Solution.java

class Solution {
    private List<Integer>[] g;
    private int ans;
    private long mx;
    private int n;

    public int countHighestScoreNodes(int[] parents) {
        n = parents.length;
        g = new List[n];
        Arrays.setAll(g, i -> new ArrayList<>());
        for (int i = 1; i < n; ++i) {
            g[parents[i]].add(i);
        }
        dfs(0, -1);
        return ans;
    }

    private int dfs(int i, int fa) {
        int cnt = 1;
        long score = 1;
        for (int j : g[i]) {
            if (j != fa) {
                int t = dfs(j, i);
                cnt += t;
                score *= t;
            }
        }
        if (n - cnt > 0) {
            score *= n - cnt;
        }
        if (mx < score) {
            mx = score;
            ans = 1;
        } else if (mx == score) {
            ++ans;
        }
        return cnt;
    }
}