Find a linear$-$time algorithm to determine, as efficiently as possible, the smallest and second smallest element in an array of n numbers. $1.$ After you show that the algorithm runs in linear time, establish eaxactly how many compari$-$ son your algorithm executes in worst$-$case. So$,$ we are interested in the constant looking only at comparisons though. $2.$ Analogously, the largest and second largest element in that array can be found. What would be your algorithm? $3.$ Alternately, if you don$$t want to write a new algorithm for $2.,$ how could you use an imple$-$ mentation of your algorithm from $1.$ to solve $2$ by transforming the input appropriately and in linear time? $4.$ Now, using the above two algorithms $($from $1.$ and $2.),$ you should be able to find the median of the elements stored in the array. How? What is the time complexity? $5.$ Next, using the concept of loop invariant, prove that this algorithm correctly finds the median of a set of n elements.