PPT-1 Dynamic Programming (1)

2 Dynamic Programming The dynamic programming archetype is used to solve problems that can be defined by recurrences with overlapping subproblems Invented by mathematician Richard Bellman in the . . Dynamic Programming. CSE 680. Prof. Roger Crawfis. Fibonacci Numbers. . Computing the n. th. Fibonacci number recursively:. F(n) = F(n-1) + F(n-2). F(0) = 0. F(1) = 1. Top-down approach. . F. Systems Applied . to Humanoid Walking. Eric . C. Whitman . & Christopher . G. . Atkeson. Carnegie Mellon University. Related Work. Trajectory generation + trajectory tracking. Takanishi. 1990, . Lecture 10. Fang Yu. Department of Management Information Systems. National . Chengchi. University. Fall 2010. Fundamental Algorithms. Brute force, Greedy, Dynamic Programming:. Matrix Chain-Products . Dynamic Programming. 11.1 A Prototype Example for Dynamic Programming. The stagecoach problem. Mythical fortune-seeker . travels . West by stagecoach to join the gold rush in the mid-1900s. The origin . Dynamic Programming. Dynamic programming is a useful mathematical technique for making a sequence of interrelated decisions. It provides a systematic procedure for determining the optimal combination of decisions.. Dividing a problem into . subproblems. Dynamic programming . vs. divide and conquer. - Dynamic programming : . subproblems. are overlapped. - Divide and conquer : . subproblems. are independent . ". Thus, I thought . dynamic programming . was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my . activities". - Richard E. Bellman. Origins. A method for solving complex problems by breaking them into smaller, easier, sub problems. Excel . Perspective. Dynamic . Programming From . An Excel . Perspective. Dynamic Programming. From An Excel Perspective. Ranette Halverson, Richard . Simpson. Catherine . Stringfellow. Department of Computer Science. ". Thus, I thought . dynamic programming . was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my . activities". - Richard E. Bellman. Origins. A method for solving complex problems by breaking them into smaller, easier, sub problems. Originally the “Tabular Method”. Key idea:. Problem solution has one or more . subproblems. that can be solved recursively. The . subproblems. are overlapping. The same . subproblem. will get solved multiple times. 1. Lecture Content. Fibonacci Numbers Revisited. Dynamic Programming. Examples. Homework. 2. 3. Fibonacci Numbers Revisited. Calculating the n-. th. Fibonacci Number with recursion has proved to be . Basic Algorithm Design Techniques. Divide and conquer. Dynamic Programming. Greedy. Common Theme: To solve a large, complicated problem, break it into many smaller sub-problems.. Dynamic Programming. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. Application: DNA Sequence Alignment. DNA sequences can be viewed as strings of . VINAY ABHISHEK MANCHIRAJU. SCOPE. Apply dynamic . programming to gene finding and other bioinformatics problems. .. Power of DNA Sequence Comparison. A revisit to the Change Problem. The Manhattan Tourist Problem.