CS223-0415-Dynamic1

# CS223-0415-Dynamic1 - Recursive Equation Evaluation -= + =...

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CS223 Advanced Data Structures and Algorithms 1 Dynamic Programming 1 Dynamic Programming 1 Neil Tang Neil Tang 4/15/2008 4/15/2008

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CS223 Advanced Data Structures and Algorithms 2 Class Overview Class Overview Basic Idea Fibonacci numbers Recursive equation evaluation All-pairs shortest paths
CS223 Advanced Data Structures and Algorithms 3 Basic Idea Basic Idea Mathematically express the problem in the recursive form. Solve it by a non-recursive algorithm that systematically records the answers to the subproblems in a table.

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CS223 Advanced Data Structures and Algorithms 4 Fibonacci Numbers Fibonacci Numbers fib(N) = fib(N-1) + fib(N-2)
CS223 Advanced Data Structures and Algorithms 5 Fibonacci Numbers Fibonacci Numbers

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CS223 Advanced Data Structures and Algorithms 6 Fibonacci Numbers Fibonacci Numbers A dynamic programming based algorithm
CS223 Advanced Data Structures and Algorithms 7 Recursive Equation Evaluation

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Unformatted text preview: Recursive Equation Evaluation -= + = 1 ) ( 2 ) ( N i N i C N N C CS223 Advanced Data Structures and Algorithms 8 Recursive Equation Evaluation Recursive Equation Evaluation CS223 Advanced Data Structures and Algorithms 9 Recursive Equation Evaluation Recursive Equation Evaluation A dynamic programming based algorithm CS223 Advanced Data Structures and Algorithms 10 All-pairs Shortest Path All-pairs Shortest Path The all-pairs shortest path problem: Given a weighted graph G, find the shortest (minimum cost) path between every pair of nodes in G. CS223 Advanced Data Structures and Algorithms 11 All-Pairs Shortest Path All-Pairs Shortest Path Recursive expression for node pair (i, j) D k,i,j = min{D k-1,i,j, D k-1,i,k +D k-1,k,j } CS223 Advanced Data Structures and Algorithms 12 All-Pairs Shortest Path All-Pairs Shortest Path...
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## This note was uploaded on 04/17/2008 for the course CS 223 taught by Professor Tang during the Spring '07 term at MSU Bozeman.

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CS223-0415-Dynamic1 - Recursive Equation Evaluation -= + =...

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