# Ternary Search

• Difficulty Level : Easy
• Last Updated : 16 Jan, 2023

## Why Ternary Search?

Maximize your search capabilities and reduce time complexity with the introduction of the Ternary Search algorithm. One can look at this article as unlocking the power of efficient searching with the lesser-known, but highly effective algorithm known as the Ternary Search.

Ternary search is a decrease(by constant) and conquer algorithm that can be used to find an element in an array. It is similar to binary search where we divide the array into two parts but in this algorithm, we divide the given array into three parts and determine which has the key (searched element). We can divide the array into three parts by taking mid1 and mid2 which can be calculated as shown below. Initially, l and r will be equal to 0 and n-1 respectively, where n is the length of the array.

It is same as the binary search. The only difference is that, it reduces the time complexity a bit more. Its time complexity is O(log n base 3) and that of binary search is O(log n base 2).

mid1 = l + (r-l)/3
mid2 = r – (r-l)/3

Note: Array needs to be sorted to perform ternary search on it.

Steps to perform Ternary Search:

1. First, we compare the key with the element at mid1. If found equal, we return mid1.
2. If not, then we compare the key with the element at mid2. If found equal, we return mid2.
3. If not, then we check whether the key is less than the element at mid1. If yes, then recur to the first part.
4. If not, then we check whether the key is greater than the element at mid2. If yes, then recur to the third part.
5. If not, then we recur to the second (middle) part.

Example:

Recursive Implementation of Ternary Search

## C++

 `// C++ program to illustrate` `// recursive approach to ternary search` `#include ` `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 `   `// 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\n"``, 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` `        ``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` `        ``Console.WriteLine(``"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` `        ``Console.WriteLine(``"Index of "` `+ key + ``" is "` `+ p);` `    ``}` `}`   `// This code is contributed by Ryuga`

## PHP

 `= ``\$l``)` `    ``{`   `        ``// Find the mid1 and mid2` `        ``\$mid1` `= (int)(``\$l` `+ (``\$r` `- ``\$l``) / 3);` `        ``\$mid2` `= (int)(``\$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`   `// Get the array` `// Sort the array if not sorted` `\$ar` `= ``array``( 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` `echo` `"Index of "``, ``\$key``,` `     ``" is "``, (int)``\$p``, ``"\n"``;`   `// 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` `echo` `"Index of "``, ``\$key``, ` `     ``" is "``, (int)``\$p``, ``"\n"``;`   `// This code is contributed by Arnab Kundu` `?>`

## Javascript

 ``

Output:

```Index of 5 is 4
Index of 50 is -1```

Time Complexity: O(log3n)
Auxiliary Space: O(log3n)

Iterative Approach of Ternary Search

## C++

 `// C++ program to illustrate` `// iterative approach to ternary search`   `#include ` `using` `namespace` `std;`   `// Function to perform Ternary Search` `int` `ternarySearch(``int` `l, ``int` `r, ``int` `key, ``int` `ar[])`   `{` `    ``while` `(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` `            ``r = mid1 - 1;` `        ``}` `        ``else` `if` `(key > ar[mid2]) {`   `            ``// The key lies in between mid2 and r` `            ``l = mid2 + 1;` `        ``}` `        ``else` `{`   `            ``// The key lies in between mid1 and mid2` `            ``l = mid1 + 1;` `            ``r = mid2 - 1;` `        ``}` `    ``}`   `    ``// 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 "``<

## C

 `// C program to illustrate` `// iterative approach to ternary search`   `#include `   `// Function to perform Ternary Search` `int` `ternarySearch(``int` `l, ``int` `r, ``int` `key, ``int` `ar[])`   `{` `    ``while` `(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` `            ``r = mid1 - 1;` `        ``}` `        ``else` `if` `(key > ar[mid2]) {`   `            ``// The key lies in between mid2 and r` `            ``l = mid2 + 1;` `        ``}` `        ``else` `{`   `            ``// The key lies in between mid1 and mid2` `            ``l = mid1 + 1;` `            ``r = mid2 - 1;` `        ``}` `    ``}`   `    ``// 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\n"``, 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` `// the iterative approach to ternary search`   `class` `GFG {`   `    ``// Function to perform Ternary Search` `    ``static` `int` `ternarySearch(``int` `l, ``int` `r, ``int` `key, ``int` `ar[])`   `    ``{` `        ``while` `(r >= l) {`   `            ``// Find the mid1  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` `                ``r = mid1 - ``1``;` `            ``}` `            ``else` `if` `(key > ar[mid2]) {`   `                ``// The key lies in between mid2 and r` `                ``l = mid2 + ``1``;` `            ``}` `            ``else` `{`   `                ``// The key lies in between mid1 and mid2` `                ``l = mid1 + ``1``;` `                ``r = mid2 - ``1``;` `            ``}` `        ``}`   `        ``// 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

 `# Python 3 program to illustrate iterative` `# approach to ternary search`   `# Function to perform Ternary Search` `def` `ternarySearch(l, r, key, ar):` `    ``while` `r >``=` `l:` `        `  `        ``# Find mid1 and mid2` `        ``mid1 ``=` `l ``+` `(r``-``l) ``/``/` `3` `        ``mid2 ``=` `r ``-` `(r``-``l) ``/``/` `3`   `        ``# Check if key is at any mid` `        ``if` `key ``=``=` `ar[mid1]:` `            ``return` `mid1` `        ``if` `key ``=``=` `mid2:` `            ``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]:` `            ``# key lies between l and mid1` `            ``r ``=` `mid1 ``-` `1` `        ``elif` `key > ar[mid2]:` `            ``# key lies between mid2 and r` `            ``l ``=` `mid2 ``+` `1` `        ``else``:` `            ``# key lies between mid1 and mid2` `            ``l ``=` `mid1 ``+` `1` `            ``r ``=` `mid2 ``-` `1`   `    ``# key not found` `    ``return` `-``1`   `# Driver code`   `# Get the list` `# Sort the list if not sorted` `ar ``=` `[``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10``]`   `# Starting index` `l ``=` `0`   `# Length of list` `r ``=` `9`   `# Checking for 5` `# Key to be searched in the list` `key ``=` `5`   `# Search the key using ternary search` `p ``=` `ternarySearch(l, r, key, ar)`   `# Print the result` `print``(``"Index of"``, key, ``"is"``, p)`   `# Checking for 50` `# Key to be searched in the list` `key ``=` `50`   `# Search the key using ternary search` `p ``=` `ternarySearch(l, r, key, ar)`   `# Print the result` `print``(``"Index of"``, key, ``"is"``, p)`   `# This code has been contributed by Sujal Motagi`

## C#

 `// C# program to illustrate the iterative` `// approach to ternary search` `using` `System;`   `public` `class` `GFG {`   `    ``// Function to perform Ternary Search` `    ``static` `int` `ternarySearch(``int` `l, ``int` `r,` `                             ``int` `key, ``int``[] ar)`   `    ``{` `        ``while` `(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` `                ``r = mid1 - 1;` `            ``}` `            ``else` `if` `(key > ar[mid2]) {`   `                ``// The key lies in between mid2 and r` `                ``l = mid2 + 1;` `            ``}` `            ``else` `{`   `                ``// The key lies in between mid1 and mid2` `                ``l = mid1 + 1;` `                ``r = mid2 - 1;` `            ``}` `        ``}`   `        ``// 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` `        ``Console.WriteLine(``"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` `        ``Console.WriteLine(``"Index of "` `+ key + ``" is "` `+ p);` `    ``}` `}`   `// This code has been contributed by 29AjayKumar`

## Javascript

 ``

## PHP

 `= ``\$l``) {`   `        ``// Find the mid1  mid2` `        ``\$mid1` `= ``\$l` `+ (int) ((``\$r` `- ``\$l``) / 3);` `        ``\$mid2` `= ``\$r` `- (int) ((``\$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` `            ``\$r` `= ``\$mid1` `- 1;` `        ``} ``elseif` `(``\$key` `> ``\$ar``[``\$mid2``]) {`   `            ``// The key lies in between mid2 and r` `            ``\$l` `= ``\$mid2` `+ 1;` `        ``} ``else` `{`   `            ``// The key lies in between mid1 and mid2` `            ``\$l` `= ``\$mid1` `+ 1;` `            ``\$r` `= ``\$mid2` `- 1;` `        ``}` `    ``}`   `    ``// Key not found` `    ``return` `-1;` `}`   `// 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` `echo` `"Index of \$key is \$p\n"``;`   `// 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` `echo` `"Index of \$key is \$p\n"``;` `//This code is contributed by faizan sayeed` `?>`

Output:

```Index of 5 is 4
Index of 50 is -1```

Time Complexity: O(log3n), where n is the size of the array.
Auxiliary Space: O(1)

## Binary search Vs Ternary Search

The time complexity of the binary search is more than  the ternary search but it does not mean that ternary search is better. In reality, the number of comparisons in ternary search much more which makes it slower than binary search.

Uses: In finding the maximum or minimum of a unimodal function.
Hackerearth Problems on Ternary search

• Ternary Search has a time complexity of O(log3n), which is more efficient than linear search and comparable to binary search.
• Number of comparisons get reduced.
• Works well for large datasets.
• Fits well with optimization problems.
• Ternary Search is a non-recursive algorithm, so it does not require additional memory to store function call stack, thus it’s space efficient.

• Ternary Search is only applicable to ordered lists or arrays, and cannot be used on unordered or non-linear data sets.
• Requires an in depth understanding of recursion.
• Implementation is not easy.
• Ternary search is not suitable for non-continuous function as it is based on dividing the search space into 3 parts.

## When to use:

• When you have a large ordered array or list and need to find the position of a specific value.
• When you need to find the maximum or minimum value of a function.
• When you need an alternative algorithm for binary search with an efficient time complexity.
• When you are interested in reducing the number of comparisons.

## Summary:

• Ternary Search is a divide-and-conquer algorithm that is used to find the position of a specific value in a given array or list.
• It works by dividing the array into three parts and recursively performing the search operation on the appropriate part until the desired element is found.
• The algorithm has a time complexity of O(log3n) and is more efficient than a linear search, but less commonly used than other search algorithms like binary search.
• It’s important to note that the array to be searched must be sorted for Ternary Search to work correctly.

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