Follow the example solution to algorithm to solve number 2.

Consider the following input for the maximum-weight independent set problem: V = {V1, V2, ..., V13) and W = {2, 7, 8, 4, 3, 1, 7, 1,1,5, 1,8,6}. Use the dynamic programming algorithm to find the value of the the maximum-weight independent set. Show the array A. Use the reconstruction algorithm to obtain the maximum-weight independent set S. Show S for all iterations of the while loop. Then give the sum W(S) and its value. Solution: W= [2, 7, 8. 4. 3. 1. 7. 1, 1, 5, 1. 8, 6] [2, 7, 10, 11, 13. 13. 20. 20. 21. 25. 25. 33. 33] i = 13 - S = = 12 S i = 10: S = [12] 8S = [12. 10] : S = (12. 10] S = 12. 10.7 : S = (12. 10. 7.51 S [12. 10. 7. 5. 3] S 12. 10. 7. 5.3. 11 W(S) = 8 + 5+7+3 8+ 2 = 33 7 ---- 2. Answer the question with V = {V1.02, ..., 418), and Wis your CBU 899 number written twice. For example if your number is 899123456 then W = {8.9.9. 1,2,3,4,5,6.8.9.9.1,2,3,4,5,6). Consider the following input for the maximum-weight independent set problem: V = {V1, V2, ..., V13) and W = {2,7,8, 4, 3, 1, 7, 1, 1,5, 1,8,6}. Use the dynamic programming algorithm to find the value of the the maximum-weight independent set. Show the array A. Use the reconstruction algorithm to obtain the maximum-weight independent set S. Show S for all iterations of the while loop. Then give the sum W(S) and its value. Solution: W = [2, 7, 8, 4, 3. 1. 7. 1, 1.5, 1. 8, 6] A = [2, 7, 10, 11, 13. 13. 20. 20. 21. 25. 25. 33. 33] = 13 S = = 12S i = 10: S = 12 8 S = [12. 10] i = 7: S = (12. 10) = 5 : S = 12. 1071 S= (12. 10. 751 11 S [12. 10. 7. 5. 3] S 12. 10. 7. 5.3. 11 W(S) = 8 + 5 + 7 + 3 + 8 + 233 1 2. Answer the question with V = {V1.02. -.., U18), and W is your CBU 899 number written twice. For example if your number is 899123456 then W = {8,9,9,1,2,3,4,5,6.8.9.9.1, 2.3.4.5.6)