#include <bits/stdc++.h>
using namespace std;
/*Topological BFS + Binary Search approach
Topological BFS adapted from https://cp-algorithms.com/graph/breadth-first-search.html and https://cp-algorithms.com/graph/topological-sort.html
Modifications:
- Topological DFS changed to topological BFS
- Queue and in-degree array instead of recursion
- Zero in-degree nodes processed first
Binary Search adapted from https://cp-algorithms.com/num_methods/binary_search.html
Modifications:
- Binary search is used for max possible K days instead of sorted array
- Each check does leaf removal through Topological BFS*/
int n, m;
vector<vector<int>> adj;
vector<int> inDegree;
bool topBFS(int k, vector<vector<int>>& s){
queue<int> q;
vector<int> remainingInDegree = inDegree;
for (int i = 0; i < n; i++){
if (remainingInDegree[i] == 0){
q.push(i);
}
}
int days = 0;
int processed = 0;
for (int day = 0; day < k; day++){
if (q.empty()){
return false;
}
vector<int> todayFallen;
int size = q.size();
while (size--){
int node = q.front();
q.pop();
todayFallen.push_back(node);
processed++;
for (int parent : adj[node]){
remainingInDegree[parent]--;
if (remainingInDegree[parent] == 0){
q.push(parent);
}
}
}
set<int> todaySet(todayFallen.begin(), todayFallen.end());
for (int v = 0; v < m; v++){
int start = (day == 0) ? 0 : (day * (n - 1) / k);
int end = min((day + 1) * (n - 1) / k, (int)s[v].size());
for (int i = start; i < end; i++){
if (todaySet.find(s[v][i]) == todaySet.end()){
return false;
}
}
}
days++;
}
return (processed == n - 1);
}
int binSearch(vector<vector<int>>& s){
int left = 1, right = n - 1, ans = 1;
while (left <= right){
int mid = (left + right) / 2;
if (topBFS(mid, s)){
ans = mid;
left = mid + 1;
}
else{
right = mid - 1;
}
}
return ans;
}
int solve(int N, int M, vector<int> F, vector<vector<int>> S){
n = N;
m = M;
adj.assign(n, vector<int>());
inDegree.assign(n, 0);
for (int i = 1; i < n; i++){
int parent = F[i];
adj[parent].push_back(i);
inDegree[i]++;
}
return binSearch(S);
}
