This slides gives a strong overview of backtracking algorithm. How it came and general approaches of the techniques. Also some well-known problem and solution of backtracking algorithm.
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons each partial candidate c ("backtracks") as soon as it determines that c cannot possibly be completed to a valid solution.
P, NP, NP-Complete, and NP-Hard
Reductionism in Algorithms
NP-Completeness and Cooks Theorem
NP-Complete and NP-Hard Problems
Travelling Salesman Problem (TSP)
Travelling Salesman Problem (TSP) - Approximation Algorithms
PRIMES is in P - (A hope for NP problems in P)
Millennium Problems
Conclusions
Artificial Intelligence: Introduction, Typical Applications. State Space Search: Depth Bounded
DFS, Depth First Iterative Deepening. Heuristic Search: Heuristic Functions, Best First Search,
Hill Climbing, Variable Neighborhood Descent, Beam Search, Tabu Search. Optimal Search: A
*
algorithm, Iterative Deepening A*
, Recursive Best First Search, Pruning the CLOSED and OPEN
Lists
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons each partial candidate c ("backtracks") as soon as it determines that c cannot possibly be completed to a valid solution.
P, NP, NP-Complete, and NP-Hard
Reductionism in Algorithms
NP-Completeness and Cooks Theorem
NP-Complete and NP-Hard Problems
Travelling Salesman Problem (TSP)
Travelling Salesman Problem (TSP) - Approximation Algorithms
PRIMES is in P - (A hope for NP problems in P)
Millennium Problems
Conclusions
Artificial Intelligence: Introduction, Typical Applications. State Space Search: Depth Bounded
DFS, Depth First Iterative Deepening. Heuristic Search: Heuristic Functions, Best First Search,
Hill Climbing, Variable Neighborhood Descent, Beam Search, Tabu Search. Optimal Search: A
*
algorithm, Iterative Deepening A*
, Recursive Best First Search, Pruning the CLOSED and OPEN
Lists
Minmax Algorithm In Artificial Intelligence slidesSamiaAziz4
Mini-max algorithm is a recursive or backtracking algorithm that is used in decision-making and game theory. Mini-Max algorithm uses recursion to search through the game-tree.
Min-Max algorithm is mostly used for game playing in AI. Such as Chess, Checkers, tic-tac-toe, go, and various tow-players game. This Algorithm computes the minimax decision for the current state.
This presentation discuses the following topics:
What is A-Star (A*) Algorithm in Artificial Intelligence?
A* Algorithm Steps
Why is A* Search Algorithm Preferred?
A* and Its Basic Concepts
What is a Heuristic Function?
Admissibility of the Heuristic Function
Consistency of the Heuristic Function
Problem solving
Problem formulation
Search Techniques for Artificial Intelligence
Classification of AI searching Strategies
What is Search strategy ?
Defining a Search Problem
State Space Graph versus Search Trees
Graph vs. Tree
Problem Solving by Search
Minmax Algorithm In Artificial Intelligence slidesSamiaAziz4
Mini-max algorithm is a recursive or backtracking algorithm that is used in decision-making and game theory. Mini-Max algorithm uses recursion to search through the game-tree.
Min-Max algorithm is mostly used for game playing in AI. Such as Chess, Checkers, tic-tac-toe, go, and various tow-players game. This Algorithm computes the minimax decision for the current state.
This presentation discuses the following topics:
What is A-Star (A*) Algorithm in Artificial Intelligence?
A* Algorithm Steps
Why is A* Search Algorithm Preferred?
A* and Its Basic Concepts
What is a Heuristic Function?
Admissibility of the Heuristic Function
Consistency of the Heuristic Function
Problem solving
Problem formulation
Search Techniques for Artificial Intelligence
Classification of AI searching Strategies
What is Search strategy ?
Defining a Search Problem
State Space Graph versus Search Trees
Graph vs. Tree
Problem Solving by Search
Analysis & Design of Algorithms
Backtracking
N-Queens Problem
Hamiltonian circuit
Graph coloring
A presentation on unit Backtracking from the ADA subject of Engineering.
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete:
An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set.
A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems.
StarCompliance is a leading firm specializing in the recovery of stolen cryptocurrency. Our comprehensive services are designed to assist individuals and organizations in navigating the complex process of fraud reporting, investigation, and fund recovery. We combine cutting-edge technology with expert legal support to provide a robust solution for victims of crypto theft.
Our Services Include:
Reporting to Tracking Authorities:
We immediately notify all relevant centralized exchanges (CEX), decentralized exchanges (DEX), and wallet providers about the stolen cryptocurrency. This ensures that the stolen assets are flagged as scam transactions, making it impossible for the thief to use them.
Assistance with Filing Police Reports:
We guide you through the process of filing a valid police report. Our support team provides detailed instructions on which police department to contact and helps you complete the necessary paperwork within the critical 72-hour window.
Launching the Refund Process:
Our team of experienced lawyers can initiate lawsuits on your behalf and represent you in various jurisdictions around the world. They work diligently to recover your stolen funds and ensure that justice is served.
At StarCompliance, we understand the urgency and stress involved in dealing with cryptocurrency theft. Our dedicated team works quickly and efficiently to provide you with the support and expertise needed to recover your assets. Trust us to be your partner in navigating the complexities of the crypto world and safeguarding your investments.
Show drafts
volume_up
Empowering the Data Analytics Ecosystem: A Laser Focus on Value
The data analytics ecosystem thrives when every component functions at its peak, unlocking the true potential of data. Here's a laser focus on key areas for an empowered ecosystem:
1. Democratize Access, Not Data:
Granular Access Controls: Provide users with self-service tools tailored to their specific needs, preventing data overload and misuse.
Data Catalogs: Implement robust data catalogs for easy discovery and understanding of available data sources.
2. Foster Collaboration with Clear Roles:
Data Mesh Architecture: Break down data silos by creating a distributed data ownership model with clear ownership and responsibilities.
Collaborative Workspaces: Utilize interactive platforms where data scientists, analysts, and domain experts can work seamlessly together.
3. Leverage Advanced Analytics Strategically:
AI-powered Automation: Automate repetitive tasks like data cleaning and feature engineering, freeing up data talent for higher-level analysis.
Right-Tool Selection: Strategically choose the most effective advanced analytics techniques (e.g., AI, ML) based on specific business problems.
4. Prioritize Data Quality with Automation:
Automated Data Validation: Implement automated data quality checks to identify and rectify errors at the source, minimizing downstream issues.
Data Lineage Tracking: Track the flow of data throughout the ecosystem, ensuring transparency and facilitating root cause analysis for errors.
5. Cultivate a Data-Driven Mindset:
Metrics-Driven Performance Management: Align KPIs and performance metrics with data-driven insights to ensure actionable decision making.
Data Storytelling Workshops: Equip stakeholders with the skills to translate complex data findings into compelling narratives that drive action.
Benefits of a Precise Ecosystem:
Sharpened Focus: Precise access and clear roles ensure everyone works with the most relevant data, maximizing efficiency.
Actionable Insights: Strategic analytics and automated quality checks lead to more reliable and actionable data insights.
Continuous Improvement: Data-driven performance management fosters a culture of learning and continuous improvement.
Sustainable Growth: Empowered by data, organizations can make informed decisions to drive sustainable growth and innovation.
By focusing on these precise actions, organizations can create an empowered data analytics ecosystem that delivers real value by driving data-driven decisions and maximizing the return on their data investment.
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...John Andrews
SlideShare Description for "Chatty Kathy - UNC Bootcamp Final Project Presentation"
Title: Chatty Kathy: Enhancing Physical Activity Among Older Adults
Description:
Discover how Chatty Kathy, an innovative project developed at the UNC Bootcamp, aims to tackle the challenge of low physical activity among older adults. Our AI-driven solution uses peer interaction to boost and sustain exercise levels, significantly improving health outcomes. This presentation covers our problem statement, the rationale behind Chatty Kathy, synthetic data and persona creation, model performance metrics, a visual demonstration of the project, and potential future developments. Join us for an insightful Q&A session to explore the potential of this groundbreaking project.
Project Team: Jay Requarth, Jana Avery, John Andrews, Dr. Dick Davis II, Nee Buntoum, Nam Yeongjin & Mat Nicholas
2. Backtracking
History
• ‘Backtrack’ the Word was first introduced by Dr. D.H.
Lehmer in 1950s.
• R.J Walker Was the First man who gave algorithmic
description in 1960.
• Later developed by S. Golamb and L. Baumert.
3. Backtracking
• What is Backtracking?
----- Backtracking is nothing but the modified process of the brute
force approach. where the technique systematically searches for a
solution to a problem among all available options. It does so by
assuming that the solutions are represented by vectors (v1, ..., in) of
values and by traversing through the domains of the vectors until
the solutions is found.
4. Backtracking
• The Algorithmic Approach
– Backtracking systematically try and search possibilities to find the
solution. Also it is an important process for solving constraint
satisfaction problem like crossword, Sudoku and many other puzzles. It
can be more continent technique for parsing other combinatorial
optimization problem.
– Basically the process is used when the problem has a number of option
and just one solution have to be selected. After having a new option set
means recursion, the procedure is repeated over and over until final
stage.
5. Backtracking
Algorithm Backtrack (v1,Vi)
If (V1,……., Vi) is a Solution Then
Return (V1,…, Vi)
For each v DO
If (V1,…….,Vi) is acceptable vector THEN
Sol = try (V1,…,Vi, V)
If sol != () Then
RETURN sol
End
End
Return ( )
6. Backtracking
• Advantages
– Comparison with the Dynamic Programming, Backtracking Approach is more effective in some cases.
– Backtracking Algorithm is the best option for solving tactical problem.
– Also Backtracking is effective for constraint satisfaction problem.
– In greedy Algorithm, getting the Global Optimal Solution is a long procedure and depends on user
statements but in Backtracking It Can Easily getable.
– Backtracking technique is simple to implement and easy to code.
– Different states are stored into stack so that the data or Info can be usable anytime.
– The accuracy is granted.
7. Backtracking
• Disadvantages
– Backtracking Approach is not efficient for solving strategic Problem.
– The overall runtime of Backtracking Algorithm is normally slow
– To solve Large Problem Sometime it needs to take the help of other
techniques like Branch and bound.
– Need Large amount of memory space for storing different state function
in the stack for big problem.
– Thrashing is one of the main problem of Backtracking.
– The Basic Approach Detects the conflicts too late.
8. Backtracking
• Application of Backtracking
• Optimization and tactical problems
• Constraints Satisfaction Problem
• Electrical Engineering
• Robotics
• Artificial Intelligence
• Genetic and bioinformatics Algorithm
• Materials Engineering
• Network Communication
• Solving puzzles and path
9. Backtracking
• Some Problem Solved with Backtracking Technique
– N- Queens Problem
– Sum of Subset
– Sudoku Puzzle
– Maze Generation
– Hamiltonian Cycle
10. N-Queens Problem
• History:
First Introduced in 1848 which was known as 8- queens Puzzle. Surprisingly,
The First Solution was created in 1950 by Franz Nauck. Nauck made an 8X8
Chessboard to find the first Feasible Solution.
11. N-Queens Problem
• Problem Description
In a NxN square board N – number of queens need to be
placed considering three Condition ---
• No two Queens can be placed in same row.
• No two Queens Can be places in same Column
• No two queens Can be placed in same Diagonal.
12. N-Queens Problem
• Backtracking approach for solution
- - The Algorithm will check each position [i , j] for each queens . If any Suitable places found , It will
place a queen on that position. If not Algorithm will try same approach for next position.
Algorithm Nqueen(K,n){
For i= 1 to n {
If Place(K,i){
X[k] = I;
If(k = n) then
Write x[1:n];
Else
Nqueen(k+1, n) ;
}
}
}
Place(k,i){
For j=1 to k-1{
If((x[j] = i) or abs(x[j] – 1 = abs(j-k)))
Return false;
}
Return true;
}
14. Maze Generation
Problem Description
A N X N board is made in a way So that 1 or 0 can be placed in
each box where 1 is for valid path for moving towards exit and 0 is
the Closed path. Now, by using Backtracking Algorithm The path to
the exit need to be find.
15. Maze Generation
• -- Algorithm will try to follow the box which has the value 1 and
generate a path. Again, it will check for 1 at the next box. If not
found it will go through next box. If entire row is complete, then it will
move to the next row and look for 1.
18. Hamiltonian Cycle
Hamiltonian Cycle is a graph theory problem where the graph cycle
through a graph can visit each node only once. The puzzle was first
devised by Sir William Rowan Hamilton and the Problem is named after
Him.
Condition: The Cycle Started with a Starting Node, and visit all the Nodes in the Graph
(Not necessary to visit in sequential Order and not creating edge that is not given) And
Stop at The Starting Point/Node.
19. Hamiltonian Cycle
• The Backtracking Approach
The Algorithm First Check the Starting Node, if there is any edge to the next node. If
yes, then the Algorithm will check that node for the edge to the next Node. It will Also
Check If any Node is visited twice by the previous Node. If there is any then the
Algorithm Will Ignore One and Choose the Optimal One for the Solution.
The Important thing is the tour must finish at the starting point.
20. Hamiltonian Cycle
Algorithm Hamilton_Cycle(k){
Repeat{
NextVal(k);
If(x[k]==0) then
Return;
If (k ==n) then
Write (x[1:n]);
Else
Hamilton_Cycle(k+1);
}
Until (false);
}
AlgortihmNextVal(k){
Repeat{
X[k] = (x[k]+1) mod (n+1);
If(x[k]=0) then return;
If (G[x[k-1],x[k]] != 0 ) then{
For j = 1 to k-1 do
If(x[j]=x[k]) then
Break;
If(j = k) then
If ((k<n or k=n) && G[x[n],x[1]] != 0)
Then return;
}
}
Until (false);
}
22. Sudoku Puzzle
• The Word ‘Sudoku’ is a Japanese Word. But The Sudoku Puzzle Was First
Invented in Switzerland
• In a N X N Square Board, The Numbers 1 to N to be Placed in a way that:
– All the Number from 1 to N can be Placed in each row.
– All the Number from 1 to N can be Placed in each Column.
– All The Number from 1 to N Can be Placed in Sub Square boxes of the given box.
23. Sudoku Puzzle
• Backtracking Approach
The Algorithm Will Check Each Box’s value if the value is in the same
row, or same column or same sub-square box. If not,then it placed the value
in the box. And go to the next box for the next value, and check the Above
Condition. If there is any duplicate value, then The Algorithm check for the
next value.
24. Sudoku Puzzle
Algorithm Sudoku_Solver(canvas, row,
col){
If(anyEmptyLocation(canvas, row, col))
Return true;
For I = 1 to n do, {
If (find_location(canvas, row,col, i))
{
Canvas[row][col] = i;
If (Sudoku_Solver(canvas))
Return true;
Canvas [row][col] = -1;
}
}
Return false;
}
25. Sum of Subset
• The Sum of Subset Problem is, there will be a set of distinct positive
Numbers X and a given Number N. Now, we have to find all the
combination of numbers from X that sum up to N. Make a Set of
those Number.
W = {4,5,6,3}
M = 13
27. Sum of Subset
• Backtracking Approach
First, organize the numbers in non decreasing order. Then generating a tree, we
can find the solution by adding the weight of the nodes. Note that, here more than
necessary nodes can be generated. The algorithm will search for the weighted amount
of the nodes. If it goes beyond given Number N, then it stops generating nodes and
move to other parent nodes for finding solution.
Algorithm SumOfSubset(s,k,y){
X[k] = 1;
If(s+w[k] = m)
Write (x[1:n]);
Else if((s+w[k] + w[k+1]) <= m)
SumOfSubset(s+w[k], k+1, y-w[k]);
If ((s+ y-w[k]>=m) &&(s =w[k+1] <=m)) {
X[k] =0;
SumOfSubset(s,k+1,y-w[k]);
}
}
29. References
• Chapter 6, Backtracking, Design and Analysis of Algorithms – V.V. Muniswami
• Chapter – 4, Non- Chronological Backtracking, Handbook on Constraint Programming – F.
Rossi, Van Beek
• web.cse.ohio-state.edu/~gurari/course/cis680/cis680Ch19.html
• www.classle.net/faq/comparisons-divide-and-conquergreedy-methoddynamic-
programmingbacktracking-and-branch-and-bound-
• Backtracking algorithms for constraint satisfaction problems; a survey
R. Dechter, D. Frost, in Constraints, International Journal, 1998.
• Bessiere C., Maestre A., Meseguer P., Distributed dynamic backtracking, in M.C. Silaghi, editor,
Proceedings of the IJCAI’01 workshop on Distributed Constraint Reasoning, Seattle WA,
2001, pp. 9–16.
• A First Look at Graph Theory – Jhon Clark, Allan Holton
• Principles and Practice of Constraint Programming- CP 2001: 7th International Conference,
CP 2001, Paphos, Cyprus, November 26 - December 1, 2001