You are asked to provide a Dynamic Programming solution to the problem of maximizingthe number of users for the routers subject to the above constraints. You have to do thefollowing.(a)(3 points) Identify the recurrence equation that expresses the maximum number ofexpected users if a router is placed at locationi. Justify your answer.(b)(6 points) Write the pseudo code of an iterative algorithm that builds up solutions tolarger and larger subproblems. You have to show the time complexity of your algorithm(The time complexity must beO(n)).(c)(3 points) Prove the correctness of your algorithm.