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data structure

The data structure was sorted out by myself before the final exam, and some places were not very detailed. Some of them have illustrations and examples, which you can also use to prepare for exams and review.

Edited at 2023-06-05 13:15:04

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data structure

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Outline

data structure

introduction

logical structure

Linear

Linear list, stack, queue, string, array

nonlinear

picture

Tree

storage structure

order

chain

Data operations

Insert, delete, modify, search, sort

Analysis of Algorithms

time complexity

space complexity

linear table

Sequence table

storage

LOC ( ai ) = LOC ( a1 ) L * (i -1)

Operation

Insert and delete (move forward and backward as a whole)

linked list

Single list

Create table

Head plug (in reverse order)

tail plug

insert, delete

Reverse order

Classic question

Whether there is a cycle and determine the intersection point

Whether they intersect and determine the intersection point

speed pointer

Joseph problem

Delete duplicates

Merge linked lists

Is it symmetrical?

Double linked list

circular linked list

static linked list

Don't use pointers

There is maxsize

stacks and queues

stack

sequence stack

chain stack

application

Expression evaluation

queue

chain team

sequential team

False overflow: front-end space cannot be released

circular queue

How to judge if the queue is empty or full

string

storage

order

Fixed length

s[0] stores the string length

Heap allocation

chain

Block chain chunk

pattern matching algorithm

There is backtracking and the speed is slow.

Position the next character of the main string i=i-j 2

KMP

next[j]

Arrays and generalized tables

array

sequential storage

row precedence

Column first

chain storage

Compressed storage of coefficient matrix

triple table

cross linked list

triplet matrix

Triplet with auxiliary vectors

coefficient matrix transpose

compressed transpose

Scan column sequence

Quick transpose

generalized table

Header and footer

get head may be an atom or a table, get tail must be a table

storage

Atomic node

table node

Trees and Binary Trees

nature

Binary tree

nature

n0=n2 1

The left and right child node numbers are 2i, 2i 1 respectively (complete binary tree)

operate

Traverse

recursion

non-recursive

Level traversal

reconstruction

preorder midorder

after middle

Convert

Trees and Binary Trees

Forest and binary trees

clue binary tree

In-order clue binary tree

Huffman tree

make achievements

Choose the two with the smallest weight each time

Compile and code

Left 0 Right 1

sort

Overview

stable/unstable

inside/outside

storage and processing

Sort sequentially (mostly)

Linked list sorting

Address sorting (adding one-dimensional array)

Sorting Algorithm

insertion sort

insert directly

Linear search O(n^2)

Insert in half

O(n^2) The number of comparisons is reduced, but the number of moves is not reduced.

2-way insertion

table insert

Add pointer component to each record

The pointer content is changed to the sorted successor address.

Hill sort (shrinking increment)

unstable

swap sort

Bubble Sort

Constantly comparing pairs

Quick sort

process

unstable

selection sort

Simple selection sort

Each time, find a minimum value and exchange it with the front of the column to be sorted.

Tournament sorting (tree selection sorting)

complete binary tree

It can be agreed that the node is smaller on the left and larger on the right

Heap sort

Build a pile

sort

Time efficiency O(nlog2n), space efficiency O(1), unstable

merge sort

Continuously merge into ordered subsequences

Time efficiency O(nlog2n), space efficiency O(n)

Radix sort

Multiple keywords sorted by different bit values

sorting method

Most significant bit first MSD

Least Significant First LSD

storage method

order

chain

Find

static lookup table

Sequential (linear) search

ASL=(n 1)/2

Search in half in ordered sequence list

ASL=[log2 n] 1

Index sequence table block search

ASL=index ASL sequence table ASL

Static tree table lookup (suboptimal tree)

Performance analysis

Find

Sorted sequence list O(log2 n)

insert delete

Linked list O(1)

Dynamic lookup tree table

Binary search (sort) tree

insert

delete

leaf

Change the parent corresponding pointer field to empty

Only left/right subtree

The parent pointer field points to the remaining left/right subtree

There are left and right subtrees

Binary balanced tree AVL tree

balanced rotation

Single rotation (straight line)

Double rotation (polyline)

Hash table (hash table)

Hash function construction

direct addressing

Linear function Hash(key)=a*key b

Divide and leave remainder

Hash(key)=key mod p

p is a prime number or a composite number with a prime factor not less than 20

digital analysis

Get certain keywords

Find the center of the square

After squaring, take the middle digits

fold

Split, superposition and sum

Split, transpose, sum

random number

Hash(key)=random(key) pseudo-random number

handling conflicts

Open addressing (open address)

Linear probing (finding the next empty address)

Hi=(Hash(key) di) mod m (di is the increment, m is the table length)

secondary detection

pseudo-random detection

di is a pseudo-random sequence

chain address

Thought

ASL calculation (as in the above example)

(Re)Double Hash Function

If a collision occurs, calculate another hash function

Create a public overflow area

Performance analysis

ASL is related to the filling factor (number/length of data filled in)

picture

the term

There are undirected, completely, (strongly) connected graphs (components)

Adjacent points, arc head and tail, ingress and egress

path, path length, simple path

storage structure

Adjacency matrix (array)

Undirected graph

directed graph

weighted graph

Boundless is infinite

Adjacency list (chained)

Not unique

Directed graph, out-degree adjacency list and inverse adjacency list

cross linked list

adjacency multiple list

Traverse

Breadth-First BFS (Queue)

Depth-first DFS (recursive)

Adjacency list (sparse graph)

Adjacency matrix (dense graph)

Each call gets a connected component

connectivity

Minimum Spanning Tree MST

n vertices, n-1 edges, minimum weight

Prim algorithm

Merge vertices (dense net)

Kruskal algorithm

Merge edges without generating loops (sparse network)

shortest path problem

Dijkstra's algorithm (source point to each vertex)

Floyd algorithm (between pairs of vertices)

application

Topological sorting (no loops)

Select a vertex with an in-degree of 0, and the in-degree of the arc vertex is -1

Critical Path