Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 33.2, Problem 3E
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To have random-access lookup, a grid should have a scheme for numbering the tiles.For example, a square grid has rows and columns, which give a natural numberingfor the tiles. Devise schemes for triangular and hexagonal grids. Use the numberingscheme to define a rule for determining the neighbourhood (i.e. adjacent tiles) of agiven tile in the grid. For example, if we have a four-connected square grid, wherethe indices are i for rows and j for columns, the neighbourhood of tile i, j can bedefined asneighbourhood(i, j) = {i ± 1, j,i, j ± 1}
The function Ecol_M M in the Python programme that implements this approach discovers the minimum edge colours for a graph that is passed to it in the form of an incidence matrix. To discover the maximal matching in the graph, we utilise the Maximal Match function from the earlier constructed module MATCH within this function. The list edges is used to retain uncolored edges, while the list edge color is used to hold the current edge colours. The while loop continues to run until the edges list is empty, at which point all edges have been coloured. At each iteration, the graph is reduced by removing the columns associated with the matched edges.
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Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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