graph & optimal scheduling, Data Structure & Algorithms

You are given an undirected graph G = (V, E) in which the edge weights are highly restricted. In particular, each edge has a positive integer weight of either {1,2,...,W}, where W is a constant (independent of the number of edges or vertices). Show that it is possible to compute the single-source shortest paths in such a graph in O(n + m) time, where n = |V | and m = |E|. (Hint: Because W is a constant, a running time of O(W (n + m)) is as good as O(n + m).)
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