What is Big O notation and why does it matter?

Big O describes how an algorithm's time/space grows as input size (n) increases. Common complexities: O(1) constant — hash table lookup. O(log n) logarithmic — binary search. O(n) linear — simple loop. O(n log n) — merge sort, quicksort average. O(n²) quadratic — nested loops, bubble sort. O(2ⁿ) exponential — brute force subset problems. Why it matters: O(n²) with n=1000 → 1M operations. O(n log n) → ~10K operations. Choosing the right algorithm can mean seconds vs hours.