⏱ Big O Complexity Calculator & Time Complexity Analyzer

Time complexity describes how the runtime of an algorithm scales with input size n. Common complexities are O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n) linearithmic, O(n²) quadratic, and O(2ⁿ) exponential. For interviews, always analyze your solution before coding.

Best case is the fastest scenario (e.g., target found at index 0). Average case is the expected runtime for random inputs. Worst case (Big-O) is the upper bound — what interviewers typically ask about. Quicksort has O(n log n) average but O(n²) worst case.

Space complexity counts all memory your algorithm uses relative to input size. This includes: variables and data structures you create (auxiliary space), and the call stack for recursive functions. In-place algorithms have O(1) space. HashMap-based solutions usually O(n) space.

Amortized complexity averages the cost of operations over a sequence. For example, appending to a dynamic array is O(1) amortized even though resizing is O(n) — because resizing is rare. Python lists and Java ArrayLists use this.

Multiply the complexities of nested loops. One loop O(n) nested inside another O(n) = O(n²). If the inner loop size depends on the outer variable (like j goes from 0 to i), it's still O(n²) but with a coefficient of 0.5 — drop constants, keep O(n²).