Please answer in C$++$ and Java and include explanations. Thank you!

The Set Cover Problem is a classical problem in computer science where the task is to find the smallest subset of a given set of sets $($a collection of subsets$)$ that covers all elements in the universal set. A detailed problem description can be found in Exercise $9$ from Chapter $22$ of your course material.

Assignment Tasks:

Test your implementation with different input sets, including instances as large as possible, and analyze the efficiency of your solution.

Record the largest instance you tested and the time it takes for each program to solve it$.$

Sample test cases:

Test case $1$:

Universe Set: $\{1,2,3,4,5\}$

Collection of Subsets: $[\{1,5\},\{1,2,3\},\{2,4\},\{3,4\},\{4,5\}]$

Test case $2$:

Universe Set: $\{1,2,3,4,5,6,7,8,9,10,11,12\}$

Collection of Subsets: $[\{1,2,3,4,5,6\},\{5,6,8,9\},\{1,4,7,10\},\{2,5,8,11\},\{3,6,9,12\},\{10,11,12\}]$

Test case $3$:

Universe Set: $\{0,1,2,3,4,5,6,7,8,9\}$

Collection of Subsets: $[\{5\},\{0,1\},\{0,5,7\},\{1,4,5,9\},\{8,3\},\{8,4,7\},\{8,1,3,4\},\{2,6\}]$

Test case $4$:

Universe Set: $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}$

Collection of Subsets: $[\{1,2,3,4,8,9,10,11\},\{5,6,12,13\},\{1,2,3,4,5,6,7\},\{7,14\},\{8,9,10,11,1213,14\}]$

Test case $5$:

Universe Set: $\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30\}$

Collection of Subsets: $[\{1,2,3,4,5,6,7,8,16,17,18,19,20,21,22,23\},\{9,10,11,12,24,25,26,27\},\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\},\{13,14,28,29\},\{15,20\},\{16,17,18,19,20,21,22,23,24,25,26,27,28,29,30\}]$