s A person is considering choosing multiple Apps from n candidates to provide a set of m functions. For each function, out of n candidates, exactly $2$ Apps are offering this function. Each App provides a set of functions, and the number of functions varies from one App to another. An App pi may offer a set of fi functions, and the value of fi is between $1$ and m$.$ The goal is to select the minimum number of Apps to offer all m functions $$ for each function, there is at least $1$ chosen App that provides this function.a$.$ Use $2-3$ sentences to describe the overall idea of this algorithm. b$.$ Present your algorithm in pseudo code format, with necessary notations and enough details $($similar to those algorithms presented in the textbook$).$ c$.$ For optimization problem that requires to minimize or maximize an objective, specify whether this algorithm is optimal or approximation algorithm. For approximation algorithm, specify its approximation guarantee: a quantity of the guarantee that how close the solution produced by this algorithm is to the optimum. d$.$ Construct a small $(5<=$ n $<=10)$ problem instance $($you may use the given example if provided$)$ to illustrate how your algorithm works and show the steps and the final solution too. e$.$ Analyze the time complexity of your algorithm, present the lowest upper bound of the running time as a function on input size n in big$-$O notation. For example, the time complexity of MergeSort is O$($nlogn$).$ f$.$ Demonstrate$/$explain the correctness of your algorithm if your algorithm is a greedy algorithm