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# ca02 - | V | | E | the former is the number of vertices and...

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In the Name of God Fall 2005 Discrete Mathematics Computer Assignment 2 Due: Azar 30 Suppose that G = ( V, E ) is a directed graph. Each edge of the graph, ( i, j ) , connecting vertex i to vertex j , has a weight which is an integer value. Consider v V and all its adjacent edges. The operation Transfer(v,d) is performed when the weights of all the incoming edges to vertex v are decremented by an integer value d , and that of all the outgoing edges from this vertex are incremented by d . We want to perform a sequence of these operations in a way that all the edge weights become positive. Write a program that, given a graph G and its edge weights, finds a sequence of these operations such that after performing the last one, all the edge weights turn positive. Input The first row of the input file consists of two integers

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Unformatted text preview: | V | , | E | ; the former is the number of vertices and the latter is the number of edges. Each of the following | E | rows denotes a single edge. In each of these lines, there are three integers; the Frst is the source vertex, the second is the target vertex and the third is the edge weight. You can suppose that the graph is simple and it consists of at most 100 vertices. Output Each row of the output Fle contains integers v, d , which denotes the operation Transfer(v,d) . If there is no solution to the given graph, the output should contain the single string “NO SOLUTION”. Sample Input 4 5 2 3 4 4 2 5 3 4 2 3 1 0 1 2 -1 1 Output for Sample Input 3 3 1 2 2...
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