Tag Archives: graph

Competitive programming in Haskell: BFS, part 4 (implementation via STUArray)

In a previous post, we saw one way to implement our BFS API, but I claimed that it is not fast enough to solve Modulo Solitaire. Today, I want to demonstrate a faster implementation. (It’s almost certainly possible to make … Continue reading

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Competitive programming in Haskell: BFS, part 3 (implementation via HashMap)

In a previous post, I showed how we can solve Modulo Solitaire (and hopefully other BFS problems as well) using a certain API for BFS, and we also explored some alternatives. I had a very interesting discussion with Andrey Mokhov … Continue reading

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Competitive programming in Haskell: BFS, part 2 (alternative APIs)

In my last post, I showed how we can solve Modulo Solitaire (and hopefully other BFS problems as well) using a certain API for BFS, which returns two functions: one, level :: v -> Maybe Int, gives the level (i.e. … Continue reading

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Competitive programming in Haskell: BFS, part 1

In a previous post, I challenged you to solve Modulo Solitaire. In this problem, we are given a starting number and are trying to reach in as few moves as possible. At each move, we may pick one of up … Continue reading

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Computing Eulerian paths is harder than you think

Everyone who has studied any graph theory at all knows the celebrated story of the Seven Bridges of Königsberg, and how Euler gave birth to modern graph theory while solving the problem. Euler’s proof is clever, incisive, not hard to … Continue reading

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The network reliability problem and star semirings

In a previous post I defined the network reliability problem. Briefly, we are given a directed graph whose edges are labelled with probabilities, which we can think of as giving the likelihood of a message successfully traversing a link in … Continue reading

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The network reliability problem

Let be a directed graph with vertices and edges . Multiple edges between the same pair of vertices are allowed. For concreteness’ sake, think of the vertices as routers, and the edges as (one-way) connections. Let denote the set of … Continue reading

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