Algorithm Learning notes (i)

There are two kinds of ideas , like the jeweler on the Velvet Gem Bald , one is Calculus , the other is the algorithm. Calculus and the Mathematical analysis system established on the basis of calculus have created modern science, while algorithms have created the modern world. --"The advent of Algorithms "

Basic Data Structures

1. Linear data structure

(1) array : " string " ( e.g. data string , binary string )

(2) linked list: single linked list : data + address pointer for next element

doubly linked list : The address pointer of the previous element + data + The address pointer of the next element

Note : The difference between an array and a linked list : access is different , the array is direct single access , and the linked list is a chain-based access.

(3) Linear list :

stack: "LIFO" ( LIFO), "a stack of plates"

Insert and delete operations at end-of- stack top

queue : " FIFO", " Customer queue "

Remove Team head -and- out team

Insert -- team tail -- queue

Priority Queue : ( task ) , find or maximum element, insert a new element- - Heap

2. Figure

Graph without direction

A map of the direction

difference: whether vertex pairs (U,V) and vertex pairs (V,u) same

definition: Figure G=<v,e>

V is a finite set whose elements are vertices

E is a finite set whose elements are a pair of vertices and are edges.

Note: Do not block the ring,0<=| e|<=| v| (| V|-1)/2

depending on the number of sides : full circle, dense circle, sparse circle.

the representation of the graph :

adjacency Matrix: A boolean matrix of N*n

Adjacency list: A column with a value of 1 in the adjacency matrix

weighted circles: assigning values to edges ( weight / cost )

paths and Loops:

path: the contiguous vertex sequence starting with u ending at V

Simple path:a,c,e,f length is 3

non-simple path : a,c,e,c,f length is 4

Note: For a direction map, a forward path

Connectivity : Whether connectivity--- depends on the presence of connected components

no loop diagram: No loop included

3. Tree ( connected without circuit diagram )

Forest ( no loop but not necessarily connected, its connected component is a tree )

There is a root tree: ( application ) Describe hierarchical relationships

State space tree: Backtracking and branch boundaries

distinction / discrimination: ancestors, true ancestors, parents, children, brothers, leaf nodes, parent nodes, descendants, subtrees.

The depth of the vertex

Height of the tree

4. Ordered Tree

Binary tree, binary search tree, multi-path lookup tree.

Note: first child after brother notation

5. Collections and dictionaries

a method that represents a collection: a bit vector, Linear list Structure

Abstract data type: A collection of abstract objects for data items and a series of operations on those objects

Collection Merge Issues

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Algorithm Learning notes (i)