recitation6

recitation6 - Dynamic Programming: The Edit Distance...

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Unformatted text preview: Dynamic Programming: The Edit Distance Problem CS 2: Introduction to Programming Methods 8 February 2006 The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 2 Today A review of dynamic programming. The Edit Distance problem. Review: Dynamic Programming The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 4 Dynamic programming A method for developing algorithms. Given a problem to solve, dynamic programming says: Solve subproblems of the problem first. Remember these solutions for later. Then put together a solution to the problem. Think of this as a bottom-up approach. Solve problems in order of increasing size. The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 5 Example: The fibonacci sequence fib(0) = 0 fib(1) = 1 fib(2) = 1 fib(3) = 2 fib(4) = 3 fib(5) = 5 fib(n) = fib(n-1) + fib(n-2) The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 6 Navely computing fib(n) int fib( int n) { if (n == 0 || n == 1) { return n; } else { return (fib(n-1) + fib(n-2)); } } The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 7 Navely computing fib(n) fib(n) fib(n-2) fib(n-1) fib(n-4) fib(n-3) fib(n-3) fib(n-2) fib(n-6) fib(n-5) fib(n-5) fib(n-4) fib(n-5) fib(n-4) fib(n-4) fib(n-3) The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 8 Navely computing fib(n) fib(n) fib(n-2) fib(n-1) fib(n-4) fib(n-3) fib(n-3) fib(n-2) fib(n-6) fib(n-5) fib(n-5) fib(n-4) fib(n-5) fib(n-4) fib(n-4) fib(n-3) The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 9 Navely computing fib(n) fib(n) fib(n-2) fib(n-1) fib(n-4) fib(n-3) fib(n-3) fib(n-2) fib(n-6) fib(n-5) fib(n-5) fib(n-4) fib(n-5) fib(n-4) fib(n-4) fib(n-3) The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 10 Navely computing fib(n) fib(n) fib(n-2) fib(n-1) fib(n-4) fib(n-3) fib(n-3) fib(n-2) fib(n-6) fib(n-5) fib(n-5) fib(n-4) fib(n-5) fib(n-4) fib(n-4) fib(n-3) The Edit Distance Problem 8 Feburary 2006 CS 2: Introduction to Programming Methods http://www.cs.caltech.edu/courses/cs2/ 11 How to fix things... The solution to fib(n) depends on: The solution to fib(n - 1). The solution to fib(n - 2). Use dynamic programming to organize everything: Each subproblem is characterized by the value of its input....
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recitation6 - Dynamic Programming: The Edit Distance...

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