Time Complexity Analyzer

Analyze and compare time complexities of common algorithms with detailed breakdowns.

AlgorithmBestAverageWorstSpaceStable
Bubble SortO(n)O(n²)O(n²)O(1)
Selection SortO(n²)O(n²)O(n²)O(1)
Insertion SortO(n)O(n²)O(n²)O(1)
Merge SortO(n log n)O(n log n)O(n log n)O(n)
Quick SortO(n log n)O(n log n)O(n²)O(log n)
Heap SortO(n log n)O(n log n)O(n log n)O(1)
Counting SortO(n+k)O(n+k)O(n+k)O(k)
Radix SortO(nk)O(nk)O(nk)O(n+k)

Analyzing Algorithm Time Complexity

Time complexity analysis is fundamental to computer science and software engineering. It allows you to predict how an algorithm's performance scales with input size, helping you make informed decisions about which algorithms to use in different scenarios.

This tool provides comprehensive comparison tables for sorting, searching, and graph algorithms. Understanding these complexities helps you write efficient code and excel in technical interviews at top tech companies.

Sorting Algorithm Selection

Choose Quick Sort or Merge Sort for general-purpose sorting (O(n log n)). Use Counting Sort or Radix Sort for integers with known range. Insertion Sort works well for small or nearly-sorted arrays. Avoid Bubble Sort except for educational purposes.

Search Algorithm Efficiency

Binary Search is incredibly efficient at O(log n) but requires sorted data. Hash tables provide O(1) average lookup but need extra space. Linear search is simple but slow for large datasets. Choose based on your data characteristics.

Graph Algorithm Applications

BFS finds shortest paths in unweighted graphs. DFS is useful for topological sorting and cycle detection. Dijkstra handles weighted graphs efficiently. Understanding when to use each is crucial for solving real-world problems.

Stability in Sorting

A stable sort maintains the relative order of equal elements. This matters when sorting by multiple keys. Merge Sort and Insertion Sort are stable. Quick Sort and Heap Sort are not stable by default.