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: 4
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 doesn’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 <bits/stdc++.h>using namespace std;// Node for linked listclass Node {public: int data; Node* next;};// Function to insert a node at// the head of the linked listNode* 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 listint 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 codeint 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 listclass Node: def __init__(self, data): self.data = data self.next = None # Function to insert a node at# the head of the linked listdef 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 listdef 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 codeif __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
<script>// JavaScript implementation of the approach// Node for linked listclass Node { constructor() { this.data = 0; this.next = null; }}// Function to insert a node at// the head of the linked listfunction push( head_ref, data){ var 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 listfunction bitonic_point( 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; } let 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 Codevar 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);document.write(bitonic_point(head)); </script> |
Output:
490
Time complexity: O(N) where N is the size of the given linked list.
Auxiliary space: O(1)
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