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Problem. 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).)
Requirement: algorithm running time needs to be in DIJKstra's running time or better.
Comparison Test or Limit Comparison Test In the preceding section we saw how to relate a series to an improper integral to find out the convergence of a series. When the inte
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Chain Rule : If f(x) and g(x) are both differentiable functions and we describe F(x) = (f. g)(x) so the derivative of F(x) is F′(x) = f ′(g(x)) g′(x). Proof We will s
I need help with compound shapes
Find out the absolute extrema for the given function and interval. g (t ) = 2t 3 + 3t 2 -12t + 4 on [-4, 2] Solution : All we actually need to do here is follow the pr
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Maths For Fun : Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and
Recently I had an insight regarding the difference between squares of sequential whole numbers and the sum of those two whole numbers. I quickly realized the following: x + (x+1)
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