We are given a set {I1, . . . , In} of intervals on the real line, where for all 1 j n, interval Ij = (sj,tj]. Additionally, for each interval Ij, we are given a color cj, which is either red or blue. The goal is to compute a subset A of intervals, such that: no two intervals in A intersect; there is an equal number of red and blue intervals in A; and the total length of all intervals in A is maximized. Design an efficient algorithm for this problem, prove its correctness and analyze its running time..

The question is basically saying that there some intervals and they also have a color. You need to maximize the length of intervals that are scheduled in such a way that the set of intervals that you run need to have equal number of red and blue intervals.