Rotate List
Fill out the following sections:
Define the Interface Input: head, k (integer) Output: head
How is the number of nodes in the linked list related to value of k. The highest value for the length of the linked list is 500, but k can be 501 Rotating 501 times is the same as rotating just once Can we avoid doing unnecessary work (rotation) What is the minimum rotation we need to perform. Figure out how many nodes is in the linked list Compute k % n (modular arithmetic) 501 % 500 = 1
Identify the Invariants The values of the nodes will not change The number of nodes will not change
Identify the constraints
 no of nodes [0, 500]
 k [0, 2*10^9]
Search the Problem Space
Classify the Problem
Analyze the Examples
Solve the Problem by Hand If I rotate the linked list by the same number of times as the number of nodes in the linked list
How do we express this in code?
Traverse the linked list and when the pointer reaches the last node Last node’s next pointer must point to head We need more than one pointer because, I need to set the node before the last node to be f.next = l.next (make the new tail) l.next = head ()
Go to the second last node Save the last node Assign second_last.next to null Assign last_node.next = head Assign head = last_node
Iteration or Recursion
Iteration
 Figure out the value of k (modulo)
 Rotate k number of times
 Terminating condition is the value of k
 Return the head of the rotated linked list
If we have 0 or 1 node, there is nothing to rotate Just return the head. If k = 0, no rotation required, return the head
Describe the Pattern
Brute Force Approach
Analyze Time and Space Complexity


Fill out the following sections:
Define the Interface Input: head, k (integer) Output: head
How is the number of nodes in the linked list related to value of k. The highest value for the length of the linked list is 500, but k can be 501 Rotating 501 times is the same as rotating just once Can we avoid doing unnecessary work (rotation) What is the minimum rotation we need to perform. Figure out how many nodes is in the linked list Compute k % n (modular arithmetic) 501 % 500 = 1
Identify the Invariants The values of the nodes will not change The number of nodes will not change
Identify the constraints
 no of nodes [0, 500]
 k [0, 2*10^9]
Search the Problem Space
Classify the Problem
Analyze the Examples
Solve the Problem by Hand If I rotate the linked list by the same number of times as the number of nodes in the linked list
How do we express this in code?
Traverse the linked list and when the pointer reaches the last node Last node’s next pointer must point to head We need more than one pointer because, I need to set the node before the last node to be f.next = l.next (make the new tail) l.next = head ()
Go to the second last node Save the last node Assign second_last.next to null Assign last_node.next = head Assign head = last_node
Iteration or Recursion
Iteration
 Figure out the value of k (modulo)
 Rotate k number of times
 Terminating condition is the value of k
 Return the head of the rotated linked list
If we have 0 or 1 node, there is nothing to rotate Just return the head. If k = 0, no rotation required, return the head
Describe the Pattern
Brute Force Approach
Analyze Time and Space Complexity
Time: O(N) Space: O(1)
Next Problems
Rotate Array Split Linked List in Parts
Outline the Solution
Key Takeaways


This code first calculates the length of the linked list and then finds the effective rotations. After identifying the rotation point, it updates the pointers to rotate the list to the right by ( k ) places.
The time complexity is ( O(N) ), where ( N ) is the number of nodes in the linked list, as we have two iterations through the list. The space complexity is ( O(1) ), as we only use a constant amount of extra space.


Language Agnostic Coding Drills
Understanding Data Structures: The first step in understanding this code is to understand data structures, specifically the queue and list data structures. Understand how these data structures work, how to add and remove elements, and how they can be used to store data.
 Drill: Use any language to implement a queue data structure and perform basic operations like enqueue (inserting an element at the end) and dequeue (removing an element from the front).
Condition Checking: The code uses a lot of condition checking (if statements) to decide what to do. This is a fundamental part of most programming languages.
 Drill: Write a function that takes an input, checks if it meets a certain condition, and returns different results based on that condition.
Loops: Loops are used to iterate over elements in a list or queue, or to keep a block of code running as long as a certain condition is true.
 Drill: Write a function that uses a loop to process or generate a sequence of values.
Functions/Methods: Functions or methods are blocks of reusable code that perform a certain task. Understanding how to define and use functions/methods is crucial.
 Drill: Define a function that takes in parameters, performs a calculation or operation, and returns a result.
Recursion: The given code uses recursion, which is the concept where a function calls itself in its definition. Recursive solutions are common for problems involving trees or graphs.
 Drill: Implement a simple recursive function, such as one that calculates the factorial of a number.
Tree Data Structure: The code is written for a tree data structure. Understanding trees is necessary to follow along. This includes understanding terms like root, node, child, etc.
 Drill: Implement a simple binary tree data structure and write functions to add nodes and traverse the tree.
Graph Traversal Algorithms (DFS, BFS): The code seems to be using a Breadthfirst Search (BFS) traversal algorithm to navigate through the tree. Understanding how these algorithms work is crucial.
 Drill: Implement a BFS and DFS traversal on a tree or graph.
Complexity Analysis: Analyze and understand the time and space complexity of your code.
 Drill: Practice calculating the time and space complexity of various pieces of code.
Each of these drills isolates a particular concept, allowing you to focus on understanding and mastering that concept. Once you’re comfortable with these concepts, you can then combine them as demonstrated in the initial code sample.
Targeted Drills in Python
 Understanding Data Structures (Queue)


 Condition Checking


 Loops


 Functions/Methods


 Recursion


 Tree Data Structure


 Graph Traversal Algorithms (BFS)


 Complexity Analysis This is more of a theoretical concept and understanding, but you can practice it by implementing different algorithms and analyzing their time and space complexity. For instance, you can check the time complexity of a simple sorting algorithm:


This script will print out the time taken for bubble sort, which has a time complexity of O(n^2).