Describe and analyze a data structure to support the following operations on an array a[1 . . n] as quickly as possible. initially, a[i] = 0 for all i. • settoone(i) given an index i such that a[i] = 0, set a[i] to 1. • getvalue(i) given an index i, return a[i] • getclosestrightzero(i) given an index i, return the smallest index j ≥ i such that a[j] = 0, or report that no such index exists. the first two operations should run in worst-case constant time, and the amortized cost of the third operation should be as small as possible. 3

Calculate the bore of a cylinder that has a stroke of 18 inches and an extension time of 6 seconds at a flow rate of 4 gal/min.

For a gate width of 2 m into the paper, determine the force required to hold the gate abc at its location.

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj