Algorithms - Longest Path Bottom up (Dynamic Programming)
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(Algorithms)Bottom-Up Longest-Paths
Previously you wrote Longest-Path-Memoized, a recursive (top-down) dynamic programming solution to the longest paths problem.
Here you will solve the same problem in Θ(V+E) using a bottom-up dynamic programming approach. Hint: We need to arrange to solve smaller problems before larger ones: use topological sort (which you may assume has already been written).
(a) Write the pseudocode for Longest-Path-Bottom-Up.
(b) Explain why it works; in particular, why topological sort is useful.
(c) Analyze its asymptotic run time.
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