Consider a tree with nodes: edges (,), (,), (,). Run the down pass from root .
size[4] = 1, down[4] = 0. size[3] = 2, down[3] = 0 + 1 = 1. size[2] = 1, down[2] = 0. size[1] = 4, down[1] = 0 + 1 + 1 + 2 = 4.
Now the up pass. answer[1] = 4. answer[2] = 4 + 4 - 2(1) = 6. answer[3] = 4 + 4 - 2(2) = 4. answer[4] = 4 + 4 - 2(1) = 6.
Verify by hand: from node , distances are . Correct. From node , distances are . Correct.