clrs4e-solutions
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B-3c
The solution is not clear. It should be elaborated to mention that the procedure aims to remove edges so that at the end, the total number of nodes in the cutoff subtrees is $\lfloor n/2\rfloor$, and the number of nodes in the main tree is $\lceil n/2\rceil$. It should also clarify that after removing an edge, the branch in the main tree changes, and at each step the procedure removes a largest subtree while not exceeding the total $\lfloor n/2\rfloor$ of nodes removed.