l, mid1 - 1, key, ar);
        }
        else if (key > ar[mid2]) {
 
            // The key lies in between mid2 and r
            return ternarySearch(mid2 + 1, r, key, ar);
        }
        else {
 
            // The key lies in between mid1 and mid2
            return ternarySearch(mid1 + 1, mid2 - 1, key, ar);
        }
    }
 
    // Key not found
    return -1;
}
 
// Driver code
int main()
{
    int l, r, p, key;
 
    // Get the array
    // Sort the array if not sorted
    int ar[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
 
    // Starting index
    l = 0;
 
    // length of array
    r = 9;
 
    // Checking for 5
 
    // Key to be searched in the array
    key = 5;
 
    // Search the key using ternarySearch
    p = ternarySearch(l, r, key, ar);
 
    // Print the result
    cout << "Index of " << key
         << " is " << p << endl;
 
    // Checking for 50
 
    // Key to be searched in the array
    key = 50;
 
    // Search the key using ternarySearch
    p = ternarySearch(l, r, key, ar);
 
    // Print the result
    cout << "Index of " << key
         << " is " << p << endl;
}
 
// This code is contributed
// by Akanksha_Rai

C

// C program to illustrate
// recursive approach to ternary search
 
#include <stdio.h>
 
// Function to perform Ternary Search
int ternarySearch(int l, int r, int key, int ar[])
{
    if (r >= l) {
 
        // Find the mid1 and mid2
        int mid1 = l + (r - l) / 3;
        int mid2 = r - (r - l) / 3;
 
        // Check if key is present at any mid
        if (ar[mid1] == key) {
            return mid1;
        }
        if (ar[mid2] == key) {
            return mid2;
        }
 
        // Since key is not present at mid,
        // check in which region it is present
        // then repeat the Search operation
        // in that region
 
        if (key < ar[mid1]) {
 
            // The key lies in between l and mid1
            return ternarySearch(l, mid1 - 1, key, ar);
        }
        else if (key > ar[mid2]) {
 
            // The key lies in between mid2 and r
            return ternarySearch(mid2 + 1, r, key, ar);
        }
        else {
 
            // The key lies in between mid1 and mid2
            return ternarySearch(mid1 + 1, mid2 - 1, key, ar);
        }
    }
 
    // Key not found
    return -1;
}
 
// Driver code
int main()
{
    int l, r, p, key;
 
    // Get the array
    // Sort the array if not sorted
    int ar[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
 
    // Starting index
    l = 0;
 
    // length of array
    r = 9;
 
    // Checking for 5
 
    // Key to be searched in the array
    key = 5;
 
    // Search the key using ternarySearch
    p = ternarySearch(l, r, key, ar);
 
    // Print the result
    printf("Index of %d is %d ", key, p);
 
    // Checking for 50
 
    // Key to be searched in the array
    key = 50;
 
    // Search the key using ternarySearch
    p = ternarySearch(l, r, key, ar);
 
    // Print the result
    printf("Index of %d is %d", key, p);
}

Java

// Java program to illustrate
// recursive approach to ternary search
 
class GFG {
 
    // Function to perform Ternary Search
    static int ternarySearch(int l, int r, int key, int ar[])
    {
        if (r >= l) {
 
            // Find the mid1 and mid2
            int mid1 = l + (r - l) / 3;
            int mid2 = r - (r - l) / 3;
 
            // Check if key is present at any mid
            if (ar[mid1] == key) {
                return mid1;
            }
            if (ar[mid2] == key) {
                return mid2;
            }
 
            // Since key is not present at mid,
            // check in which region it is present
            // then repeat the Search operation
            // in that region
 
            if (key < ar[mid1]) {
 
                // The key lies in between l and mid1
                return ternarySearch(l, mid1 - 1, key, ar);
            }
            else if (key > ar[mid2]) {
 
                // The key lies in between mid2 and r
                return ternarySearch(mid2 + 1, r, key, ar);
            }
            else {
 
                // The key lies in between mid1 and mid2
                return ternarySearch(mid1 + 1, mid2 - 1, key, ar);
            }
        }
 
        // Key not found
        return -1;
    }
 
    // Driver code
    public static void main(String args[])
    {
        int l, r, p, key;
 
        // Get the array
        // Sort the array if not sorted
        int ar[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
 
        // Starting index
        l = 0;
 
        // length of array
        r = 9;
 
        // Checking for 5
 
        // Key to be searched in the array
        key = 5;
 
        // Search the key using ternarySearch
        p = ternarySearch(l, r, key, ar);
 
        // Print the result
        System.out.println("Index of " + key + " is " + p);
 
        // Checking for 50
 
        // Key to be searched in the array
        key = 50;
 
        // Search the key using ternarySearch
        p = ternarySearch(l, r, key, ar);
 
        // Print the result
        System.out.println("Index of " + key + " is " + p);
    }
}

Python3

# Python3 program to illustrate
# recursive approach to ternary search
import math as mt
 
# Function to perform Ternary Search
def ternarySearch(l, r, key, ar):
 
    if (r >= l):
 
        # Find the mid1 and mid2
        mid1 = l + (r - l) //3
        mid2 = r - (r - l) //3
 
        # Check if key is present at any mid
        if (ar[mid1] == key):
            return mid1
         
        if (ar[mid2] == key):
            return mid2
         
        # Since key is not present at mid,
        # check in which region it is present
        # then repeat the Search operation
        # in that region
        if (key < ar[mid1]):
 
            # The key lies in between l and mid1
            return ternarySearch(l, mid1 - 1, key, ar)
         
        elif (key > ar[mid2]):
 
            # The key lies in between mid2 and r
            return ternarySearch(mid2 + 1, r, key, ar)
         
        else:
 
            # The key lies in between mid1 and mid2
            return ternarySearch(mid1 + 1,
                                 mid2 - 1, key, ar)
         
    # Key not found
    return -1
 
# Driver code
l, r, p = 0, 9, 5
 
# Get the array
# Sort the array if not sorted
ar = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
 
# Starting index
l = 0
 
# length of array
r = 9
 
# Checking for 5
 
# Key to be searched in the array
key = 5
 
# Search the key using ternarySearch
p = ternarySearch(l, r, key, ar)
 
# Print the result
print("Index of", key, "is", p)
 
# Checking for 50
 
# Key to be searched in the array
key = 50
 
# Search the key using ternarySearch
p = ternarySearch(l, r, key, ar)
 
# Print the result
print("Index of", key, "is", p)
 
# This code is contributed by
# Mohit kumar 29

C#

// CSharp program to illustrate
// recursive approach to ternary search
using System;
 
class GFG {
 
    // Function to perform Ternary Search
    static int ternarySearch(int l, int r, int key, int[] ar)
    {
        if (r >= l) {
 
            // Find the mid1 and mid2
            int mid1 = l + (r - l) / 3;
            int mid2 = r - (r - l) / 3;
 
            // Check if key is present at any mid
            if (ar[mid1] == key) {
                return mid1;
            }
            if (ar[mid2] == key) {
                return mid2;
            }
 
            // Since key is not present at mid,
            // check in which region it is present
            // then repeat the Search operation
            // in that region
 
            if (key < ar[mid1]) {
 
                // The key lies in between l and mid1
                return ternarySearch(l, mid1 - 1, key, ar);
            }
            else if (key > ar[mid2]) {
 
                // The key lies in between mid2 and r
                return ternarySearch(mid2 + 1, r, key, ar);
            }
            else {
 
                // The key lies in between mid1 and mid2
                return ternarySearch(mid1 + 1, mid2 - 1, key, ar);
            }
        }
 
        // Key not found
        return -1;
    }
 
    // Driver code
    public static void Main()
    {
        int l, r, p, key;
 
        // Get the array
        // Sort the array if not sorted
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