Computer science in Dynamic programming .pptx

Computer science in Dynamic programming .pptx

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  1 Presented By: Md.Akash Hosen Welcome To My Demonstration On
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  Dynamic programming Dynamic programmingis an algorithmic technique that solves problems by breaking them down into smaller sub-problems and storing the results of sub-problems to avoid re-computing them. It is useful for optimization problems with overlapping sub- problems. 2 o The problem should be able to be divided into smaller overlapping sub-problem. o Final optimum solution can be achieved by using an optimum solution of smaller sub-problems. o Dynamic algorithms use memorization. So we can say that −
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  Dynamic programming Approaches 3 DynamicProgramming techniques can be categorized into two main approaches:
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  Top-Down Approach 4 💭“Think recursively,store wisely!”  The Top-Down Approach starts with the original problem and divides it into smaller sub-problems.  The sub-problems are solved recursively, and their solutions are cached (stored) to avoid recomputation.  If a subproblem has already been solved (i.e., its solution is in the cache), it’s directly used without recalculating. The following recursive relations define the Fibonacci numbers:
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  Bottom-Up Approach 5 💭“Build fromthe ground up!”  The Bottom-Up Approach starts with the simplest sub-problems (base cases) and iteratively solves larger sub-problems.  The solution to the main problem is built step-by-step by filling up a table (or array) from the smallest sub-problems to the largest. The following iteration relations define the Fibonacci numbers:
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  Difference between Top-Down& Bottom-Up Approach 6 Aspect Top-Down Approach Bottom-Up Approach Approach Uses recursion and caching (memoization) Uses loops and table (tabulation) Memory Usage May use more space due to recursion stack More memory efficient with fixed-size table Speed Can be slower due to recursion overhead Usually faster, avoids recursion Ease of Use Easier to write if you're comfortable with recursion Requires manual table setup, more optimized Best Use Case Best when not all sub-problems are needed Best when all sub-problems must be solved
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  7 Advantages of DynamicProgramming  Avoids Repetition: DP stores solutions to sub-problems, preventing redundant calculations and speeding up the process.  Fast Performance: By converting slow recursive algorithms into efficient ones, DP reduces time complexity (e.g., O(2^n) to O(n²)).  Easy to Debug: The clear structure of DP (building tables step-by-step) makes it simple to trace and debug.  Optimal Solutions: DP guarantees the best solution when the problem satisfies overlapping sub-problems and optimal substructure.
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  8 Limitations of DynamicProgramming  High Memory Usage: DP requires memory to store intermediate results, which can become an issue for large-scale problems.  Problem-Specific: DP only works for problems that have overlapping sub- problems and optimal substructure. It’s not universally applicable.  Requires Insight: Successfully applying DP requires careful understanding of the problem's structure and how sub-problems relate.
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  9 Why Use DP? Because: Boosts Efficiency: DP transforms slow recursive algorithms into fast solutions by avoiding redundant calculations. This saves time, especially for large problems.  Ensures Optimal Solutions: DP doesn’t just solve problems, it finds the best possible solution by systematically solving sub-problems and combining their results.  Saves Time and Resources: By storing intermediate results in a table, DP avoids recalculating the same values, making the process much quicker and more memory-efficient.  Improves Performance: DP reduces time complexity, turning problems that would take too long (like O(2^n)) into more manageable ones (like O(n²)).
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  Applications of DynamicProgramming 10  Text Processing: Spell check using Edit Distance to find the closest match between words.  Bioinformatics: DNA Sequence Alignment to compare genetic sequences and find similarities.  Machine Learning: Speech recognition using the Viterbi Algorithm to decode spoken words.  Finance: Stock portfolio optimization to maximize returns while minimizing risk.  Networking: Optimal routing and shortest path algorithms to find the best network paths.  Compression: Video/Audio compression (e.g., Huffman Coding) to reduce file sizes.
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  11 Thank You SoMuch !