Give an algorithm that, given an undirected graph g and node s, creates an array shortestcount in which shortestcount[i] is the number of shortest paths from s to vertex i. provide a proof by induction that your algorithm is correct. derive its runtime. (tip: start with the bfs algorithm as given in the text, in which nodes are organized into layers li based on distance from s, and update the counts as you build the tree.)

Aloaded platform of total mass 500 kg is supported by a dashpot and by a set of springs of effective stiffness 72 kn/m. it is observed that when the platform is depressed through a distance x = 12.5 cm below its equilibrium position and then released without any initial velocity; it reaches its equilibrium position in the shortest possible time without overshoot. find the position and velocity of the loaded platform 0.10 sec. after its release. if a further load of 400 kg is added to the platform, find, i) the frequency of damped vibrations, and i) the amplitude of vibration after 2 complete oscillations, given that the initial amplitude is 15 cm.

Adouble-strand no. 60 roller chain is used to transmit power between a 13-tooth driving sprocket rotating at 300 rev/min and a 52-tooth driven sprocket. a) what is the allowable horsepower of this drive? b) estimate the center-to-center distance if the chain length is 82 pitches. c) estimate the torque and bending force on the driving shaft by the chain if the actual horsepower transmitted is 30 percent less than the corrected (allowable) power.

Journeyman training is usually related (clo2) a)-to specific tasks b)-to cost analysis of maintenance task c)-to control process to ensure quality d)-to installation of machinery