Dynamic Programming is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions using a memory-based data structure (array, map,etc).
Introduction to Dynamic Programming, Principle of OptimalityBhavin Darji
Introduction
Dynamic Programming
How Dynamic Programming reduces computation
Steps in Dynamic Programming
Dynamic Programming Properties
Principle of Optimality
Problem solving using Dynamic Programming
After a long period, I bring you new - fresh Presentation which gives you a brief idea on sub-problem of Dynamic Programming which is called as -"Longest Common Subsequence".I hope this presentation may help to all my viewers....
Dynamic Programming :
Dynamic programming is a technique for solving problems by breaking them down into smaller subproblems, solving each subproblem once, and storing the solution to each subproblem so that it can be reused in the future. Some characteristics of dynamic programming include:
Optimal substructure: Dynamic programming problems typically have an optimal substructure, meaning that the optimal solution to the problem can be obtained by solving the subproblems optimally and combining their solutions.
Overlapping subproblems: Dynamic programming problems often involve overlapping subproblems, meaning that the same subproblems are solved multiple times. To avoid solving the same subproblem multiple times, dynamic programming algorithms store the solutions to the subproblems in a table or array, so that they can be reused later.
Bottom-up approach: Dynamic programming algorithms usually solve problems using a bottom-up approach, meaning that they start by solving the smallest subproblems and work their way up to the larger ones.
Efficiency: Dynamic programming algorithms can be very efficient, especially when the subproblems overlap significantly. By storing the solutions to the subproblems and reusing them, dynamic programming algorithms can avoid redundant computations and achieve good time and space complexity.
Applicability: Dynamic programming is applicable to a wide range of problems, including optimization problems, decision problems, and problems that involve sequential decisions. It is often used to solve problems in computer science, operations research, and economics.
Algorithm Design Techniques
Iterative techniques, Divide and Conquer, Dynamic Programming, Greedy Algorithms.
Dynamic Programming is a method for solving a complex problem by breaking it down into a collection of simpler subproblems, solving each of those subproblems just once, and storing their solutions using a memory-based data structure (array, map,etc).
Introduction to Dynamic Programming, Principle of OptimalityBhavin Darji
Introduction
Dynamic Programming
How Dynamic Programming reduces computation
Steps in Dynamic Programming
Dynamic Programming Properties
Principle of Optimality
Problem solving using Dynamic Programming
After a long period, I bring you new - fresh Presentation which gives you a brief idea on sub-problem of Dynamic Programming which is called as -"Longest Common Subsequence".I hope this presentation may help to all my viewers....
Dynamic Programming :
Dynamic programming is a technique for solving problems by breaking them down into smaller subproblems, solving each subproblem once, and storing the solution to each subproblem so that it can be reused in the future. Some characteristics of dynamic programming include:
Optimal substructure: Dynamic programming problems typically have an optimal substructure, meaning that the optimal solution to the problem can be obtained by solving the subproblems optimally and combining their solutions.
Overlapping subproblems: Dynamic programming problems often involve overlapping subproblems, meaning that the same subproblems are solved multiple times. To avoid solving the same subproblem multiple times, dynamic programming algorithms store the solutions to the subproblems in a table or array, so that they can be reused later.
Bottom-up approach: Dynamic programming algorithms usually solve problems using a bottom-up approach, meaning that they start by solving the smallest subproblems and work their way up to the larger ones.
Efficiency: Dynamic programming algorithms can be very efficient, especially when the subproblems overlap significantly. By storing the solutions to the subproblems and reusing them, dynamic programming algorithms can avoid redundant computations and achieve good time and space complexity.
Applicability: Dynamic programming is applicable to a wide range of problems, including optimization problems, decision problems, and problems that involve sequential decisions. It is often used to solve problems in computer science, operations research, and economics.
Algorithm Design Techniques
Iterative techniques, Divide and Conquer, Dynamic Programming, Greedy Algorithms.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
it contains the detail information about Dynamic programming, Knapsack problem, Forward / backward knapsack, Optimal Binary Search Tree (OBST), Traveling sales person problem(TSP) using dynamic programming
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
What Is Dynamic Programming? | Dynamic Programming Explained | Programming Fo...Simplilearn
This presentation on 'What Is Dynamic Programming?' will acquaint you with a clear understanding of how this programming paradigm works with the help of a real-life example. In this Dynamic Programming Tutorial, you will understand why recursion is not compatible and how you can solve the problems involved in recursion using DP. Finally, we will cover the dynamic programming implementation of the Fibonacci series program. So, let's get started!
The topics covered in this presentation are:
1. Introduction
2. Real-Life Example of Dynamic Programming
3. Introduction to Dynamic Programming
4. Dynamic Programming Interpretation of Fibonacci Series Program
5. How Does Dynamic Programming Work?
What Is Dynamic Programming?
In computer science, something is said to be efficient if it is quick and uses minimal memory. By storing the solutions to subproblems, we can quickly look them up if the same problem arises again. Because there is no need to recompute the solution, this saves a significant amount of calculation time. But hold on! Efficiency comprises both time and space difficulty. But, why does it matter if we reduce the time required to solve the problem only to increase the space required? This is why it is critical to realize that the ultimate goal of Dynamic Programming is to obtain considerably quicker calculation time at the price of a minor increase in space utilized. Dynamic programming is defined as an algorithmic paradigm that solves a given complex problem by breaking it into several sub-problems and storing the results of those sub-problems to avoid the computation of the same sub-problem over and over again.
What is Programming?
Programming is an act of designing, developing, deploying an executlable software solution to the given user-defined problem.
Programming involves the following stages.
- Problem Statement
- Algorithms and Flowcharts
- Coding the program
- Debug the program.
- Documention
- Maintainence
Simplilearn’s Python Training Course is an all-inclusive program that will introduce you to the Python development language and expose you to the essentials of object-oriented programming, web development with Django and game development. Python has surpassed Java as the top language used to introduce U.S.
Learn more at: https://www.simplilearn.com/mobile-and-software-development/python-development-training
Design and Analysis of Algorithm help to design the algorithms for solving different types of problems in Computer Science. It also helps to design and analyze the logic of how the program will work before developing the actual code for a program.
One of the main reasons for the popularity of Dijkstra's Algorithm is that it is one of the most important and useful algorithms available for generating (exact) optimal solutions to a large class of shortest path problems. The point being that this class of problems is extremely important theoretically, practically, as well as educationally.
it contains the detail information about Dynamic programming, Knapsack problem, Forward / backward knapsack, Optimal Binary Search Tree (OBST), Traveling sales person problem(TSP) using dynamic programming
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
What Is Dynamic Programming? | Dynamic Programming Explained | Programming Fo...Simplilearn
This presentation on 'What Is Dynamic Programming?' will acquaint you with a clear understanding of how this programming paradigm works with the help of a real-life example. In this Dynamic Programming Tutorial, you will understand why recursion is not compatible and how you can solve the problems involved in recursion using DP. Finally, we will cover the dynamic programming implementation of the Fibonacci series program. So, let's get started!
The topics covered in this presentation are:
1. Introduction
2. Real-Life Example of Dynamic Programming
3. Introduction to Dynamic Programming
4. Dynamic Programming Interpretation of Fibonacci Series Program
5. How Does Dynamic Programming Work?
What Is Dynamic Programming?
In computer science, something is said to be efficient if it is quick and uses minimal memory. By storing the solutions to subproblems, we can quickly look them up if the same problem arises again. Because there is no need to recompute the solution, this saves a significant amount of calculation time. But hold on! Efficiency comprises both time and space difficulty. But, why does it matter if we reduce the time required to solve the problem only to increase the space required? This is why it is critical to realize that the ultimate goal of Dynamic Programming is to obtain considerably quicker calculation time at the price of a minor increase in space utilized. Dynamic programming is defined as an algorithmic paradigm that solves a given complex problem by breaking it into several sub-problems and storing the results of those sub-problems to avoid the computation of the same sub-problem over and over again.
What is Programming?
Programming is an act of designing, developing, deploying an executlable software solution to the given user-defined problem.
Programming involves the following stages.
- Problem Statement
- Algorithms and Flowcharts
- Coding the program
- Debug the program.
- Documention
- Maintainence
Simplilearn’s Python Training Course is an all-inclusive program that will introduce you to the Python development language and expose you to the essentials of object-oriented programming, web development with Django and game development. Python has surpassed Java as the top language used to introduce U.S.
Learn more at: https://www.simplilearn.com/mobile-and-software-development/python-development-training
Design and Analysis of Algorithm help to design the algorithms for solving different types of problems in Computer Science. It also helps to design and analyze the logic of how the program will work before developing the actual code for a program.
The Shortest Path Tour Problem is an extension to the normal Shortest Path Problem and appeared in the scientific literature in Bertsekas's dynamic programming and optimal control book in 2005, for the first time. This paper gives a description of the problem, two algorithms to solve it. Results to the numeric experimentation are given in terms of graphs. Finally, conclusion and discussions are made.
What is the Covering (Rule-based) algorithm?
Classification Rules- Straightforward
1. If-Then rule
2. Generating rules from Decision Tree
Rule-based Algorithm
1. The 1R Algorithm / Learn One Rule
2. The PRISM Algorithm
3. Other Algorithm
Application of Covering algorithm
Discussion on e/m-learning application
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.
Dynamic Programming is one of the most interesting design techniques. The concise idea is to avoid recomputations. Matrix Chain Multiplication and All Pairs Shortest Paths are two interesting applications of this design technique
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.
ADA Unit — 3 Dynamic Programming and Its Applications.pdfRGPV De Bunkers
Study Material: Analysis & Design of Algorithms - Semester 3
For RGPV Students of 4th Semester in Computer Science Engineering
Discover the power of algorithms with this comprehensive study material on "Analysis & Design of Algorithms" designed specifically for RGPV students in the 4th semester of Computer Science Engineering. Dive into the world of dynamic programming and its versatile applications, equipping yourself with essential problem-solving skills.
Unit Overview: Dynamic Programming and Its Applications
Learn the fundamental concepts of dynamic programming and its diverse applications. Dynamic programming is an algorithmic technique that efficiently solves complex problems by breaking them into smaller, overlapping subproblems. This unit explores key topics, including:
Concept of Dynamic Programming: Understand the significance of dynamic programming in algorithm design, leveraging overlapping subproblems and optimal substructure properties.
0/1 Knapsack Problem: Solve the classic optimization problem of 0/1 knapsack, maximizing value while respecting the knapsack's capacity.
Multistage Graph: Model decision-making processes with multistage graphs and use dynamic programming to find optimal paths.
Reliability Design: Optimize system reliability with dynamic programming, making smart decisions on redundancy and component selection.
Floyd-Warshall Algorithm: Determine shortest paths between vertices in a weighted graph using this versatile algorithm.
Why Choose This Study Material?
Tailored for RGPV Students: Specifically designed for 4th-semester Computer Science Engineering students at RGPV, aligning with the curriculum.
Comprehensive Coverage: Detailed explanations of each topic ensure a solid grasp of dynamic programming concepts.
Real-World Relevance: Apply your knowledge to project management, network design, manufacturing, and more.
Step-by-Step Approach: Understand problem-solving through step-by-step explanations.
Practical Examples: Numerous examples, including the knapsack problem and Floyd-Warshall algorithm, enrich your learning experience.
Study Smart, Excel in Algorithms!
Build a strong foundation in analysis and design of algorithms. Practice problem-solving and hands-on implementation. Mastering dynamic programming opens doors to innovation and efficient problem-solving in your future endeavors.
Equip yourself with the knowledge to design efficient algorithms, optimize solutions, and create reliable systems. Use this study material as your guide to success in "Analysis & Design of Algorithms" in your 4th semester at RGPV. Happy learning and best wishes for an exceptional academic journey!
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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.
As Europe's leading economic powerhouse and the fourth-largest hashtag#economy globally, Germany stands at the forefront of innovation and industrial might. Renowned for its precision engineering and high-tech sectors, Germany's economic structure is heavily supported by a robust service industry, accounting for approximately 68% of its GDP. This economic clout and strategic geopolitical stance position Germany as a focal point in the global cyber threat landscape.
In the face of escalating global tensions, particularly those emanating from geopolitical disputes with nations like hashtag#Russia and hashtag#China, hashtag#Germany has witnessed a significant uptick in targeted cyber operations. Our analysis indicates a marked increase in hashtag#cyberattack sophistication aimed at critical infrastructure and key industrial sectors. These attacks range from ransomware campaigns to hashtag#AdvancedPersistentThreats (hashtag#APTs), threatening national security and business integrity.
🔑 Key findings include:
🔍 Increased frequency and complexity of cyber threats.
🔍 Escalation of state-sponsored and criminally motivated cyber operations.
🔍 Active dark web exchanges of malicious tools and tactics.
Our comprehensive report delves into these challenges, using a blend of open-source and proprietary data collection techniques. By monitoring activity on critical networks and analyzing attack patterns, our team provides a detailed overview of the threats facing German entities.
This report aims to equip stakeholders across public and private sectors with the knowledge to enhance their defensive strategies, reduce exposure to cyber risks, and reinforce Germany's resilience against cyber threats.
Data Centers - Striving Within A Narrow Range - Research Report - MCG - May 2...pchutichetpong
M Capital Group (“MCG”) expects to see demand and the changing evolution of supply, facilitated through institutional investment rotation out of offices and into work from home (“WFH”), while the ever-expanding need for data storage as global internet usage expands, with experts predicting 5.3 billion users by 2023. These market factors will be underpinned by technological changes, such as progressing cloud services and edge sites, allowing the industry to see strong expected annual growth of 13% over the next 4 years.
Whilst competitive headwinds remain, represented through the recent second bankruptcy filing of Sungard, which blames “COVID-19 and other macroeconomic trends including delayed customer spending decisions, insourcing and reductions in IT spending, energy inflation and reduction in demand for certain services”, the industry has seen key adjustments, where MCG believes that engineering cost management and technological innovation will be paramount to success.
MCG reports that the more favorable market conditions expected over the next few years, helped by the winding down of pandemic restrictions and a hybrid working environment will be driving market momentum forward. The continuous injection of capital by alternative investment firms, as well as the growing infrastructural investment from cloud service providers and social media companies, whose revenues are expected to grow over 3.6x larger by value in 2026, will likely help propel center provision and innovation. These factors paint a promising picture for the industry players that offset rising input costs and adapt to new technologies.
According to M Capital Group: “Specifically, the long-term cost-saving opportunities available from the rise of remote managing will likely aid value growth for the industry. Through margin optimization and further availability of capital for reinvestment, strong players will maintain their competitive foothold, while weaker players exit the market to balance supply and demand.”
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
2. Dynamic Programming
2
Dynamic Programming is a general algorithm design technique
for solving problems defined by recurrences with overlapping
subproblems
• Invented by American mathematician Richard Bellman in the
1950s to solve optimization problems and later assimilated by CS
• “Programming” here means “planning”
• Main idea:
- set up a recurrence relating a solution to a larger instance to
solutions of some smaller instances
- solve smaller instances once
- record solutions in a table
- extract solution to the initial instance from that table
3. Divide-and-conquer
• Divide-and-conquer method for algorithm design:
• Divide: If the input size is too large to deal with in a
straightforward manner, divide the problem into two or
more disjoint subproblems
• Conquer: conquer recursively to solve the subproblems
• Combine: Take the solutions to the subproblems and
“merge” these solutions into a solution for the original
problem
5. Dynamic programming
• Dynamic programming is a way of improving on inefficient divide-
and-conquer algorithms.
• By “inefficient”, we mean that the same recursive call is made
over and over.
• If same subproblem is solved several times, we can use table to
store result of a subproblem the first time it is computed and thus
never have to recompute it again.
• Dynamic programming is applicable when the subproblems are
dependent, that is, when subproblems share subsubproblems.
• “Programming” refers to a tabular method
6. Difference between DP and Divide-
and-Conquer
• Using Divide-and-Conquer to solve these
problems is inefficient because the same
common subproblems have to be solved many
times.
• DP will solve each of them once and their
answers are stored in a table for future use.
8. Elements of Dynamic Programming
(DP)
DP is used to solve problems with the following characteristics:
• Simple subproblems
– We should be able to break the original problem to smaller
subproblems that have the same structure
• Optimal substructure of the problems
– The optimal solution to the problem contains within optimal
solutions to its subproblems.
• Overlapping sub-problems
– there exist some places where we solve the same subproblem more
than once.
9. Steps to Designing a
Dynamic Programming Algorithm
1. Characterize optimal substructure
2. Recursively define the value of an optimal
solution
3. Compute the value bottom up
4. (if needed) Construct an optimal solution
10. Principle of Optimality
• The dynamic Programming works on a principle
of optimality.
• Principle of optimality states that in an optimal
sequence of decisions or choices, each sub
sequences must also be optimal.
14. Fibonacci Numbers
• We can calculate Fn in linear time by remembering
solutions to the solved subproblems – dynamic
programming
• Compute solution in a bottom-up fashion
• In this case, only two values need to be
remembered at any time
20. Matrix Chain Multiplication
• Given : a chain of matrices {A1,A2,…,An}.
• Once all pairs of matrices are parenthesized, they can
be multiplied by using the standard algorithm as a sub-
routine.
• A product of matrices is fully parenthesized if it is either
a single matrix or the product of two fully parenthesized
matrix products, surrounded by parentheses. [Note: since
matrix multiplication is associative, all parenthesizations yield the
same product.]
21. Matrix Chain Multiplication cont.
• For example, if the chain of matrices is {A, B, C,
D}, the product A, B, C, D can be fully
parenthesized in 5 distinct ways:
(A ( B ( C D ))),
(A (( B C ) D )),
((A B ) ( C D )),
((A ( B C )) D),
((( A B ) C ) D ).
• The way the chain is parenthesized can have a
dramatic impact on the cost of evaluating the
product.
22. Matrix Chain Multiplication Optimal
Parenthesization
• Example: A[30][35], B[35][15], C[15][5]
minimum of A*B*C
A*(B*C) = 30*35*5 + 35*15*5 = 7,585
(A*B)*C = 30*35*15 + 30*15*5 = 18,000
• How to optimize:
– Brute force – look at every possible way to
parenthesize : Ω(4n/n3/2)
– Dynamic programming – time complexity of Ω(n3) and
space complexity of Θ(n2).
23. Matrix Chain Multiplication Structure of
Optimal Parenthesization
• For n matrices, let Ai..j be the result of AiAi+1….Aj
• An optimal parenthesization of AiAi+1…An splits
the product between Ak and Ak+1 where 1 k <
n.
• Example, k = 4 (A1A2A3A4)(A5A6)
Total cost of A1..6 = cost of A1..4 plus total
cost of multiplying these two matrices
together.
24. Matrix Chain Multiplication
Overlapping Sub-Problems
• Overlapping sub-problems helps in reducing the
running time considerably.
– Create a table M of minimum Costs
– Create a table S that records index k for each optimal sub-
problem
– Fill table M in a manner that corresponds to solving the
parenthesization problem on matrix chains of increasing
length.
– Compute cost for chains of length 1 (this is 0)
– Compute costs for chains of length 2
A1..2, A2..3, A3..4, …An-1…n
– Compute cost for chain of length n
A1..nEach level relies on smaller sub-strings