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# notes83 - Notes for week of Dijkstra's Algorithm Pseudocode...

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Notes for week of 2005-04-25 Dijkstra's Algorithm Pseudocode Minimum Spanning Tree Minimum Spanning Tree Pseudocode Final Exam Review Red Black Trees Merge Sort Quick Sort Sorting Algorithms for values in a subrange of numbers. Data compression Graphs Distribution of questions. Study Cooperation Cases Strategy Dijkstra's Algorithm Shortest path from a source vertex to other vertices. Pseudocode Algorithm for Shortest Path (G, S, D) Input A weighted graph G. Paths start at S. Output An array D[U] such that D[U] will be the cought(??) of the shortest path from S to U in G. Initialize D[s] = 0 and D[U] = INF for each U != S. Initialize Q = { all vertices in G }. Q is a list (queue). It is used to keep track of visited vertices. while Q is not empty do: Get a vertex U from Q such that D[U] is the minimum among all vertices of Q. For each vertex adjacent to U such that z is in Q do: if D[U] + W[U,z] < D[z] then D[z] = D[U] + W[U,z] end if end for end while

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Let m be number of edges and n be number of vertices. Then the complexity is either O(n^2 + m) if we use a simple list or queue or O(n log n + m) if we use a heap. Minimum Spanning Tree Spanning tree with minimum total weight. Example: Connect all computers in the building with the minimum amount of cable. Properties Let V' and V'' be a partition of the vertices of G. A partition is two sets of vertices that are mutually exclusive. Let (V', V'') be an edge across the partition, such that V' E V' and V'' E V''. If the edge e = (v', v'') has the minimum weight across all the edges that join the partition, then e = (v', v'') should be in the minimum spanning tree. In the previous partition, the edge with weight of 8 should be in the minimum spanning tree (C, D). This guarantees that the partition will be joined by the minimum edge. Procedure
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notes83 - Notes for week of Dijkstra's Algorithm Pseudocode...

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