B. Identifying the correct DTs To check if a DT is correct, it should be checked on all possible permutations of the edge weights. The number of such permutations is at most . For each permutation, solve the MST problem on the given graph using any existing algorithm, and compare the result to the answer given by the DT. The running time of any MST algorithm is at most , so the total time required to check all permutations is at most .
B. Identifying the correct DTs To check if a DT is correct, it should be checked on all possible permutations of the edge weights. The number of such permutations is at most . For each permutation, solve the MST problem on the given graph using any existing algorithm, and compare the result to the answer given by the DT. The running time of any MST algorithm is at most , so the total time required to check all permutations is at most 