Replace every node in a linked list with its closest triangular number

Given a singly linked list, the task is to replace every node with its closest triangular number.

Examples:

Input: 3 -> 9 -> 21 -> 25 -> NULL
Output: 3 -> 10 -> 21 -> 28 -> NULL
Explanation: The closest Triangular numbers for each node are:

• Node 1 (value = 3): Closest Triangular number = 3.
• Node 2 (value = 9): Closest Triangular number = 10.
• Node 3 (value = 21): Closest Triangular number = 21.
• Node 4 (value = 25): Closest Triangular number = 28.

Input: 10 -> 15 -> 30 -> 40 -> 50 -> NULL
Output: 10 -> 15 -> 28-> 36 -> 45 -> NULL
Explanation: The closest Triangular numbers for each node are:

• Node 1 (value = 10): Closest Triangular number = 10.
• Node 2 (value = 15): Closest Triangular number = 15.
• Node 3 (value = 30): Closest Triangular number = 28.
• Node 4 (value = 40): Closest Triangular number = 36.
• Node 5 (value = 50): Closest Triangular number = 45.

Approach: This can be solved with the following idea:

This approach uses the concept of triangular numbers to replace every node in a linked list with its closest triangular number. Triangular numbers are the numbers that can be represented in the form of a triangular grid of points, where each row contains one more point than the previous one. The nth triangular number is the sum of the first n natural numbers, i.e., T(n) = 1 + 2 + ... + n = n(n+1)/2. To find the closest triangular number for a given integer, we first find the smallest triangular number that is greater than or equal to the given integer. We can use the formula for the nth triangular number to find this. If the difference between this triangular number and the given integer is less than the difference between the previous triangular number and the given integer, we choose this triangular number as the closest one. Otherwise, we choose the previous triangular number as the closest one. Using this approach, we iterate through the linked list and replace the value of each node with its closest triangular number. Finally, we return the head of the modified linked list and print it to verify the output.

Steps of the above approach:

• Inside the closestTriangular() function initialize a variable 'i' to 1, which represents the index of the triangular number we will start with.
• Use a while loop to iterate through each triangular number until we find the smallest triangular number that is greater than or equal to the input 'n'. The formula for the nth triangular number is n*(n+1)/2.
• Compute the two closest triangular numbers to 'n' by using the formula for the (i-1)^th triangular number and the ith triangular number.
• Determine which of the two closest triangular numbers is actually closer to the input 'n' using the absolute value function abs() and a conditional statement.
• Return the closest triangular number.
• Then inside the replaceWithClosestTriangular() function Initialize a pointer variable 'curr' to the head of the linked list.
• Use a while loop to iterate through each node in the linked list.
• Call the closest triangular () function for each node to find its closest triangular number.
• Update the value of the current node with its closest triangular number.
• Move to the next node in the linked list by updating the pointer variable 'curr' to point to the next node.
• Return the head of the modified linked list.

Below is the implementation of the above approach:

3 -> 10 -> 21 -> 28 -> NULL

Time Complexity: O(n + sqrt(n))
Auxiliary Space: O(1), since we are not using any extra space.