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**Sorting**

Sorting algorithms are a fundamental part of computer science. Being able to sort through a large data set quickly and efficiently is a problem you will be likely to encounter on nearly a daily basis.

Here are the main sorting algorithms:

Algorithm | Data Structure | Time Complexity - Best | Time Complexity - Average | Time Complexity - Worst | Worst Case Auxiliary Space Complexity |
---|---|---|---|---|---|

Quicksort | Array | O(n log(n)) | O(n log(n)) | O(n^2) | O(n) |

Merge Sort | Array | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(n) |

Heapsort | Array | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(1) |

Bubble Sort | Array | O(n) | O(n^2) | O(n^2) | O(1) |

Insertion Sort | Array | O(n) | O(n^2) | O(n^2) | O(1) |

Select Sort | Array | O(n^2) | O(n^2) | O(n^2) | O(1) |

Bucket Sort | Array | O(n+k) | O(n+k) | O(n^2) | O(nk) |

Radix Sort | Array | O(nk) | O(nk) | O(nk) | O(n+k) |

# Searching

Another crucial skill to master in the field of computer science is how to search for an item in a collection of data quickly. Here are the most common searching algorithms, their corresponding data structures, and time complexities.

Here are the main searching algorithms:

Algorithm | Data Structure | Time Complexity - Average | Time Complexity - Worst | Space Complexity - Worst |
---|---|---|---|---|

Depth First Search | Graph of |V| vertices and |E| edges | - | O(|E|+|V|) | O(|V|) |

Breadth First Search | Graph of |V| vertices and |E| edges | - | O(|E|+|V|) | O(|V|) |

Binary Search | Sorted array of n elements | O(log(n)) | O(log(n)) | O(1) |

Brute Force | Array | O(n) | O(n) | O(1) |

Bellman-Ford | Graph of |V| vertices and |E| edges | O(|V||E|) | O(|V||E|) | O(|V|) |

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# Graphs

Graphs are an integral part of computer science. Mastering them is necessary to become an accomplished software developer. Here is the data structure analysis of graphs:

Node/Edge Management | Storage | Add Vertex | Add Edge | Remove Vertex | Remove Edge | Query |
---|---|---|---|---|---|---|

Adjacency List | O(|V|+|E|) | O(1) | O(1) | O(|V| + |E|) | O(|E|) | O(|V|) |

Incidence List | O(|V|+|E|) | O(1) | O(1) | O(|E|) | O(|E|) | O(|E|) |

Adjacency Matrix | O(|V|^2) | O(|V|^2) | O(1) | O(|V|^2) | O(1) | O(1) |

Incidence Matrix | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|V| ⋅ |E|) | O(|E|) |

# Heaps

Storing information in a way that is quick to retrieve, add, and search on, is a very important technique to master. Here is what you need to know about heap data structures:

Heaps | Heapify | Find Max | Extract Max | Increase Key | Insert | Delete | Merge |
---|---|---|---|---|---|---|---|

Sorted Linked List | - | O(1) | O(1) | O(n) | O(n) | O(1) | O(m+n) |

Unsorted Linked List | - | O(n) | O(n) | O(1) | O(1) | O(1) | O(1) |

Binary Heap | O(n) | O(1) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(m+n) |

Binomial Heap | - | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) |

Fibonacci Heap | - | O(1) | O(log(n))* | O(1)* | O(1) | O(log(n))* | O(1) |

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