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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.
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
3x+y=9 5x-y=7
Ashow that sec^2x+cosec^2x cannot be less than 4
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