解题报告；

直接dp。注意mx也得longlong

 AC代码：

class Solution {
public:
    vector<int> vv[200005];
    int sum[200005];
    long long ans[200005];
    int n;
    void dfs(int x) {
        ans[x] = 1; sum[x] = 1;
        for(int i = 0; i<vv[x].size(); i++) {
            dfs(vv[x][i]);
            sum[x] += sum[vv[x][i]];
            ans[x] *= sum[vv[x][i]];
        }
        if(n-sum[x] > 0) ans[x] *= (n-sum[x]);
    }

    int countHighestScoreNodes(vector<int>& parents) {
        n = parents.size();
        for(int i = 1; i<n; i++) {
            vv[parents[i]].push_back(i);
        }
        dfs(0);
        long long mx = 0;
        int cnt = 0;
        for(int i = 0; i<=n; i++) {
            if(ans[i] > mx) {
                cnt = 1;mx = ans[i];
            } else if(ans[i] == mx) {
                cnt ++;
            }
        }
        return cnt;
    }
};