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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.
Relative maximum point The above graph of the function slopes upwards to the right between points C and A and thus has a positive slope among these two points. The function ha
Example of Word problem: There is a man who is 21 years older than his son. 5 years ago he was four times as old as his son. How older are both now? Solution: Step 1
20+20
how to remove wild points in a data set...
Write down the first few terms of each of the subsequent sequences. 1. {n+1 / n 2 } ∞ n=1 2. {(-1)n+1 / 2n} ∞ n=0 3. {bn} ∞ n=1, where bn = nth digit of ? So
For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0
Differentiate following. Solution : It requires the product rule & each derivative in the product rule will need a chain rule application as well. T ′ ( x ) =1/1+(2x) 2
Initial Conditions and Boundary Conditions In many problems on integration, an initial condition (y = y 0 when x = 0) or a boundary condition (y = y
Marketing management,Analysis,planning and implementation
The area of a parallelogram can be expressed as the binomial 2x 2 - 10x. Which of the following could be the length of the base and the height of the parallelogram? To ?nd out
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