3ec8b9143e 2013-07-19        kinaba: #include <iostream>
3ec8b9143e 2013-07-19        kinaba: #include <sstream>
3ec8b9143e 2013-07-19        kinaba: #include <iomanip>
3ec8b9143e 2013-07-19        kinaba: #include <vector>
3ec8b9143e 2013-07-19        kinaba: #include <string>
3ec8b9143e 2013-07-19        kinaba: #include <map>
3ec8b9143e 2013-07-19        kinaba: #include <set>
3ec8b9143e 2013-07-19        kinaba: #include <algorithm>
3ec8b9143e 2013-07-19        kinaba: #include <numeric>
3ec8b9143e 2013-07-19        kinaba: #include <iterator>
3ec8b9143e 2013-07-19        kinaba: #include <functional>
3ec8b9143e 2013-07-19        kinaba: #include <complex>
3ec8b9143e 2013-07-19        kinaba: #include <queue>
3ec8b9143e 2013-07-19        kinaba: #include <stack>
3ec8b9143e 2013-07-19        kinaba: #include <cmath>
3ec8b9143e 2013-07-19        kinaba: #include <cassert>
3ec8b9143e 2013-07-19        kinaba: using namespace std;
3ec8b9143e 2013-07-19        kinaba: typedef long long LL;
3ec8b9143e 2013-07-19        kinaba: typedef long double LD;
3ec8b9143e 2013-07-19        kinaba: typedef complex<double> CMP;
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: template<typename T>
3ec8b9143e 2013-07-19        kinaba: vector<int> compress(const vector<T>& xs, int origin = 0)
3ec8b9143e 2013-07-19        kinaba: {
3ec8b9143e 2013-07-19        kinaba: 	vector< pair<T,int> > xi;
3ec8b9143e 2013-07-19        kinaba: 	for(int i=0; i<xs.size(); ++i)
3ec8b9143e 2013-07-19        kinaba: 		xi.push_back( make_pair(xs[i], i) );
3ec8b9143e 2013-07-19        kinaba: 	sort(xi.begin(), xi.end());
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	vector<int> result(xs.size());
3ec8b9143e 2013-07-19        kinaba: 	for(int k=0,id=origin; k<xi.size(); ++k) {
3ec8b9143e 2013-07-19        kinaba: 		if(0<=k-1 && xi[k-1].first<xi[k].first)
3ec8b9143e 2013-07-19        kinaba: 			++id;
3ec8b9143e 2013-07-19        kinaba: 		result[xi[k].second] = id;
3ec8b9143e 2013-07-19        kinaba: 	}
3ec8b9143e 2013-07-19        kinaba: 	return result;
3ec8b9143e 2013-07-19        kinaba: }
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: std::vector<int> compress(const std::vector<int>& xs)  // convert to 1-origin rank
3ec8b9143e 2013-07-19        kinaba: {
3ec8b9143e 2013-07-19        kinaba: 	set<int> s(xs.begin(), xs.end());
3ec8b9143e 2013-07-19        kinaba: 	map<int,int> mp;
3ec8b9143e 2013-07-19        kinaba: 	int ID = 1;
3ec8b9143e 2013-07-19        kinaba: 	for(set<int>::iterator it=s.begin(); it!=s.end(); ++it)
3ec8b9143e 2013-07-19        kinaba: 		mp[*it] = ID++;
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	std::vector<int> result(xs.size());
3ec8b9143e 2013-07-19        kinaba: 	for(int k=0; k<xs.size(); ++k)
3ec8b9143e 2013-07-19        kinaba: 		result[k] = mp[xs[k]];
3ec8b9143e 2013-07-19        kinaba: 	return result;
3ec8b9143e 2013-07-19        kinaba: }
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: LL C(LL n, LL k)
3ec8b9143e 2013-07-19        kinaba: {
3ec8b9143e 2013-07-19        kinaba: 	if(n<k)
3ec8b9143e 2013-07-19        kinaba: 		return 0;
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	k = min(k, n-k);
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	LL c = 1;
3ec8b9143e 2013-07-19        kinaba: 	for(LL i=0; i<k; ++i)
3ec8b9143e 2013-07-19        kinaba: 		c *= n-i, c /= i+1;
3ec8b9143e 2013-07-19        kinaba: 	return c;
3ec8b9143e 2013-07-19        kinaba: }
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: class Excavations { public:
3ec8b9143e 2013-07-19        kinaba: 	long long count(vector <int> kind, vector <int> depth, vector <int> found, int K)
3ec8b9143e 2013-07-19        kinaba: 	{
3ec8b9143e 2013-07-19        kinaba: 		depth = compress(depth, 1);
3ec8b9143e 2013-07-19        kinaba: 		int MD = *max_element(depth.begin(), depth.end());
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		map< int, vector<int> > kind_to_depth;
3ec8b9143e 2013-07-19        kinaba: 		set<int> found_set(found.begin(), found.end());
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		for(int i=0; i<kind.size(); ++i)
3ec8b9143e 2013-07-19        kinaba: 			kind_to_depth[kind[i]].push_back(depth[i]);
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		vector< vector<LL> > tbl_f(K+1, vector<LL>(MD+1));
3ec8b9143e 2013-07-19        kinaba: 		vector< vector<LL> > tbl_nf(K+1, vector<LL>(MD+1));
3ec8b9143e 2013-07-19        kinaba: 		for(int d=0; d<=MD; ++d)
3ec8b9143e 2013-07-19        kinaba: 			tbl_f[0][d] = tbl_nf[0][d] = 1;
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		for(map<int,vector<int> >::iterator it=kind_to_depth.begin(); it != kind_to_depth.end(); ++it) {
3ec8b9143e 2013-07-19        kinaba: 			bool f = !!found_set.count(it->first);
3ec8b9143e 2013-07-19        kinaba: 			vector<int> ds = it->second;
3ec8b9143e 2013-07-19        kinaba: 			sort(ds.begin(), ds.end());
3ec8b9143e 2013-07-19        kinaba: 			vector< vector<LL> > tbl2 = calc_table(K, MD, ds, f);
3ec8b9143e 2013-07-19        kinaba: 			vector< vector<LL> >& tbl = (f ? tbl_f : tbl_nf);
3ec8b9143e 2013-07-19        kinaba: 			tbl = combine(K, MD, tbl, tbl2);
3ec8b9143e 2013-07-19        kinaba: 		}
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		LL total = 0;
3ec8b9143e 2013-07-19        kinaba: 		for(int k=0; k<=K; ++k)
3ec8b9143e 2013-07-19        kinaba: 			total += cross(tbl_f[k], tbl_nf[K-k]);
3ec8b9143e 2013-07-19        kinaba: 		return total;
3ec8b9143e 2013-07-19        kinaba: 	}
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	LL cross(const vector<LL>& f, const vector<LL>& n)
3ec8b9143e 2013-07-19        kinaba: 	{
3ec8b9143e 2013-07-19        kinaba: 		vector< pair<int,LL> > pf;
3ec8b9143e 2013-07-19        kinaba: 		for(int d=0; d<f.size(); ++d) {
3ec8b9143e 2013-07-19        kinaba: 			LL cnt = (d==0 ? f[d] : f[d]-f[d-1]);
3ec8b9143e 2013-07-19        kinaba: 			if(cnt) {
3ec8b9143e 2013-07-19        kinaba: 				pf.push_back(make_pair(d, cnt));
3ec8b9143e 2013-07-19        kinaba: 			}
3ec8b9143e 2013-07-19        kinaba: 		}
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		vector< pair<int,LL> > nf;
3ec8b9143e 2013-07-19        kinaba: 		for(int d=0; d<n.size(); ++d) {
3ec8b9143e 2013-07-19        kinaba: 			LL cnt = (d==n.size()-1 ? n[d] : n[d]-n[d+1]);
3ec8b9143e 2013-07-19        kinaba: 			if(cnt) {
3ec8b9143e 2013-07-19        kinaba: 				nf.push_back(make_pair(d, cnt));
3ec8b9143e 2013-07-19        kinaba: 			}
3ec8b9143e 2013-07-19        kinaba: 		}
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 		LL total = 0;
3ec8b9143e 2013-07-19        kinaba: 		for(int i=0; i<pf.size(); ++i)
3ec8b9143e 2013-07-19        kinaba: 		for(int k=0; k<nf.size(); ++k)
3ec8b9143e 2013-07-19        kinaba: 		{
3ec8b9143e 2013-07-19        kinaba: 			if(pf[i].first <= nf[k].first)
3ec8b9143e 2013-07-19        kinaba: 				total += pf[i].second * nf[k].second;
3ec8b9143e 2013-07-19        kinaba: 		}
3ec8b9143e 2013-07-19        kinaba: 		return total;
3ec8b9143e 2013-07-19        kinaba: 	}
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	vector< vector<LL> > calc_table(int K, int D, const vector<int>& ds, bool found)
3ec8b9143e 2013-07-19        kinaba: 	{
3ec8b9143e 2013-07-19        kinaba: 		vector< vector<LL> > tbl(K+1, vector<LL>(D+1));
3ec8b9143e 2013-07-19        kinaba: 		for(int d=0; d<=D; ++d)
3ec8b9143e 2013-07-19        kinaba: 		{
3ec8b9143e 2013-07-19        kinaba: 			int num_discover = upper_bound(ds.begin(), ds.end(), d) - ds.begin();
3ec8b9143e 2013-07-19        kinaba: 			for(int k=0; k<=K; ++k)
3ec8b9143e 2013-07-19        kinaba: 				tbl[k][d] = (found ? (k==0 ? 0 : C(num_discover, k)) : C(ds.size()-num_discover, k));
3ec8b9143e 2013-07-19        kinaba: 		}
3ec8b9143e 2013-07-19        kinaba: 		return tbl;
3ec8b9143e 2013-07-19        kinaba: 	}
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: 	vector< vector<LL> > combine(int K, int D, const vector<vector<LL> >& s, const vector<vector<LL> >& t)
3ec8b9143e 2013-07-19        kinaba: 	{
3ec8b9143e 2013-07-19        kinaba: 		vector< vector<LL> > r(K+1, vector<LL>(D+1));
3ec8b9143e 2013-07-19        kinaba: 		for(int ks=0; ks<=K; ++ks)
3ec8b9143e 2013-07-19        kinaba: 		for(int kt=0; kt<=K; ++kt) if(ks+kt<=K)
3ec8b9143e 2013-07-19        kinaba: 			for(int d=0; d<=D; ++d)
3ec8b9143e 2013-07-19        kinaba: 				r[ks+kt][d] += s[ks][d] * t[kt][d];
3ec8b9143e 2013-07-19        kinaba: 		return r;
3ec8b9143e 2013-07-19        kinaba: 	}
3ec8b9143e 2013-07-19        kinaba: };
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: // BEGIN CUT HERE
3ec8b9143e 2013-07-19        kinaba: #include <ctime>
3ec8b9143e 2013-07-19        kinaba: double start_time; string timer()
3ec8b9143e 2013-07-19        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
3ec8b9143e 2013-07-19        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
3ec8b9143e 2013-07-19        kinaba:  { os << "{ ";
3ec8b9143e 2013-07-19        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
3ec8b9143e 2013-07-19        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
3ec8b9143e 2013-07-19        kinaba: void verify_case(const long long& Expected, const long long& Received) {
3ec8b9143e 2013-07-19        kinaba:  bool ok = (Expected == Received);
3ec8b9143e 2013-07-19        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
3ec8b9143e 2013-07-19        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
3ec8b9143e 2013-07-19        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
3ec8b9143e 2013-07-19        kinaba: #define END	 verify_case(_, Excavations().count(kind, depth, found, K));}
3ec8b9143e 2013-07-19        kinaba: int main(){
3ec8b9143e 2013-07-19        kinaba: 
3ec8b9143e 2013-07-19        kinaba: CASE(0)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = {1, 1, 2, 2};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = {10, 15, 10, 20};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = {1};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = 2;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = 3LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: CASE(1)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = {1, 1, 2, 2};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = {10, 15, 10, 20};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = {1, 2};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = 2;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = 4LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: CASE(2)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = {1, 2, 3, 4};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = {10, 10, 10, 10};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = {1, 2};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = 3;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = 0LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: CASE(3)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = {1, 2, 2, 3, 1, 3, 2, 1, 2};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = {12512, 12859, 125, 1000, 99, 114, 125, 125, 114};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = {1, 2, 3};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = 7;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = 35LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: CASE(4)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = {2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = {50};
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = 18;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = 9075135300LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: /*
3ec8b9143e 2013-07-19        kinaba: CASE(5)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = ;
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = ;
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = ;
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = ;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: CASE(6)
3ec8b9143e 2013-07-19        kinaba: 	int kind_[] = ;
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> kind(kind_, kind_+sizeof(kind_)/sizeof(*kind_));
3ec8b9143e 2013-07-19        kinaba: 	int depth_[] = ;
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> depth(depth_, depth_+sizeof(depth_)/sizeof(*depth_));
3ec8b9143e 2013-07-19        kinaba: 	int found_[] = ;
3ec8b9143e 2013-07-19        kinaba: 	  vector <int> found(found_, found_+sizeof(found_)/sizeof(*found_));
3ec8b9143e 2013-07-19        kinaba: 	int K = ;
3ec8b9143e 2013-07-19        kinaba: 	long long _ = LL;
3ec8b9143e 2013-07-19        kinaba: END
3ec8b9143e 2013-07-19        kinaba: 	*/
3ec8b9143e 2013-07-19        kinaba: }
3ec8b9143e 2013-07-19        kinaba: // END CUT HERE