Maximum distance between Peaks in given Linked List

Last Updated : 30 Aug, 2024

Given a linked list of length n, the task is to determine the maximum distance between two consecutive peaks of the given linked list. A peak is a node with a value greater than its neighbours. The distance between two nodes is defined as the number of nodes present between them.

Examples:

Input: Linked List = 1 -> 2 -> 1 -> 8 -> 6 -> NULL
Output: 1
Explanation: The peaks in the Linked List are 2, 8
The distance between 2 and 8 is 1.
The maximum distance is 1.

Input: Linked List = 1 -> 5 -> 3 -> 2 -> 7 -> NULL
Output: 2
Explanation: The peaks in the Linked List are 5, 7
The distance between 5 and 7 is 2.
The maximum distance is 2.

[Expected Approach] Using Greedy Technique – O(n) Time and O(1) Space

The idea is to iterate over the Linked List and find nodes that are peaks. Keep a record of previous Index that is peak and current index if its a peak.

Follow the steps below to solve the problem:

Initialize pointers prev, curr (previous index, current index).
Traverse the list with curr pointer.
Check peak conditions and update the maximum distance if conditions are satisfied.
Update pointers and current Index.
Print maximum distance after traversal.

Below is the implementation of the above approach :

C++

// C++ code to find the maximum distance 
// between consecutive peaks in a linked list

#include <bits/stdc++.h>
using namespace std;

class Node {
public:
    int data;
    Node* next;

    Node(int new_data) {
        data = new_data;
        next = nullptr;
    }
};

// Function to find the maximum distance
void findMaxGap(Node* head) {

    // Prev points to previous of current node
    Node* prev = new Node(-1);
    prev->next = head;

    // Current is initially head
    Node* curr = head;
    int lastIndex = -1, currentIndex = 0;
    int maxGap = 0, gap = 0;

    // Loop till current is not NULL
    while (curr != nullptr) {

        // Find next of current
        Node* next = curr->next;

        // One node only
        if (prev->next == head && next == nullptr) {
            cout << maxGap;
            return;
        }

        // For the 1st node check only next
        else if (prev->next == head 
                 && next->data < curr->data) {

            // Update lastIndex if first node is a peak
            lastIndex = currentIndex;
        }

        // For the last node check only the prev node
        else if (next == nullptr && prev->data < curr->data) {

            // Update lastIndex if last node is a peak
            if (lastIndex != -1) {
                lastIndex = currentIndex;
            } else {
                // Calculate gap and update maxGap
                gap = currentIndex - lastIndex - 1;
                maxGap = max(gap, maxGap);
                lastIndex = currentIndex;
            }
        }

        // Check prev and next nodes for intermediate nodes
        else if (prev->data < curr->data 
                 && next->data < curr->data) {

            // Update lastIndex if current node is a peak
            if (lastIndex != -1) {
                lastIndex = currentIndex;
            } else {
                // Calculate gap and update maxGap
                gap = currentIndex - lastIndex - 1;
                maxGap = max(gap, maxGap);
                lastIndex = currentIndex;
            }
        }

        // Move prev and curr pointer
        prev = prev->next;
        curr = curr->next;
        currentIndex++;
    }

    cout << maxGap << "\n";
}

int main() {
  
    // Create a hard-coded linked list:
    // 1-> 2 -> 1 -> 8 -> 6 -> NULL
    Node* head = new Node(1);
    head->next = new Node(2);
    head->next->next = new Node(1);
    head->next->next->next = new Node(8);
    head->next->next->next->next = new Node(6);

    findMaxGap(head);
}

// C code to find the maximum distance 
//between consecutive peaks in a linked list

#include <stdio.h>
#include <stdlib.h>

struct Node {
    int data;
    struct Node* next;
};

struct Node* createNode(int data, struct Node* next) {
    struct Node* newNode = 
      	(struct Node*)malloc(sizeof(struct Node));
    newNode->data = data;
    newNode->next = next;
    return newNode;
}

// Function to find the maximum distance
void findMaxGap(struct Node* head) {

    // Prev points to previous of current node
    struct Node* prev = createNode(-1, head);

    // Current is initially head
    struct Node* curr = head;
    int lastIndex = -1, currentIndex = 0;
    int maxGap = 0, gap = 0;

    // Loop till current is not NULL
    while (curr != NULL) {

        // Find next of current
        struct Node* next = curr->next;

        // One node only
        if (prev->next == head && next == NULL) {
            printf("%d\n", maxGap);
            return;
        }

        // For the 1st node check only next
        else if (prev->next == head &&
                 next->data < curr->data) {

            // Update lastIndex if first node is a peak
            lastIndex = currentIndex;
        }

        // For the last node check only the prev node
        else if (next == NULL &&
                 prev->data < curr->data) {

            // Update lastIndex if last node is a peak
            if (lastIndex != -1) {
                lastIndex = currentIndex;
            } else {

                // Calculate gap and update maxGap
                gap = currentIndex - lastIndex - 1;
                maxGap = (gap > maxGap) ? gap : maxGap;
                lastIndex = currentIndex;
            }
        }

        // Check prev and next nodes for intermediate nodes
        else if (prev->data < curr->data &&
                 next->data < curr->data) {

            // Update lastIndex if current node is a peak
            if (lastIndex != -1) {
                lastIndex = currentIndex;
            } else {

                // Calculate gap and update maxGap
                gap = currentIndex - lastIndex - 1;
                maxGap = (gap > maxGap) ? gap : maxGap;
                lastIndex = currentIndex;
            }
        }

        // Move prev and curr pointer
        prev = prev->next;
        curr = curr->next;
        currentIndex++;
    }

    // Print the maximum gap
    printf("%d\n", maxGap);
}

int main() {
    
     // Create a hard-coded linked list:
    // 1-> 2 -> 1 -> 8 -> 6 -> NULL
    struct Node* head = createNode(1, NULL);
    head->next = createNode(2, NULL);
    head->next->next = createNode(1, NULL);
    head->next->next->next = createNode(8, NULL);
    head->next->next->next->next = createNode(6, NULL);
  
    findMaxGap(head);

    return 0;
}

Java

// Java code to find the maximum distance
// between consecutive peaks in a linked list
class Node {
    int data;
    Node next;

    Node(int new_data) {
        data = new_data;
        next = null;
    }
}

public class GfG {

    // Function to find the maximum distance between peaks
    static void findMaxGap(Node head) {

        // Initialize pointers and variables
        Node prev = new Node(-1);
        prev.next = head;
        Node curr = head;
        int lastIndex = -1, currentIndex = 0;
        int maxGap = 0, gap = 0;

        // Loop until current node is null
        while (curr != null) {
            Node next = curr.next;

            // Check if the current node is a peak
            boolean isPeak = (prev.data < curr.data)
                             && (next == null
                                 || next.data < curr.data);

            if (isPeak) {
                if (lastIndex != -1) {
                  
                    // Calculate gap and update maxGap
                    gap = currentIndex - lastIndex - 1;
                    maxGap = Math.max(gap, maxGap);
                }
                lastIndex = currentIndex;            
            }

            // Move prev and curr pointers
            prev = prev.next;
            curr = curr.next;
            currentIndex++;
        }

        // Print the maximum gap between peaks
        System.out.println(maxGap);
    }

    public static void main(String[] args) {
      
        // Create a hard-coded linked list: 1 -> 2 -> 1 -> 8
        // -> 6 -> NULL
        Node head = new Node(1);
        head.next = new Node(2);
        head.next.next = new Node(1);
        head.next.next.next = new Node(8);
        head.next.next.next.next = new Node(6);

        findMaxGap(head);
    }
}

Python

# Python code to find the maximum distance 
# between peaks in a linked list

class Node:
    def __init__(self, new_data):
        self.data = new_data
        self.next = None

def find_max_gap(head):

    # Prev points to previous of current node
    prev = Node(-1)
    prev.next = head

    # Current is initially head
    curr = head
    last_index = -1
    current_index = 0
    max_gap = 0
    gap = 0

    # Loop till current is not None
    while curr is not None:

        # Find next of current
        next_node = curr.next

        # One node only
        if prev.next == head and next_node is None:
            print(max_gap)
            return

        # For the 1st node check only next
        elif prev.next == head and \
             next_node.data < curr.data:

            # Update last_index if first node is a peak
            last_index = current_index

        # For the last node check only the prev node
        elif next_node is None and \
             prev.data < curr.data:

            # Update last_index if last node is a peak
            if last_index != -1:
                last_index = current_index
            else:
                # Calculate gap and update max_gap
                gap = current_index - last_index - 1
                max_gap = max(gap, max_gap)
                last_index = current_index

        # Check prev and next nodes for intermediate nodes
        elif prev.data < curr.data and \
             next_node.data < curr.data:

            # Update last_index if current node is a peak
            if last_index != -1:
                last_index = current_index
            else:
                # Calculate gap and update max_gap
                gap = current_index - last_index - 1
                max_gap = max(gap, max_gap)
                last_index = current_index

        # Move prev and curr pointer
        prev = prev.next
        curr = curr.next
        current_index += 1

    print(max_gap)

if __name__ == "__main__":

    # Create a hard-coded linked list:
    # 1-> 2 -> 1 -> 8 -> 6 -> NULL
    head = Node(1)
    head.next = Node(2)
    head.next.next = Node(1)
    head.next.next.next = Node(8)
    head.next.next.next.next = Node(6)
    
    find_max_gap(head)

// C# code to find the maximum distance 
// between peaks in a linked list

using System;

class Node {
    public int Data;
    public Node Next;

    public Node(int newData) {
        Data = newData;
        Next = null;
    }
}

class GfG {

    // Function to find the maximum distance
    static void FindMaxGap(Node head) {

        // Initialize prev with a dummy node
        Node prev = new Node(-1);
        prev.Next = head;

        // Current is initially head
        Node curr = head;
        int lastIndex = -1, currentIndex = 0;
        int maxGap = 0, gap = 0;

        // Loop till current is not null
        while (curr != null) {

            // Find next of current
            Node next = curr.Next;

            // One node only
            if (prev.Next == head && next == null) {
                Console.WriteLine(maxGap);
                return;
            }

            // For the 1st node check only next
            else if (prev.Next == head &&
                     next.Data < curr.Data) {

                // Update lastIndex if first node is a peak
                lastIndex = currentIndex;
            }

            // For the last node check only the prev node
            else if (next == null &&
                     prev.Data < curr.Data) {

                // Update lastIndex if last node is a peak
                if (lastIndex != -1) {
                    lastIndex = currentIndex;
                } else {

                    // Calculate gap and update maxGap
                    gap = currentIndex - lastIndex - 1;
                    maxGap = Math.Max(gap, maxGap);
                    lastIndex = currentIndex;
                }
            }

            // Check prev and next nodes for intermediate nodes
            else if (prev.Data < curr.Data &&
                     next.Data < curr.Data) {

                // Update lastIndex if current node is a peak
                if (lastIndex != -1) {
                    lastIndex = currentIndex;
                } else {

                    // Calculate gap and update maxGap
                    gap = currentIndex - lastIndex - 1;
                    maxGap = Math.Max(gap, maxGap);
                    lastIndex = currentIndex;
                }
            }

            // Move prev and curr pointer
            prev = prev.Next;
            curr = curr.Next;
            currentIndex++;
        }

        Console.WriteLine(maxGap);
    }

    static void Main(string[] args) {

         // Create a hard-coded linked list:
         // 1-> 2 -> 1 -> 8 -> 6 -> NULL
        Node head = new Node(1);
        head.Next = new Node(2);
        head.Next.Next = new Node(1);
        head.Next.Next.Next = new Node(8);
        head.Next.Next.Next.Next = new Node(6);

        FindMaxGap(head);
    }
}

JavaScript

// JavaScript code to find the maximum distance
// between peaks in a linked list
class Node {
    constructor(newData) {
        this.data = newData;
        this.next = null;
    }
}

function findMaxGap(head) {

    // Prev points to previous of current node
    let prev = new Node(-1);
    prev.next = head;

    // Current is initially head
    let curr = head;
    let lastIndex = -1, currentIndex = 0;
    let maxGap = 0, gap = 0;

    // Loop till current is not null
    while (curr !== null) {

        // Find next of current
        let next = curr.next;

        // One node only
        if (prev.next === head && next === null) {
            console.log(maxGap);
            return;
        }

        // For the 1st node check only next
        if (prev.next === head && next.data < curr.data) {
            lastIndex = currentIndex;
        }
        else if (next === null && prev.data < curr.data) {
        
            // For the last node check only the prev node
            if (lastIndex !== -1) {
                lastIndex = currentIndex;
            }
            else {
            
                // Calculate gap and update maxGap
                gap = currentIndex - lastIndex - 1;
                maxGap = Math.max(gap, maxGap);
                lastIndex = currentIndex;
            }
        }
        else if (prev.data < curr.data
                 && next.data < curr.data) {
                 
            // Check prev and next nodes for nodes
            if (lastIndex !== -1) {
                lastIndex = currentIndex;
            }
            else {
            
                // Calculate gap and update maxGap
                gap = currentIndex - lastIndex - 1;
                maxGap = Math.max(gap, maxGap);
                lastIndex = currentIndex;
            }
        }

        // Move prev and curr pointer
        prev = prev.next;
        curr = curr.next;
        currentIndex++;
    }

    // Print the maximum gap
    console.log(maxGap);
}

// Create a hard-coded linked list:
// 1-> 2 -> 1 -> 8 -> 6 -> NULL
let head = new Node(1);
head.next = new Node(2);
head.next.next = new Node(1);
head.next.next.next = new Node(8);
head.next.next.next.next = new Node(6);

findMaxGap(head);

Output

Time Complexity: O(n) , where n is the number of nodes.
Space Complexity: O(1)

Find a peak element in Linked List

amrithabpatil

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Maximum distance between Peaks in given Linked List

[Expected Approach] Using Greedy Technique – O(n) Time and O(1) Space

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