Time Complexity (Big-O Notation) in Algorithms

1. What is Algorithm Complexity?

Algorithm = step-by-step procedure to solve a problem.

Complexity = how much time or memory it needs as input size grows.
We measure this using Big-O notation.

2. Why Big-O Notation?

It d…


This content originally appeared on DEV Community and was authored by davinceleecode

1. What is Algorithm Complexity?

  • Algorithm = step-by-step procedure to solve a problem.
  • Complexity = how much time or memory it needs as input size grows.
  • We measure this using Big-O notation.

2. Why Big-O Notation?

  • It describes the growth rate, not the exact time.
  • Helps compare algorithms (fast vs slow) independent of hardware.
  • Example: One algorithm takes 1 second for 1000 inputs, another takes 10 seconds — Big-O tells us how this scales when inputs grow to 1 million.

3. Common Complexities (with examples)

🔹 O(1) → Constant time

  • Same time, no matter the input size.
  • Example: access arr[5], simple formula like n(n+1)/2.

🔹 O(log n) → Logarithmic time

  • Input size shrinks in half each step.
  • Example: Binary Search in a sorted array.

🔹 O(n) → Linear time

  • One loop over all n items.
  • Example: Find the max element in an array.

🔹 O(n log n) → Linearithmic time

  • Appears in efficient sorting algorithms.
  • Example: Merge Sort, Quick Sort.

🔹 O(n²) → Quadratic time

  • Double loop → compare all pairs.
  • Example: Bubble Sort, checking all pairs in a matrix.

🔹 O(2ⁿ) → Exponential time

  • Doubles work for each extra input.
  • Example: Recursive Fibonacci, brute force subsets.

🔹 O(n!) → Factorial time

  • Explodes very fast → all permutations.
  • Example: Traveling Salesman (brute force).

4. Formula vs Algorithm

  • Formula: Already solved shortcut, runs in O(1).
    • Example: Sum of first n numbers = n(n+1)/2.
  • Algorithm: Step-by-step method to compute the answer.
    • Example: Loop through numbers and add one by one = O(n).

✅ TL;DR:

  • Big-O tells us how fast/slow an algorithm grows with input size.
  • Formulas are direct (O(1)), algorithms can vary (O(n), O(n log n), etc).
  • Choosing the right algorithm = huge performance difference in real-world apps.

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This content originally appeared on DEV Community and was authored by davinceleecode


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