MindMap Gallery Algorithm design analysis
This is a mind map about algorithm design and analysis, including the general definition of algorithms, algorithm characteristics, algorithm design requirements, methods of imitating algorithm efficiency, etc.
Edited at 2022-10-21 16:57:23This Valentine's Day brand marketing handbook provides businesses with five practical models, covering everything from creating offline experiences to driving online engagement. Whether you're a shopping mall, restaurant, or online brand, you'll find a suitable strategy: each model includes clear objectives and industry-specific guidelines, helping brands transform traffic into real sales and lasting emotional connections during this romantic season.
This Valentine's Day map illustrates love through 30 romantic possibilities, from the vintage charm of "handwritten love letters" to the urban landscape of "rooftop sunsets," from the tactile experience of a "pottery workshop" to the leisurely moments of "wine tasting at a vineyard"—offering a unique sense of occasion for every couple. Whether it's cozy, experiential, or luxurious, love always finds the most fitting expression. May you all find the perfect atmosphere for your love story.
The ice hockey schedule for the Milano Cortina 2026 Winter Olympics, featuring preliminary rounds, quarterfinals, and medal matches for both men's and women's tournaments from February 5–22. All game times are listed in Eastern Standard Time (EST).
This Valentine's Day brand marketing handbook provides businesses with five practical models, covering everything from creating offline experiences to driving online engagement. Whether you're a shopping mall, restaurant, or online brand, you'll find a suitable strategy: each model includes clear objectives and industry-specific guidelines, helping brands transform traffic into real sales and lasting emotional connections during this romantic season.
This Valentine's Day map illustrates love through 30 romantic possibilities, from the vintage charm of "handwritten love letters" to the urban landscape of "rooftop sunsets," from the tactile experience of a "pottery workshop" to the leisurely moments of "wine tasting at a vineyard"—offering a unique sense of occasion for every couple. Whether it's cozy, experiential, or luxurious, love always finds the most fitting expression. May you all find the perfect atmosphere for your love story.
The ice hockey schedule for the Milano Cortina 2026 Winter Olympics, featuring preliminary rounds, quarterfinals, and medal matches for both men's and women's tournaments from February 5–22. All game times are listed in Eastern Standard Time (EST).
Algorithm design analysis
Algorithm overview
Definition (universal)
An algorithm is a description of the steps to solve a specific problem. It is represented in a computer as a limited sequence of instructions, and each instruction represents one or more operations.
Characteristics of algorithms
input Output
There is at least one input or output
Finiteness
Limited steps, no infinite loop
certainty
Each step has a definite meaning and there will be no ambiguity
feasibility
Every step is executable
Algorithm design requirements
correctness
readability
Robustness
When the input data is illegal, the algorithm can also perform relevant processing without producing abnormal or inexplicable results.
High time efficiency or low storage capacity
Try to use the least storage space, spend the least time, and accomplish the same thing is a good algorithm
But you often can’t have your cake and eat it too.
A measure of algorithm efficiency
post hoc statistical methods
Obviously this method has major flaws and is no longer adopted.
Use computer machines to compare the running times of programs to determine the efficiency of the algorithm.
ex ante analysis and estimation method
Program running time depends on factors
algorithm strategy
Problem size
Quality of code produced by compilation
Machine execution speed
The time complexity of the algorithm
Pushing to big O order method
constant order
O(1)
linear order
O(n)
Logarithmic order
O(log2n)
square order
O(n^2)
Exponential order
O(2^n)
consider the situation
worst case scenario
is a guarantee
average situation
Represents the expected running time
For specific examples, see my blog
https://mp.csdn.net/mp_blog/creation/editor/127173263
The time complexity of the algorithm
Constant order O(1)
Constant space is used in scenarios where the size of the storage space used by the algorithm is fixed and has no direct relationship with the input size.
Linear order O(n)
Linear space is used when the storage space used by the algorithm is a linear set (such as a list). The size of the linear set is proportional to the input size n. In addition, the space complexity associated with general recursive operations is mostly linear order O(n) with the recursion depth n.
Square order O(n^2
: While space, when the storage space used by the algorithm is a collection of lists, the size of both latitudes of the two-dimensional list is proportional to the input size n.
Algorithm for exchanging space for time
Please see my blog for detailed introduction
https://mp.csdn.net/mp_blog/creation/editor/127185025
NP-complete theory
effect
Determine how inherently complex the problem to be solved is
significance
If the inherent complexity of a problem to be solved is determined, whether it is simple or difficult, and the lower bound of the calculation time is determined
You can know how effective an algorithm can be designed for this problem.
easy
Polynomial time complexity is 'easy' problem
constant order
O(1)
linear order
O(n)
Logarithmic order
O(log2n)
square order
O(n^2)
Disaster
The time complexity of exponential function is ‘hard’ problem
unsolvable problem
Turing halt problem
p-type questions
All decision problems that can be solved in polynomial time constitute problems of type p
Easy-to-solve problem classes under deterministic computing models
NP type problem
non-deterministic algorithm
Divide problem solving into two stages: guessing and verification
guess
is non-deterministic
verify
deterministic
Verify that the solution given by the guessing phase of the algorithm is correct
Easy test under non-deterministic calculation model Certification issues
Often, solving a problem is much more difficult than verifying a solution to the problem
example
traveling salesperson problem
debate
From the definition
P belongs to NP
most scientists believe
P != NP
Main Topic
Main Topic