i want the answer as a text file, please solve each part. solve correctly please

Problem 1. We are given a set of intervals .,In on the real line. Each interval specified by the start and end points s, and ti, respectively: is li = (si,ti) Additionally, for each interval we are given a color c which is either red, green, or blue We want to find a subset of intervals A so that: . no two intervals in A intersect . there is an equal number of red, green, and blue intervals in A the total length of all intervals in A is maximized. Design a dynamic programming algorithm that finds the optimal solution. Specifically, do the following: 1. Define the dynamic-programming table and explain the meaning of its entries 2. Write the initialization step of your algorithm 3. Write the recurrence formula for computing entries of the table 4. Prove the correctness of the formula 5. Find the running time of your algorithm Problem 1. We are given a set of intervals .,In on the real line. Each interval specified by the start and end points s, and ti, respectively: is li = (si,ti) Additionally, for each interval we are given a color c which is either red, green, or blue We want to find a subset of intervals A so that: . no two intervals in A intersect . there is an equal number of red, green, and blue intervals in A the total length of all intervals in A is maximized. Design a dynamic programming algorithm that finds the optimal solution. Specifically, do the following: 1. Define the dynamic-programming table and explain the meaning of its entries 2. Write the initialization step of your algorithm 3. Write the recurrence formula for computing entries of the table 4. Prove the correctness of the formula 5. Find the running time of your algorithm