4fd800b3a8 2011-02-23        kinaba: #include <iostream>
4fd800b3a8 2011-02-23        kinaba: #include <sstream>
4fd800b3a8 2011-02-23        kinaba: #include <iomanip>
4fd800b3a8 2011-02-23        kinaba: #include <vector>
4fd800b3a8 2011-02-23        kinaba: #include <string>
4fd800b3a8 2011-02-23        kinaba: #include <map>
4fd800b3a8 2011-02-23        kinaba: #include <set>
4fd800b3a8 2011-02-23        kinaba: #include <algorithm>
4fd800b3a8 2011-02-23        kinaba: #include <numeric>
4fd800b3a8 2011-02-23        kinaba: #include <iterator>
4fd800b3a8 2011-02-23        kinaba: #include <complex>
4fd800b3a8 2011-02-23        kinaba: #include <queue>
4fd800b3a8 2011-02-23        kinaba: #include <stack>
4fd800b3a8 2011-02-23        kinaba: #include <cmath>
4fd800b3a8 2011-02-23        kinaba: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class PolygonDecomposition
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	int howMany(int n, int k)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( n-2 < k )
4fd800b3a8 2011-02-23        kinaba: 			return -1;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		LL dp[101][101] = {};
4fd800b3a8 2011-02-23        kinaba: 		dp[2][0] = 1;
4fd800b3a8 2011-02-23        kinaba: 		for(int N=3; N<=n; ++N)
4fd800b3a8 2011-02-23        kinaba: 			dp[N][1] = 1;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		for(int N=4; N<=n; ++N)
4fd800b3a8 2011-02-23        kinaba: 		for(int K=2; K<=k; ++K)
4fd800b3a8 2011-02-23        kinaba: 		{
4fd800b3a8 2011-02-23        kinaba: 			LL sum = 0;
4fd800b3a8 2011-02-23        kinaba: 			for(LL v=3; v<=N-1; ++v) // use 1--v and don't use 1--3, ..., 1--(v-1)
4fd800b3a8 2011-02-23        kinaba: 				for(int x=1; x<=K-1; ++x) // left: x pieces, right: K-x pieces
4fd800b3a8 2011-02-23        kinaba: 					sum += (dp[v-1][x-1]+dp[v-1][x]) * dp[N-v+2][K-x] % 1000000000;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 			// don't use 1--*; if use 2--N, we'll have dp[N-1][K-1] cuts
4fd800b3a8 2011-02-23        kinaba: 			//                 otherwise, will have dp[N-1][K] because 2--1--N
4fd800b3a8 2011-02-23        kinaba: 			//                            can be regarded as a single edge
4fd800b3a8 2011-02-23        kinaba: 			sum += dp[N-1][K-1] + dp[N-1][K];
4fd800b3a8 2011-02-23        kinaba: 			dp[N][K] = sum % 1000000000;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		return (int) dp[n][k];
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: 	public:
4fd800b3a8 2011-02-23        kinaba: 	void run_test(int Case) { if ((Case == -1) || (Case == 0)) test_case_0(); if ((Case == -1) || (Case == 1)) test_case_1(); if ((Case == -1) || (Case == 2)) test_case_2(); if ((Case == -1) || (Case == 3)) test_case_3(); if ((Case == -1) || (Case == 4)) test_case_4(); }
4fd800b3a8 2011-02-23        kinaba: 	private:
4fd800b3a8 2011-02-23        kinaba: 	template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: 	void verify_case(int Case, const int &Expected, const int &Received) { cerr << "Test Case #" << Case << "..."; if (Expected == Received) cerr << "PASSED" << endl; else { cerr << "FAILED" << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_0() { int Arg0 = 4; int Arg1 = 2; int Arg2 = 2; verify_case(0, Arg2, howMany(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_1() { int Arg0 = 100; int Arg1 = 1; int Arg2 = 1; verify_case(1, Arg2, howMany(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_2() { int Arg0 = 6; int Arg1 = 4; int Arg2 = 14; verify_case(2, Arg2, howMany(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_3() { int Arg0 = 31; int Arg1 = 20; int Arg2 = 956146480; verify_case(3, Arg2, howMany(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_4() { int Arg0 = 3; int Arg1 = 4; int Arg2 = -1; verify_case(4, Arg2, howMany(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: int main() { PolygonDecomposition().run_test(-1); }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE