time complexity analysis of algorithms code example

Example 1: algorithms and their time and space complexity

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|Sorting Algorithm |    Best Case     |   Average Case   |    Worst Case    |
|------------------|------------------|------------------|------------------|
|Selection Sort    |       Ω(n²)      |      θ(n²)       |       O(n²)      |
|Bubble Sort       |       Ω(n)       |      θ(n²)       |       O(n²)      |
|Insertion Sort    |       Ω(n)       |      θ(n²)       |       O(n²)      |
|Merge Sort        |   Ω(n logn(n))   |   θ(n logn(n))   |   O(n logn(n))   |
|Quick Sort        |   Ω(n logn(n))   |   θ(n logn(n))   |       O(n²)      |
|Heap Sort         |   Ω(n logn(n))   |   θ(n logn(n))   |   O(n logn(n))   |
|Radix Sort        |      Ω(nk)       |      θ(nk)       |       O(nk)      |
|Bucket Sort       |     Ω(n + k)     |     θ(n + k)     |       O(n²)      |
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Example 2: algorithms and their time and space complexity

--------------------------------
|Input Size |  Max Complexity  |
|-----------|------------------|
|10^18      |       O(logn)    |
|10^8       |       O(n)       |
|10^7       |       O(nlogn)   |
|10^4       |       O(n^2)     |
|10^2       |       O(n^3)     |
|9*10       |       O(n^4)     |
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