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Left right pointers

Narrow the range with low and high pointers.

Left right pointers

Binary search defines the search range with left and right pointers. Initially left=0, right=n-1.

At each step, the middle is computed: mid = (left + right) // 2. Depending on the target, left or right is updated.

Range update

If the target is greater than arr[mid], left = mid + 1: search the right half. If smaller, right = mid - 1: search the left half.

Adding +1 and -1 prevents mid from being checked again. This is important to avoid infinite loops.

Practice Find mid

Write find_mid(left, right). Return the middle index. Print 4 with print(find_mid(0, 9)).

Starter code

solution.py
def find_mid(left, right):
    # Middle index

Sample solution

solution.py
def find_mid(left, right):
    # Middle index
    return (left + right) // 2
print(find_mid(0, 9))

Expected output

4

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 Mid computation

Question 
mid = (left + ____) // 2
Answer 
mid = (left + right) // 2

Explanation: right is right.

2 Left right pointers: match the terms

Term Meaning
left Left
right Right
mid Middle
left <= right Loop condition

3 What if target is greater than arr[mid]?

  • return mid
  • return -1
  • right = mid - 1
  • left = mid + 1 Correct answer

Explanation: left = mid + 1 is set.

All lessons in Beginner

1 What is an algorithm?

  1. Algorithm definition
  2. Algorithm properties
  3. Pseudocode
  4. Summary - Algorithm concept

2 Big-O notation

  1. Time complexity
  2. Big-O definition
  3. Comparing complexities
  4. Summary - Big-O

3 Array

  1. What is an array?
  2. Array access
  3. Looping over an array
  4. Summary - Arrays

4 Linear search

  1. Linear search idea
  2. Implementing search
  3. Best and worst case
  4. Summary - Linear search

5 Search project

  1. Project: Overview
  2. Grades array setup
  3. Search function
  4. Print the result

6 Bubble sort

  1. Bubble sort idea
  2. One pass
  3. Full sort
  4. Summary - Bubble sort

7 Selection sort

  1. Selection sort idea
  2. Finding the minimum
  3. Swapping
  4. Summary - Selection sort

8 Insertion sort

  1. Insertion sort idea
  2. Shifting
  3. Placement
  4. Summary - Insertion sort

9 Sorting project

  1. Project: Overview
  2. Price array
  3. Apply sorting
  4. Print the result

10 Recursion basics

  1. What is recursion?
  2. Base case
  3. Recursive step
  4. Summary - Recursion

11 Fibonacci

  1. Fibonacci sequence
  2. Recursive Fibonacci
  3. Call tree
  4. Summary - Fibonacci

12 Factorial

  1. Factorial definition
  2. Recursive factorial
  3. Choosing the base case
  4. Summary - Factorial

13 Recursion project

  1. Project: Overview
  2. Recursive power
  3. Combination
  4. Print the results

14 Binary search

  1. Binary search idea
  2. Left right pointers
  3. Base case
  4. Summary - Binary search

15 Linked list

  1. What is a linked list?
  2. Node definition
  3. Traversing the list
  4. Summary - Linked list

16 Stack

  1. What is a stack?
  2. Push and pop
  3. Peek and is_empty
  4. Summary - Stack

17 Queue

  1. What is a queue?
  2. Enqueue and dequeue
  3. Front and back
  4. Summary - Queue

18 Hash table

  1. What is a hash table?
  2. Hash function
  3. Collision
  4. Summary - Hash table

19 Set

  1. What is a set?
  2. Add and lookup
  3. Intersection and union
  4. Summary - Set

20 Beginner final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4