Problem: Consider a hallway in a building, with N equally sized rooms, numbered 1,.... N. Several meetings are planned, which require different numbers of adj acent rooms. You are given a list of meeting requests with the number of rooms needed for each. The requests are represented by the array r[1, 1;]. For example, meeting j requires r[i] adjacent rooms. 1li'ou are offered a programmatic tooL which requires 31 steps to partition a set of n rooms, to accommodate two meeting requests of sizes s1 and s2, where sl-s2 = N. Design an algorithm that receives a set of meeting requests sl, s2, etc._ and calculates the rooms allocations in the least number of steps. Formally prove that the algorithm is correct and that the solution it provides requires the lowest cost (in computational steps}. Illustrate your solution with a concrete example