How would you explain Big-O notation to a beginner?

What Is Big‑O Notation?

Big‑O is a way to describe how the running time (or memory usage) of an algorithm grows as the size of its input gets larger.
Instead of giving an exact number of seconds, we talk about the trend:

O(1) – constant time: the work doesn’t change with input size.
O(log n) – logarithmic: each step cuts the problem size roughly in half.
O(n) – linear: work grows proportionally to the number of items.
O(n log n) – linear‑logarithmic: common for efficient sorting.
O(n²) – quadratic: work grows with the square of the input size (e.g., nested loops).

The “O” stands for “order of”. It tells you the upper bound on how bad the algorithm can get.

Why Does It Matter?

Predict performance – Know whether an algorithm will stay fast as data grows.
Compare alternatives – Choose a faster algorithm for large inputs.
Interview language – Many coding interviews ask you to state the Big‑O of your solution.

Simple, Code‑First Example

1️⃣ Linear Scan (O(n))

The loop looks at each element once.
If the array has n items, the worst‑case work is proportional to n → O(n).

2️⃣ Nested Loops (O(n²))

For each of the n elements, we run another loop of n iterations.
Total work ≈ n × n → O(n²).

3️⃣ Binary Search (O(log n))

Each step cuts the searchable range in half.
After about log₂ n steps we either find the target or run out of range → O(log n).

Quick Cheat Sheet

Complexity	Typical Pattern	Example
O(1)	Direct access, fixed work	`arr[0]`, `return 42`
O(log n)	Divide‑and‑conquer, halving	Binary search, tree lookup
O(n)	Single loop over input	Linear scan, summing an array
O(n log n)	Efficient sort, divide‑and‑conquer	Merge sort, heap sort
O(n²)	Double nested loops	Comparing every pair of items
O(2ⁿ)	Exhaustive search of subsets	Solving the traveling salesman naïvely

Bottom Line

Big‑O tells you the growth rate, not the exact time.
It helps you pick algorithms that stay fast when your data grows.
Look at the structure of your code (loops, recursion, halving) to guess the Big‑O.

Happy coding!

1def find_target(arr, target):
2    for i, val in enumerate(arr):
3        if val == target:
4            return i          # found
5    return -1                 # not found

1def find_target(arr, target):
2    for i, val in enumerate(arr):
3        if val == target:
4            return i          # found
5    return -1                 # not found

1def print_pairs(arr):
2    for i in range(len(arr)):
3        for j in range(len(arr)):
4            print(arr[i], arr[j])

1def print_pairs(arr):
2    for i in range(len(arr)):
3        for j in range(len(arr)):
4            print(arr[i], arr[j])

1def binary_search(arr, target):
2    left, right = 0, len(arr) - 1
3    while left <= right:
4        mid = (left + right) // 2
5        if arr[mid] == target:
6            return mid
7        elif arr[mid] < target:
8            left = mid + 1
9        else:
10            right = mid - 1
11    return -1

1def binary_search(arr, target):
2    left, right = 0, len(arr) - 1
3    while left <= right:
4        mid = (left + right) // 2
5        if arr[mid] == target:
6            return mid
7        elif arr[mid] < target:
8            left = mid + 1
9        else:
10            right = mid - 1
11    return -1

All Questions

Top Questions

Popular Tags

How would you explain Big-O notation to a beginner?

2 Answers

Wirte your answer here

What Is Big‑O Notation?

Why Does It Matter?

Simple, Code‑First Example

1️⃣ Linear Scan (O(n))

2️⃣ Nested Loops (O(n²))

3️⃣ Binary Search (O(log n))

Quick Cheat Sheet

Bottom Line

All Questions

Top Questions

Popular Tags

How would you explain Big-O notation to a beginner?

2 Answers

Wirte your answer here

What Is Big‑O Notation?

Why Does It Matter?

Simple, Code‑First Example

1️⃣ Linear Scan (O(n))

2️⃣ Nested Loops (O(n²))

3️⃣ Binary Search (O(log n))

Quick Cheat Sheet

Bottom Line

3️⃣ Binary Search (O(log n))