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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.
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
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If y 1 (t) and y 2 (t) are two solutions to a linear, homogeneous differential equation thus it is y (t ) = c 1 y 1 (t ) + c 2 y 2 (t ) ........................(3) Remem
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
In how many ways 30 identical balls can be DISTRIBUTED among 4 boys?? Ans) Let they get a,b,c,d respectively. You requireto find the non negative integral results of a+b+c+d=3
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Union of Sets Venn diagram presenting the union of sets A and B or A?B = Shaded area is demonstrated below: A ?B = Shaded area
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Normally, sets are given in the various ways A) ROASTER FORM OR TABULAR FORM In that form, we describe all the member of the set within braces (curly brackets) and differen
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