#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <tuple>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
set<int> detect_cycle(int N, const vector<vector<int>>& G)
{
vector<int> stk;
set<int> cycle;
function<void(int,int)> rec = [&](int pre, int v) {
stk.push_back(v);
for(int u: G[v]) if(u != pre) {
auto it = find(stk.begin(), stk.end(), u);
if(it == stk.end()) {
rec(v, u);
} else {
cycle = set<int>(it, stk.end());
}
}
stk.pop_back();
};
rec(-1, 0);
return cycle;
}
vector<vector<int>> flatten(const vector<set<int>>& GS)
{
vector<vector<int>> G;
for(const auto& s: GS)
G.emplace_back(s.begin(), s.end());
return G;
}
class SuccessfulMerger { public:
int minimumMergers(vector <int> road)
{
const int N = road.size();
vector<set<int>> Gs(N);
for(int i=0; i<N; ++i) {
Gs[i].insert(road[i]);
Gs[road[i]].insert(i);
}
vector<vector<int>> G = flatten(Gs);
set<int> cy = detect_cycle(N, G);
if(cy.empty())
return solve(N, G);
int best = N-1;
set<int> cyl = cy;
for(int survive: cyl) {
cy.erase(survive);
map<int,int> remap;
int XN = N - cy.size() + 1;
for(int v=0; v<N; ++v) {
if(cy.count(v)) {
remap[v] = XN - 1;
} else {
int idx = 0;
for(int u=0; u<v; ++u)
if(!cy.count(u))
++idx;
remap[v] = idx;
}
}
vector<set<int>> XGs(XN);
for(int i=0; i<N; ++i) {
int a = remap[i];
int b = remap[road[i]];
if(a != b) {
XGs[a].insert(b);
XGs[b].insert(a);
}
}
vector<vector<int>> XG = flatten(XGs);
best = min<int>(best, solve(XN, XG) + cy.size() - 1);
cy.insert(survive);
}
return best;
}
int solve(int N, const vector<vector<int>>& G) {
if(N <= 2)
return 0;
int best = N-1;
for(int root=0; root<N; ++root)
best = min(best, solve(N, root, G));
return best;
}
int solve(int N, int root, const vector<vector<int>>& G)
{
function<int(int,int)> non_leaf_cnt = [&](int pre, int v) {
if(G[v].size() == 1)
return 0;
int sum = 1;
for(int u: G[v]) if(u != pre)
sum += non_leaf_cnt(v, u);
return sum;
};
int total = 0;
for(int ch: G[root])
total += non_leaf_cnt(root, ch);
return total;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, SuccessfulMerger().minimumMergers(road));}
int main(){
CASE(0)
int road_[] = {2, 2, 1, 1, 1};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = 1;
END
CASE(1)
int road_[] = {3, 4, 5, 4, 5, 3};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = 2;
END
CASE(2)
int road_[] = {1, 0, 1, 0, 0, 0, 1, 0, 1, 1};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = 1;
END
CASE(3)
int road_[] = {1, 2, 3, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = 2;
END
CASE(4)
int road_[] = {31, 19, 0, 15, 30, 32, 15, 24, 0, 20, 40, 1, 22, 21, 39, 28, 0, 23, 15, 5, 19, 22, 6, 32, 8, 38, 35, 30, 4, 28, 32, 18, 18, 9, 22, 41, 20, 18, 6, 25, 41, 34, 4};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = 25;
END
CASE(5)
int road_[] = {1, 0};
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = 0;
END
/*
CASE(6)
int road_[] = ;
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = ;
END
CASE(7)
int road_[] = ;
vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
int _ = ;
END
*/
}
// END CUT HERE