问题：
"Consider a hallway in a building, with N equally sized rooms, numbered 1,..., N. Several meetings are planned, which require different numbers of adjacent rooms. You are given a list of meeting requests with the number of rooms need for each. The requests are represented by the array r[1, ..., k]. For example, meeting j requires r[j] adjacent rooms. You are offered a programmatic tool, which requires n steps to partition a set of n rooms, to accommodate two meeting requests of sizes s1 and s2, where s1+s2 = N.
Design an algorithm that receives a set of meeting requests s1, 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."
关于partition problem，要用dynamic programming。我看也没看懂这个问的什么，用recursion做也不会做。这问题啥意思？教授说是partition problem