# Bitonic point in the given linked list

• Last Updated : 11 Oct, 2022

Given a linked list with distinct elements, the task is to find the bitonic point in the given linked list. If there is no such point then print -1.

Examples:

Input: 1 -> 2 -> 3 -> 4 -> 3 -> 2 -> 1 -> NULL
Output:
1 -> 2 -> 3 -> 4 is strictly increasing.
4 -> 3 -> 2 -> 1 -> NULL is strictly decreasing.

Input: 97 -> 98 -> 99 -> 91 -> NULL
Output: 99

Approach: A Bitonic Point is a point in bitonic sequence before which elements are strictly increasing and after which elements are strictly decreasing. A Bitonic point doesnâ€™t exist if array is only decreasing or only increasing. So, find the first node such that the value of the node next to it is strictly smaller. Start traversing the linked list from that node onwards and if every other node is strictly smaller than its previous node then the found node was out bitonic sequence else the given linked list doesn’t contain a valid bitonic sequence.
Note that an empty list or a list with a single node doesn’t represent a valid bitonic sequence.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Node for linked list``class` `Node {``public``:``    ``int` `data;``    ``Node* next;``};` `// Function to insert a node at``// the head of the linked list``Node* push(Node** head_ref, ``int` `data)``{``    ``Node* new_node = ``new` `Node;``    ``new_node->data = data;``    ``new_node->next = (*head_ref);``    ``(*head_ref) = new_node;``}` `// Function to return the bitonic``// of the given linked list``int` `bitonic_point(Node* node)``{``    ``// If list is empty``    ``if` `(node == NULL)``        ``return` `-1;` `    ``// If list contains only``    ``// a single node``    ``if` `(node->next == NULL)``        ``return` `-1;` `    ``// Invalid bitonic sequence``    ``if` `(node->data > node->next->data)``        ``return` `-1;` `    ``while` `(node->next != NULL) {` `        ``// If current node is the bitonic point``        ``if` `(node->data > node->next->data)``            ``break``;` `        ``// Get to the next node in the list``        ``node = node->next;``    ``}` `    ``int` `bitonicPoint = node->data;``    ``// Nodes must be in descending``    ``// starting from here``    ``while` `(node->next != NULL) {` `        ``// Out of order node``        ``if` `(node->data < node->next->data)``            ``return` `-1;` `        ``// Get to the next node in the list``        ``node = node->next;``    ``}` `    ``return` `bitonicPoint;``}` `// Driver code``int` `main()``{``    ``Node* head = NULL;` `    ``push(&head, 100);``    ``push(&head, 201);``    ``push(&head, 399);``    ``push(&head, 490);``    ``push(&head, 377);``    ``push(&head, 291);``    ``push(&head, 100);` `    ``cout << bitonic_point(head);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{``    ` `// Node for linked list``static` `class` `Node``{``    ``int` `data;``    ``Node next;``};` `// Function to insert a node at``// the head of the linked list``static` `Node push(Node head_ref, ``int` `data)``{``    ``Node new_node = ``new` `Node();``    ``new_node.data = data;``    ``new_node.next = (head_ref);``    ``(head_ref) = new_node;``    ``return` `head_ref;``}` `// Function to return the bitonic``// of the given linked list``static` `int` `bitonic_point(Node node)``{``    ``// If list is empty``    ``if` `(node == ``null``)``        ``return` `-``1``;` `    ``// If list contains only``    ``// a single node``    ``if` `(node.next == ``null``)``        ``return` `-``1``;` `    ``// Invalid bitonic sequence``    ``if` `(node.data > node.next.data)``        ``return` `-``1``;` `    ``while` `(node.next != ``null``)``    ``{` `        ``// If current node is the bitonic point``        ``if` `(node.data > node.next.data)``            ``break``;` `        ``// Get to the next node in the list``        ``node = node.next;``    ``}` `    ``int` `bitonicPoint = node.data;``    ` `    ``// Nodes must be in descending``    ``// starting from here``    ``while` `(node.next != ``null``)``    ``{` `        ``// Out of order node``        ``if` `(node.data < node.next.data)``            ``return` `-``1``;` `        ``// Get to the next node in the list``        ``node = node.next;``    ``}` `    ``return` `bitonicPoint;``}` `// Driver code``public` `static` `void` `main(String args[])``{``    ``Node head = ``null``;` `    ``head=push(head, ``100``);``    ``head=push(head, ``201``);``    ``head=push(head, ``399``);``    ``head=push(head, ``490``);``    ``head=push(head, ``377``);``    ``head=push(head, ``291``);``    ``head=push(head, ``100``);` `    ``System.out.println(bitonic_point(head));``}``}` `// This code is contributed by Arnab Kundu`

## Python3

 `# Python3 implementation of the approach`` ` `# Node for linked list``class` `Node:  ``    ``def` `__init__(``self``, data):``        ``self``.data ``=` `data``        ``self``.``next` `=` `None`` ` `# Function to insert a node at``# the head of the linked list``def` `push(head_ref, data):` `    ``new_node ``=` `Node(data)``    ``new_node.``next` `=` `head_ref``    ``head_ref ``=` `new_node``    ``return` `head_ref``    ` `# Function to return the bitonic``# of the given linked list``def` `bitonic_point(node):` `    ``# If list is empty``    ``if` `(node ``=``=` `None``):``        ``return` `-``1``;`` ` `    ``# If list contains only``    ``# a single node``    ``if` `(node.``next` `=``=` `None``):``        ``return` `-``1``;`` ` `    ``# Invalid bitonic sequence``    ``if` `(node.data > node.``next``.data):``        ``return` `-``1``;``    ``while` `(node.``next` `!``=` `None``):`` ` `        ``# If current node is the bitonic point``        ``if` `(node.data > node.``next``.data):``            ``break``;`` ` `        ``# Get to the next node in the list``        ``node ``=` `node.``next``;``    ``bitonicPoint ``=` `node.data;``    ` `    ``# Nodes must be in descending``    ``# starting from here``    ``while` `(node.``next` `!``=` `None``):`` ` `        ``# Out of order node``        ``if` `(node.data < node.``next``.data):``            ``return` `-``1``;`` ` `        ``# Get to the next node in the list``        ``node ``=` `node.``next``;``    ``return` `bitonicPoint;`` ` `# Driver code``if` `__name__``=``=``'__main__'``:``    ` `    ``head ``=` `None``;`` ` `    ``head ``=` `push(head, ``100``);``    ``head ``=` `push(head, ``201``);``    ``head ``=` `push(head, ``399``);``    ``head ``=` `push(head, ``490``);``    ``head ``=` `push(head, ``377``);``    ``head ``=` `push(head, ``291``);``    ``head ``=` `push(head, ``100``);`` ` `    ``print``(bitonic_point(head))`` ` `# This code is contributed by rutvik_56`

## C#

 `// C# implementation of the approach``using` `System;``    ` `class` `GFG``{``    ` `// Node for linked list``public` `class` `Node``{``    ``public` `int` `data;``    ``public` `Node next;``};` `// Function to insert a node at``// the head of the linked list``static` `Node push(Node head_ref, ``int` `data)``{``    ``Node new_node = ``new` `Node();``    ``new_node.data = data;``    ``new_node.next = (head_ref);``    ``(head_ref) = new_node;``    ``return` `head_ref;``}` `// Function to return the bitonic``// of the given linked list``static` `int` `bitonic_point(Node node)``{``    ``// If list is empty``    ``if` `(node == ``null``)``        ``return` `-1;` `    ``// If list contains only``    ``// a single node``    ``if` `(node.next == ``null``)``        ``return` `-1;` `    ``// Invalid bitonic sequence``    ``if` `(node.data > node.next.data)``        ``return` `-1;` `    ``while` `(node.next != ``null``)``    ``{` `        ``// If current node is the bitonic point``        ``if` `(node.data > node.next.data)``            ``break``;` `        ``// Get to the next node in the list``        ``node = node.next;``    ``}` `    ``int` `bitonicPoint = node.data;``    ` `    ``// Nodes must be in descending``    ``// starting from here``    ``while` `(node.next != ``null``)``    ``{` `        ``// Out of order node``        ``if` `(node.data < node.next.data)``            ``return` `-1;` `        ``// Get to the next node in the list``        ``node = node.next;``    ``}` `    ``return` `bitonicPoint;``}` `// Driver code``public` `static` `void` `Main(String []args)``{``    ``Node head = ``null``;` `    ``head=push(head, 100);``    ``head=push(head, 201);``    ``head=push(head, 399);``    ``head=push(head, 490);``    ``head=push(head, 377);``    ``head=push(head, 291);``    ``head=push(head, 100);` `    ``Console.WriteLine(bitonic_point(head));``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`490`

Time complexity: O(N) where N is the size of the given linked list.
Auxiliary space: O(1)

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