Common linked list patterns (runner technique) in Data Structures Theory - Mini Project: Build & Apply

Common linked list patterns (runner technique)

📖 Scenario: You are learning about linked lists, a way to store items where each item points to the next one. Sometimes, to solve problems faster, we use two pointers moving at different speeds. This is called the runner technique.Imagine you have a chain of train cars, and you want to find the middle car quickly. Using two runners, one moving twice as fast as the other, helps you find the middle without counting all cars first.

🎯 Goal: Build a simple linked list and use the runner technique to find the middle element of the list.

📋 What You'll Learn

Create a linked list with exactly 5 nodes containing values 10, 20, 30, 40, 50

Create two pointers called slow and fast starting at the head of the list

Move fast pointer two steps and slow pointer one step until fast reaches the end

Identify the middle node using the slow pointer

💡 Why This Matters

🌍 Real World

The runner technique helps quickly find the middle of a list or detect cycles without extra memory, useful in many software applications like navigation, scheduling, and data processing.

💼 Career

Understanding linked list patterns and the runner technique is important for software developers and engineers to write efficient code for data structures and algorithms.

1

Create the linked list with 5 nodes

Create a linked list by defining a Node class with value and next properties. Then create 5 nodes with values 10, 20, 30, 40, and 50 linked together starting from a variable called head.

Data Structures Theory

# Define Node class and create linked list nodes
# Your code here

Hint

Start by defining a simple Node class. Then link nodes by setting the next property of each node to the next node.

2

Initialize the runner pointers

Create two variables called slow and fast and set both to point to the head of the linked list.

Data Structures Theory

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

head = Node(10)
head.next = Node(20)
head.next.next = Node(30)
head.next.next.next = Node(40)
head.next.next.next.next = Node(50)

# Initialize slow and fast pointers
# Your code here

Hint

Both pointers start at the beginning of the list, which is the head.

3

Move the pointers using the runner technique

Use a while loop to move fast two steps and slow one step forward until fast is None or fast.next is None. Use slow = slow.next and fast = fast.next.next inside the loop.

Data Structures Theory

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

head = Node(10)
head.next = Node(20)
head.next.next = Node(30)
head.next.next.next = Node(40)
head.next.next.next.next = Node(50)

slow = head
fast = head

# Move slow and fast pointers using runner technique
# Your code here

Hint

Keep moving fast two steps and slow one step until fast reaches the end.

4

Identify the middle node

After the loop ends, the slow pointer will be at the middle node. Assign the middle node's value to a variable called middle_value using middle_value = slow.value.

Data Structures Theory

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

head = Node(10)
head.next = Node(20)
head.next.next = Node(30)
head.next.next.next = Node(40)
head.next.next.next.next = Node(50)

slow = head
fast = head

while fast is not None and fast.next is not None:
    slow = slow.next
    fast = fast.next.next

# Assign the middle node's value to middle_value
# Your code here

Hint

The slow pointer now points to the middle node. Get its value.

Practice

1. What is the main purpose of the runner technique in linked lists?

easy

A. To use two pointers moving at different speeds to solve problems efficiently

B. To sort the linked list elements in ascending order

C. To convert a linked list into an array

D. To delete all nodes from the linked list

Solution

1. Step 1: Understand the runner technique concept

   The runner technique involves two pointers moving through the list at different speeds to solve problems like finding the middle or detecting loops.

2. Step 2: Identify the main purpose

   This technique is used to efficiently solve linked list problems in one pass without extra memory.

3. Final Answer:

   To use two pointers moving at different speeds to solve problems efficiently -> Option A

4. Quick Check:

   Runner technique = two pointers at different speeds [OK]

Hint: Runner technique uses two pointers at different speeds [OK]

Common Mistakes:

• Thinking it sorts the list
• Confusing it with list conversion
• Assuming it deletes nodes

2. Which of the following is the correct way to initialize two pointers for the runner technique in a singly linked list?

easy

A. slow = head; fast = null

B. slow = head; fast = head.next

C. slow = null; fast = head

D. slow = head.next; fast = head

Solution

1. Step 1: Understand pointer initialization for runner technique

   Typically, slow pointer starts at head, and fast pointer starts at the next node to move faster.

2. Step 2: Check each option

   slow = head; fast = head.next correctly sets slow to head and fast to head.next, allowing fast to move two steps ahead.

3. Final Answer:

   slow = head; fast = head.next -> Option B

4. Quick Check:

   Fast pointer starts one step ahead [OK]

Hint: Fast pointer starts one node ahead of slow [OK]

Common Mistakes:

• Setting slow ahead of fast
• Starting pointers at null
• Both pointers starting at same node without offset

3. Consider the following linked list: 1 -> 2 -> 3 -> 4 -> 5 -> null.
Using the runner technique where slow moves one step and fast moves two steps, what value will slow point to when fast reaches the end?

medium

A. 5

B. 2

C. 4

D. 3

Solution

1. Step 1: Trace slow and fast pointers through the list

   Start: slow=1, fast=1
   Move 1: slow=2, fast=3
   Move 2: slow=3, fast=5
   Move 3: fast tries to move two steps but reaches null, stop.

2. Step 2: Identify slow pointer's position when fast ends

   When fast reaches the end (node 5), slow is at node 3.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   Middle node = 3 [OK]

Hint: Slow pointer at middle when fast reaches end [OK]

Common Mistakes:

• Stopping too early and picking 2
• Assuming slow moves as fast as fast pointer
• Confusing node values with pointer positions

4. In the runner technique, if the fast pointer is not moving two steps but only one step each time, what problem might occur?

medium

A. The fast pointer will never reach the end, causing an infinite loop

B. The slow pointer will move too fast and skip nodes

C. The technique will still work correctly without issues

D. The slow pointer will become null immediately

Solution

1. Step 1: Understand the role of fast pointer speed

   The fast pointer moves two steps to catch up or reach the end faster than slow pointer.

2. Step 2: Analyze effect if fast moves only one step

   If fast moves one step, both pointers move at same speed, so fast never overtakes slow, possibly causing infinite loop in cycle detection.

3. Final Answer:

   The fast pointer will never reach the end, causing an infinite loop -> Option A

4. Quick Check:

   Fast pointer speed crucial to avoid infinite loops [OK]

Hint: Fast pointer must move faster to avoid infinite loops [OK]

Common Mistakes:

• Assuming slow pointer moves too fast
• Thinking technique works with equal speeds
• Ignoring infinite loop possibility

5. You want to detect if a linked list has a cycle using the runner technique. Which of the following best describes the condition to confirm a cycle?

hard

A. The slow pointer reaches the end of the list

B. The fast pointer becomes null

C. The slow and fast pointers meet at the same node

D. The slow pointer moves two steps at a time

Solution

1. Step 1: Recall cycle detection with runner technique

   If a cycle exists, fast pointer will eventually catch up to slow pointer inside the loop.

2. Step 2: Identify the condition for cycle detection

   The pointers meeting at the same node means the list has a cycle.

3. Final Answer:

   The slow and fast pointers meet at the same node -> Option C

4. Quick Check:

   Pointers meeting = cycle detected [OK]

Hint: Cycle detected when pointers meet [OK]

Common Mistakes:

• Thinking fast pointer reaching null means cycle
• Assuming slow pointer reaches end means cycle
• Confusing pointer speeds