CSES 1674 Subordinates - Algorithm

Run DFS from root (node $1$). For each node, visit children first, then compute subtree size.

function dfs(u, parent)
    size[u] := 1
    for each child v of u
        if v != parent then
            dfs(v, u)
            size[u] := size[u] + size[v]

After DFS, subordinates[u] = size[u] - 1 (subtract the node itself). This runs in $O(n)$ time, visiting each node once. The subtree size is a building block for many tree DP problems.

Space complexity is $O(n)$ for the data structures used.