# Sorting In Swift

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## Sorting in Swift

## This course helps you get started with sorting algorithms in Swift.

- Bubble Sort
- Insertion Sort
- Selection Sort
- Merge Sort

**What is Big-O notation?**

Big-O notation is a way to tell how well an algorithm scales as the # of elements increase. In other words, how efficient the algorithm is as the data scales. When you are measuring the performance of a sorting algorithm, you compare the worst-case scenario (e.g. the longest amount of time the method can take to sort an array).

**Complexities**

###### O(n!) - Factorial Complexity

Example: Say a sorting algorithm has a factorial complexity. If there are 10 elements in the array, it will take 3628800 steps (10! or 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) to sort the array.

##### O(2^{n}) - Exponential Complexity

Example: Say a sorting algorithm has a exponential complexity. If there are 10 elements in the array, it will take 1024 steps (2^10) to sort the array.

##### O(n^{2}) - Quadratic Complexity

Example: Say a sorting algorithm has a quadratic complexity. If there are 10 elements in the array, it will take 100 steps (10^2) to sort the array.

##### O(n log_{2}n) - Linearithmic Complexity

Example: Say a sorting algorithm has a linearithmic complexity. If there are 10 elements in the array, it will take ~33-34 steps (10 * (log_{2}10)) to sort the array.

##### O(n) - Linear Complexity

Example: Say a sorting algorithm has a linear complexity. If there are 10 elements in the array, it will take 10 steps to sort the array. Linear complexities takes as many steps as the number of elements.

##### O(log_{2}n) - Logarithmic Complexity

Example: Say a sorting algorithm has a logarithmic complexity. If there are 10 elements in the array, it will take ~3-4 steps (log_{2}10) to sort the array.