062d1ffb7c 2016-03-28        kinaba: #include <iostream>
062d1ffb7c 2016-03-28        kinaba: #include <sstream>
062d1ffb7c 2016-03-28        kinaba: #include <iomanip>
062d1ffb7c 2016-03-28        kinaba: #include <vector>
062d1ffb7c 2016-03-28        kinaba: #include <string>
062d1ffb7c 2016-03-28        kinaba: #include <map>
062d1ffb7c 2016-03-28        kinaba: #include <set>
062d1ffb7c 2016-03-28        kinaba: #include <algorithm>
062d1ffb7c 2016-03-28        kinaba: #include <numeric>
062d1ffb7c 2016-03-28        kinaba: #include <iterator>
062d1ffb7c 2016-03-28        kinaba: #include <functional>
062d1ffb7c 2016-03-28        kinaba: #include <complex>
062d1ffb7c 2016-03-28        kinaba: #include <queue>
062d1ffb7c 2016-03-28        kinaba: #include <stack>
062d1ffb7c 2016-03-28        kinaba: #include <cmath>
062d1ffb7c 2016-03-28        kinaba: #include <cassert>
062d1ffb7c 2016-03-28        kinaba: #include <tuple>
062d1ffb7c 2016-03-28        kinaba: using namespace std;
062d1ffb7c 2016-03-28        kinaba: typedef long long LL;
062d1ffb7c 2016-03-28        kinaba: typedef complex<double> CMP;
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: set<int> detect_cycle(int N, const vector<vector<int>>& G)
062d1ffb7c 2016-03-28        kinaba: {
062d1ffb7c 2016-03-28        kinaba: 	vector<int> stk;
062d1ffb7c 2016-03-28        kinaba: 	set<int> cycle;
062d1ffb7c 2016-03-28        kinaba: 	function<void(int,int)> rec = [&](int pre, int v) {
062d1ffb7c 2016-03-28        kinaba: 		stk.push_back(v);
062d1ffb7c 2016-03-28        kinaba: 		for(int u: G[v]) if(u != pre) {
062d1ffb7c 2016-03-28        kinaba: 			auto it = find(stk.begin(), stk.end(), u);
062d1ffb7c 2016-03-28        kinaba: 			if(it == stk.end()) {
062d1ffb7c 2016-03-28        kinaba: 				rec(v, u);
062d1ffb7c 2016-03-28        kinaba: 			} else {
062d1ffb7c 2016-03-28        kinaba: 				cycle = set<int>(it, stk.end());
062d1ffb7c 2016-03-28        kinaba: 			}
062d1ffb7c 2016-03-28        kinaba: 		}
062d1ffb7c 2016-03-28        kinaba: 		stk.pop_back();
062d1ffb7c 2016-03-28        kinaba: 	};
062d1ffb7c 2016-03-28        kinaba: 	rec(-1, 0);
062d1ffb7c 2016-03-28        kinaba: 	return cycle;
062d1ffb7c 2016-03-28        kinaba: }
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: vector<vector<int>> flatten(const vector<set<int>>& GS)
062d1ffb7c 2016-03-28        kinaba: {
062d1ffb7c 2016-03-28        kinaba: 	vector<vector<int>> G;
062d1ffb7c 2016-03-28        kinaba: 	for(const auto& s: GS)
062d1ffb7c 2016-03-28        kinaba: 		G.emplace_back(s.begin(), s.end());
062d1ffb7c 2016-03-28        kinaba: 	return G;
062d1ffb7c 2016-03-28        kinaba: }
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: class SuccessfulMerger { public:
062d1ffb7c 2016-03-28        kinaba: 	int minimumMergers(vector <int> road)
062d1ffb7c 2016-03-28        kinaba: 	{
062d1ffb7c 2016-03-28        kinaba: 		const int N = road.size();
062d1ffb7c 2016-03-28        kinaba: 		vector<set<int>> Gs(N);
062d1ffb7c 2016-03-28        kinaba: 		for(int i=0; i<N; ++i) {
062d1ffb7c 2016-03-28        kinaba: 			Gs[i].insert(road[i]);
062d1ffb7c 2016-03-28        kinaba: 			Gs[road[i]].insert(i);
062d1ffb7c 2016-03-28        kinaba: 		}
062d1ffb7c 2016-03-28        kinaba: 		vector<vector<int>> G = flatten(Gs);
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 		set<int> cy = detect_cycle(N, G);
062d1ffb7c 2016-03-28        kinaba: 		if(cy.empty())
062d1ffb7c 2016-03-28        kinaba: 			return solve(N, G);
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 		int best = N-1;
062d1ffb7c 2016-03-28        kinaba: 		set<int> cyl = cy;
062d1ffb7c 2016-03-28        kinaba: 		for(int survive: cyl) {
062d1ffb7c 2016-03-28        kinaba: 			cy.erase(survive);
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 			map<int,int> remap;
062d1ffb7c 2016-03-28        kinaba: 			int XN = N - cy.size() + 1;
062d1ffb7c 2016-03-28        kinaba: 			for(int v=0; v<N; ++v) {
062d1ffb7c 2016-03-28        kinaba: 				if(cy.count(v)) {
062d1ffb7c 2016-03-28        kinaba: 					remap[v] = XN - 1;
062d1ffb7c 2016-03-28        kinaba: 				} else {
062d1ffb7c 2016-03-28        kinaba: 					int idx = 0;
062d1ffb7c 2016-03-28        kinaba: 					for(int u=0; u<v; ++u)
062d1ffb7c 2016-03-28        kinaba: 						if(!cy.count(u))
062d1ffb7c 2016-03-28        kinaba: 							++idx;
062d1ffb7c 2016-03-28        kinaba: 					remap[v] = idx;
062d1ffb7c 2016-03-28        kinaba: 				}
062d1ffb7c 2016-03-28        kinaba: 			}
062d1ffb7c 2016-03-28        kinaba: 			vector<set<int>> XGs(XN);
062d1ffb7c 2016-03-28        kinaba: 			for(int i=0; i<N; ++i) {
062d1ffb7c 2016-03-28        kinaba: 				int a = remap[i];
062d1ffb7c 2016-03-28        kinaba: 				int b = remap[road[i]];
062d1ffb7c 2016-03-28        kinaba: 				if(a != b) {
062d1ffb7c 2016-03-28        kinaba: 					XGs[a].insert(b);
062d1ffb7c 2016-03-28        kinaba: 					XGs[b].insert(a);
062d1ffb7c 2016-03-28        kinaba: 				}
062d1ffb7c 2016-03-28        kinaba: 			}
062d1ffb7c 2016-03-28        kinaba: 			vector<vector<int>> XG = flatten(XGs);
062d1ffb7c 2016-03-28        kinaba: 			best = min<int>(best, solve(XN, XG) + cy.size() - 1);
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 			cy.insert(survive);
062d1ffb7c 2016-03-28        kinaba: 		}
062d1ffb7c 2016-03-28        kinaba: 		return best;
062d1ffb7c 2016-03-28        kinaba: 	}
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 	int solve(int N, const vector<vector<int>>& G) {
062d1ffb7c 2016-03-28        kinaba: 		if(N <= 2)
062d1ffb7c 2016-03-28        kinaba: 			return 0;
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 		int best = N-1;
062d1ffb7c 2016-03-28        kinaba: 		for(int root=0; root<N; ++root)
062d1ffb7c 2016-03-28        kinaba: 			best = min(best, solve(N, root, G));
062d1ffb7c 2016-03-28        kinaba: 		return best;
062d1ffb7c 2016-03-28        kinaba: 	}
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 	int solve(int N, int root, const vector<vector<int>>& G)
062d1ffb7c 2016-03-28        kinaba: 	{
062d1ffb7c 2016-03-28        kinaba: 		function<int(int,int)> non_leaf_cnt = [&](int pre, int v) {
062d1ffb7c 2016-03-28        kinaba: 			if(G[v].size() == 1)
062d1ffb7c 2016-03-28        kinaba: 				return 0;
062d1ffb7c 2016-03-28        kinaba: 			int sum = 1;
062d1ffb7c 2016-03-28        kinaba: 			for(int u: G[v]) if(u != pre)
062d1ffb7c 2016-03-28        kinaba: 				sum += non_leaf_cnt(v, u);
062d1ffb7c 2016-03-28        kinaba: 			return sum;
062d1ffb7c 2016-03-28        kinaba: 		};
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: 		int total = 0;
062d1ffb7c 2016-03-28        kinaba: 		for(int ch: G[root])
062d1ffb7c 2016-03-28        kinaba: 			total += non_leaf_cnt(root, ch);
062d1ffb7c 2016-03-28        kinaba: 		return total;
062d1ffb7c 2016-03-28        kinaba: 	}
062d1ffb7c 2016-03-28        kinaba: };
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: // BEGIN CUT HERE
062d1ffb7c 2016-03-28        kinaba: #include <ctime>
062d1ffb7c 2016-03-28        kinaba: double start_time; string timer()
062d1ffb7c 2016-03-28        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
062d1ffb7c 2016-03-28        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
062d1ffb7c 2016-03-28        kinaba:  { os << "{ ";
062d1ffb7c 2016-03-28        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
062d1ffb7c 2016-03-28        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
062d1ffb7c 2016-03-28        kinaba: void verify_case(const int& Expected, const int& Received) {
062d1ffb7c 2016-03-28        kinaba:  bool ok = (Expected == Received);
062d1ffb7c 2016-03-28        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
062d1ffb7c 2016-03-28        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
062d1ffb7c 2016-03-28        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
062d1ffb7c 2016-03-28        kinaba: #define END	 verify_case(_, SuccessfulMerger().minimumMergers(road));}
062d1ffb7c 2016-03-28        kinaba: int main(){
062d1ffb7c 2016-03-28        kinaba: 
062d1ffb7c 2016-03-28        kinaba: CASE(0)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = {2, 2, 1, 1, 1};
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = 1;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: CASE(1)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = {3, 4, 5, 4, 5, 3};
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = 2;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: CASE(2)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = {1, 0, 1, 0, 0, 0, 1, 0, 1, 1};
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = 1;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: CASE(3)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = {1, 2, 3, 0};
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = 2;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: CASE(4)
062d1ffb7c 2016-03-28        kinaba: 	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};
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = 25;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: CASE(5)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = {1, 0};
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = 0;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: /*
062d1ffb7c 2016-03-28        kinaba: CASE(6)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = ;
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = ;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: CASE(7)
062d1ffb7c 2016-03-28        kinaba: 	int road_[] = ;
062d1ffb7c 2016-03-28        kinaba: 	  vector <int> road(road_, road_+sizeof(road_)/sizeof(*road_));
062d1ffb7c 2016-03-28        kinaba: 	int _ = ;
062d1ffb7c 2016-03-28        kinaba: END
062d1ffb7c 2016-03-28        kinaba: */
062d1ffb7c 2016-03-28        kinaba: }
062d1ffb7c 2016-03-28        kinaba: // END CUT HERE