jeus

+--------------------+-----------------+-----------------------------------------+
|                    |space complexity |             time complexity             |
| Sorting Algorithms +-----------------+------------+--------------+-------------+
|                    | worst case      | best case  | average case | worst case  |
+--------------------+-----------------+------------+--------------+-------------+
| Bubble Sort        | O(1)            | O(n)       | O(n2)        | O(n2)       |
+--------------------+-----------------+------------+--------------+-------------+
| Heapsort           | O(1)            | O(n log n) | O(n log n)   | O(n log n)  |
+--------------------+-----------------+------------+--------------+-------------+
| Insertion Sort     | O(1)            | O(n)       | O(n2)        | O(n2)       |

jeus

+-------------------------------------------------------------------------------------+
|                                    growth-rates                                     |
+---------------+---------+---------+----------+------------+-----------+-------------+
| n f(n)        | log n   | n       | n log n  | n2         | 2n        | n!          |
+---------------+---------+---------+----------+------------+-----------+-------------+
| 10            | 0.003ns | 0.01ns  | 0.033ns  | 0.1ns      | 1ns       | 3.65ms      |
+---------------+---------+---------+----------+------------+-----------+-------------+
| 20            | 0.004ns | 0.02ns  | 0.086ns  | 0.4ns      | 1ms       | 77years     |
+---------------+---------+---------+----------+------------+-----------+-------------+
| 30            | 0.005ns | 0.03ns  | 0.147ns  | 0.9ns      | 1sec      | 8.4x1015yrs |

jeus

+----------------------------+--------------------------------+--------------------------------+
|                            |          Average case          |           Worst case           |
|       Data Structures      +----------+----------+----------+----------+----------+----------+
|                            |  Search  |  Insert  |  Delete  |  Search  |  Insert  |  Delete  |
+----------------------------+----------+----------+----------+----------+----------+----------+
| Array                      |   O(n)   |    N/A   |    N/A   |   O(n)   |    N/A   |    N/A   |
+----------------------------+----------+----------+----------+----------+----------+----------+
| AVL Tree                   | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |
+----------------------------+----------+----------+----------+----------+----------+----------+
| B-Tree                     | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |