If there's one thing every developer has heard, it's: "first make it work, then optimize". And it's true - you can't write the most performant code in the world if it doesn't actually solve the problem.
But there comes a point in your journey when just "working" isn't enough. That's when I stumbled upon the famous Big O Notation. At first, it seemed like a monster with seven heads - full of letters and graphs that didn't make much sense. But when I started applying it to my code, I realized it wasn't just some college theory: it actually makes a real difference in day-to-day programming.
What Big O Is (in Simple Terms)
Big O Notation is a way to describe an algorithm's efficiency in relation to the growth of its input.
The name comes from "Order of," meaning the "growth order" of an algorithm. The O() in the notation is a mathematical way of saying:
"As the number of inputs grows, the time or space required by the algorithm grows in this order."
So, when we say an algorithm is O(n), we mean its execution time grows proportionally to the number of input elements (n). Meanwhile, O(1) means the time doesn't change, regardless of input size.
👉 In other words, the O symbol is like a label indicating how the cost of the algorithm grows.
We're not worried about the exact time in seconds, but about its behavior as the data size increases.
Main Types of Big O with C# Examples
O(1) - Constant
Explanation: Time doesn't depend on input size.
Pros: Best type of complexity, extremely fast and scalable.
Cons: Not always possible; depends on the problem.
Example: Accessing an array element by index: arr[5]
C# Example:
int x = numbers[5];
O(n) - Linear
Explanation: Grows proportionally to the number of items.
Pros: Usually acceptable for large inputs.
Cons: Can be slow if the input is huge.
Example: Iterating through all items in a list
C# Example:
foreach (var n in numbers) {
Console.WriteLine(n);
}
O(n²) - Quadratic
Explanation: *Grows quickly due to nested loops.
**Pros: **Easy to implement, but generally only suitable for small inputs.
* Cons: **Worst complexity here; not scalable for large inputs.
**Example: Nested loops
C# Example:
foreach (var a in numbers) {
foreach (var b in numbers) {
if(a != b){ /* ... / }
}
}
**O(log n) - Logarithmic*
Explanation: Grows slowly, even with large inputs.
Pros: Very efficient; grows slowly even with large data sets.
Cons: Usually requires data to be specially structured (like a tree or sorted array).
Example: Binary search in a sorted array
C# Example:
int BinarySearch(List list, int target) {
int left = 0, right = list.Count - 1;
while(left <= right){
int mid = (left + right) / 2;
if(list[mid] == target) return mid;
if(list[mid] < target) left = mid + 1;
else right = mid - 1;
}
return -1;
}
O(n log n) - Linearithmic
Explanation: More efficient than O(n²), often used in sorting.
Pros: Acceptable for most inputs; great for tasks like sorting.
Cons: Slower than linear or logarithmic, but still scalable.
Example: **Efficient sorting algorithms, like MergeSort or QuickSort (average case)
**C# Example:
var sorted = numbers.OrderBy(x => x).ToList();
Graphs generated by ChatGPT to help visualize each case.
Why This Matters
In practice, Big O helped me understand that not all code scales well.
Two algorithms can solve the exact same problem, but one stays fast even with millions of records, while the other becomes practically unusable.
Knowing this made me start looking at my code differently.
It's no longer just: "does it work?", but also: "will it still work well if the data grows 10x or 100x?".
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