| Algorithm | Time Complexity | Comparison | Explanation |
|---|---|---|---|
| Linear Search | O(n) | Slower than Jump, Binary, Interpolation Search | Searches every element until it finds the target. |
| Binary Search | O(log n) | Faster than Linear Search | Divides the sorted list in half repeatedly to search. |
| Jump Search | O(√n) | Faster than Linear Search, Slower than Binary Search | Searches in a sorted array by jumping fixed steps. |
| Exponential Search | O(log i) | Faster than Linear, Jump, Comparable to Binary Search | Useful when the target is near the beginning. |
| Ternary Search | O(log₃ n) | Comparable to Binary Search | Divides array into three parts instead of two. |
| Interpolation Search | O(log(log n)) | Faster than Binary, Jump, and Linear Search for uniformly distributed data | Estimates the position based on the key. |
| Bubble Sort | O(n²) | Slower than Merge, Quick, Heap, Radix Sort | Sorts by repeatedly swapping adjacent elements. |
| Selection Sort | O(n²) | Similar to Bubble Sort, Slower than Merge and Quick Sort | Finds the minimum repeatedly and moves it to sorted portion. |
| Insertion Sort | O(n²) | Faster than Bubble Sort for nearly sorted data, Slower than Quick and Merge Sort | Builds the sorted list one item at a time. |
| Merge Sort | O(n log n) | Faster than Bubble, Selection, Insertion Sort | Divides the list in halves recursively and merges them. |
| Quick Sort | O(n log n) | Faster than Bubble, Selection, Insertion Sort, Comparable to Merge Sort | Sorts using a partitioning strategy. |
| Heap Sort | O(n log n) | Faster than Bubble, Selection, Insertion Sort | Uses a binary heap to sort elements. |
| Radix Sort | O(nk) | Faster than Bubble, Selection Sort for large integers, but Slower than Quick Sort on small datasets | Sorts numbers by individual digits. |
| Counting Sort | O(n+k) | Faster than Comparison-based Sorts for small range of numbers | Uses counting of elements for sorting. |
| Bucket Sort | O(n + k) | Faster than Bubble, Comparable to Radix Sort for uniformly distributed inputs | Divides elements into buckets and sorts them. |
| Dijkstra’s Algorithm | O((V + E) log V) | Faster than Bellman-Ford, but not a direct comparison to sorting | Finds shortest paths from a single source. |
| Bellman-Ford Algorithm | O(VE) | Slower than Dijkstra’s Algorithm | Finds shortest paths in a graph with negative weights. |
| Floyd-Warshall Algorithm | O(V³) | Slower than Dijkstra’s Algorithm | Finds shortest paths between all pairs of vertices. |
| A Search Algorithm* | O(E) (heuristic) | Faster than Dijkstra for specific heuristic-based searches | Finds the shortest path in graphs using heuristics. |
| DFS (Depth-First Search) | O(V + E) | Faster than Breadth-First Search for deep graphs | Explores as far as possible along a branch. |
| BFS (Breadth-First Search) | O(V + E) | Faster for shortest unweighted paths than DFS | Explores level by level. |
| Kruskal’s Algorithm | O(E log E) | Faster than Prim’s for sparse graphs | Finds the minimum spanning tree. |
| Prim’s Algorithm | O(V²) or O(E log V) | Comparable to Kruskal’s Algorithm | Finds the minimum spanning tree. |
| Tree Type | Applications |
|---|---|
| General Trees | File systems, Scene graphs |
| Binary Search Trees | Databases, Searching, Auto-complete |
| Heaps | Task scheduling, Shortest path algorithms |
| Tries | Auto-complete, Dictionary lookups |
| B-trees/B+ trees | Database indexing |
| Syntax Trees | Compilers, Programming language interpreters |
| Decision Trees | Machine learning models |
| Merkle Trees | Blockchain, Cryptography |