lecture 24 sorting algorithms

certainly! while i don’t have access to specific lecture materials, i can provide you with a comprehensive overview of sorting algorithms that are commonly covered in lectures, along with code examples in python. let's discuss several popular sorting algorithms, their time complexities, and provide examples for each.

sorting algorithms overview

sorting algorithms are algorithms that put elements of a list in a certain order (most commonly in numerical or lexicographical order). here are some of the most common sorting algorithms:

1. **bubble sort**
2. **selection sort**
3. **insertion sort**
4. **merge sort**
5. **quick sort**
6. **heap sort**
7. **counting sort**
8. **radix sort**

1. bubble sort

bubble sort is a simple comparison-based algorithm that repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order.

**time complexity:**
- best: o(n)
- average: o(n²)
- worst: o(n²)

**python code example:**

2. selection sort

selection sort divides the input list into two parts: a sorted and an unsorted part. it repeatedly selects the smallest (or largest) element from the unsorted part and moves it to the sorted part.

**time complexity:**
- best: o(n²)
- average: o(n²)
- worst: o(n²)

**python code example:**

3. insertion sort

insertion sort builds the final sorted array one element at a time. it is much less efficient on large lists than the similar algorithms (like quicksort, heapsort, or merge sort).

**time complexity:**
- best: o(n)
- average: o(n²)
- worst: o(n²)

**python code example:**

4. merge sort

merge sort is a divide-and-conquer algorithm that was invented by john von neumann in 1945. it divides the unsorted list into n sublists, each containing one element, and then merges those sublists to produce new sorted sublists until there is only one sublist remaining.

**time complexity:**
- best: o(n log n)
- average: o(n log n)
- worst: o(n log n)

**python code example:**

5. quick sort

qui ...

#SortingAlgorithms #DataStructures #numpy
sorting algorithms
bubble sort
quicksort
mergesort
heapsort
insertion sort
selection sort
time complexity
space complexity
algorithm efficiency
stability in sorting
divide and conquer
comparison-based sorting
non-comparison sorting
worst-case scenario