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whoparthgarg/Data-Structures-and-Algorithms:

原作者: [db:作者] 来自: 网络 收藏 邀请

开源软件名称：

whoparthgarg/Data-Structures-and-Algorithms

开源软件地址：

https://github.com/whoparthgarg/Data-Structures-and-Algorithms

开源编程语言：

C++ 100.0%

开源软件介绍：

Data-Structures-and-Algorithms

logo

A repository which contains DSA questions from basic to advanced for interview preparation.

Setting up and running the project

Fork the repo and clone it.

git clone https://github.com/whoparthgarg/Data-Structures-and-Algorithms.git

Contents

SNo Name
1 Mathematics
2 Bit Manipulation
3 Recursion
4 Arrays
5 Searching
6 Sorting
7 Matrix
8 Hashing
9 Strings
10 Linked List
11 Stack
12 Queue
13 Deque
14 Binary Tree
15 Binary Search Tree
16 Heap
17 Graph
18 Greedy
19 Backtracking
20 Dynamic Programming

Big O Notation

Big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows. On the chart below you may find most common orders of growth of algorithms specified in Big O notation.

Big O graphs

Source: Big O Cheat Sheet.

Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.

Big O Notation Computations for 10 elements Computations for 100 elements Computations for 1000 elements
O(1) 1 1 1
O(log N) 3 6 9
O(N) 10 100 1000
O(N log N) 30 600 9000
O(N^2) 100 10000 1000000
O(2^N) 1024 1.26e+29 1.07e+301
O(N!) 3628800 9.3e+157 4.02e+2567

Data Structure Operations Complexity

Data Structure Access Search Insertion Deletion Comments
Array 1 n n n
Stack n n 1 1
Queue n n 1 1
Linked List n n 1 n
Hash Table - n n n In case of perfect hash function costs would be O(1)
Binary Search Tree n n n n In case of balanced tree costs would be O(log(n))
B-Tree log(n) log(n) log(n) log(n)
Red-Black Tree log(n) log(n) log(n) log(n)
AVL Tree log(n) log(n) log(n) log(n)
Bloom Filter - 1 1 - False positives are possible while searching

Array Sorting Algorithms Complexity

Name Best Average Worst Memory Stable Comments
Bubble sort n n2 n2 1 Yes
Insertion sort n n2 n2 1 Yes
Selection sort n2 n2 n2 1 No
Heap sort n log(n) n log(n) n log(n) 1 No
Merge sort n log(n) n log(n) n log(n) n Yes
Quick sort n log(n) n log(n) n2 log(n) No Quicksort is usually done in-place with O(log(n)) stack space
Shell sort n log(n) depends on gap sequence n (log(n))2 1 No
Counting sort n + r n + r n + r n + r Yes r - biggest number in array
Radix sort n * k n * k n * k n + k Yes k - length of longest key



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