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**Data Structures and Algorithms cheat sheet pdf**

This page includes detailed tutorials on various Data Structures types with question-wise problem. A data structure is a special way of storing data in computers for efficient use. This page contains tutorials about various data structures. Topics include: An array Linked List Stack, Queue ,Binary Tree, Binary Search Tree, Handling Graph, Matrix Object-Driven Array. By example a list of items has a same data type using the array data structure. What are C programming languages which can be used to construct lists that extend head points in the list in relational logics? If I have links I can change nodes from one to the other unless I need to exchange data.

## Graph processing.

- A graph processing framework (GPF) is a set of tools oriented to process graphs. Graph vertices are used to model data and edges model relationships between vertices. Since real graphs can be large, complex, and dynamic, GPFs have to deal with the three challenges of data growth: volume, velocity, and variety

## Asymptotic Notations: Properties.

Notation | Meaning |
---|---|

T(n) = O(f(n)) | Asymptotically, T does not grow faster than f. |

T(n) = Omega(f(n)) | Asymptotically, T does not grow slower than f. |

T(n) = Theta(f(n)),when T(n) = O(f(n)) and T(n) = Omega(f(n)) | Asymptotically, T grows equally fast as f. |

T(n) = o(f(n)),means that lim_{n ->infinity}T(n)/f(n)=0 | Asymptotically, T grows slower than f. |

T(n) = omega(f(n)),means that lim_{n ->infinity} T(n)/f(n)=infty. | Asymptotically, T grows faster than f. |

**Table: Standard notations and their meanings**

## Asymptotic Notations: Definitions.

- Asymptotic notations are languages that allow us to analyze an algorithm’s running time by identifying its behavior as the input size for the algorithm increases.

## Common orders of Growth.

- An order of growth is a set of functions whose asymptotic growth behavior is considered equivalent.
**For example:**2n, 100n and n+1 belong to the same order of growth, which is written O(n) in Big-Oh notation and often called linear because every function in the set grows linearly with n.

## Divide and Conquer Recurrences.

- The divide-and-conquer technique involves taking a large-scale problem and dividing it into similar sub-problems of a smaller scale, and recursively solving each of these sub-problems. Generally, a problem is divided into sub-problems repeatedly until the resulting sub-problems are very easy to solve.

## Properties of Logarithms.

log_{a} (uv) = log_{a} u + log_{a} v | ln (uv) = ln u + ln v |

log_{a} (u / v) = log_{a} u – log_{a} v | ln (u / v) = ln u – ln v |

log_{a} u^{n} = n log_{a} u | ln u^{n} = n ln u |

**Figure: The properties on the left hold for any base a.**

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