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 FairTournament
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	vector<string> memo;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	string add(const string& a, const string& b)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		int n = max(a.size(), b.size()), carry=0;
4fd800b3a8 2011-02-23        kinaba: 		string c(n, '0');
4fd800b3a8 2011-02-23        kinaba: 		for(int i=0; i<n; ++i) {
4fd800b3a8 2011-02-23        kinaba: 			int x = (a.size()<=i ? 0 : a[a.size()-1-i]-'0')
4fd800b3a8 2011-02-23        kinaba: 			      + (b.size()<=i ? 0 : b[b.size()-1-i]-'0') + carry;
4fd800b3a8 2011-02-23        kinaba: 			c[n-1-i] = char('0'+x%10);
4fd800b3a8 2011-02-23        kinaba: 			carry = x/10;
4fd800b3a8 2011-02-23        kinaba: 		}
4fd800b3a8 2011-02-23        kinaba: 		if( carry ) c = char('0'+carry)+c;
4fd800b3a8 2011-02-23        kinaba: 		return c;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	string countPermutations(int n, int k)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		memo.clear();
4fd800b3a8 2011-02-23        kinaba: 		memo.resize(n<<k+1+k, "X");
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		int pending = (1<<k+1) - 1; // 0b00111 (case k=2)
4fd800b3a8 2011-02-23        kinaba: 		return rec(pending, 0, n, k);
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	string rec(int pending, int i, int n, int k)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( i == n )
4fd800b3a8 2011-02-23        kinaba: 			return "1";
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		int key = (i<<k+1+k) | pending;
4fd800b3a8 2011-02-23        kinaba: 		if( memo[key]!="X" )
4fd800b3a8 2011-02-23        kinaba: 			return memo[key];
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		string sum = "";
4fd800b3a8 2011-02-23        kinaba: 		for(int m=1,j=k; m<=pending; m<<=1,j--)
4fd800b3a8 2011-02-23        kinaba: 			if( (pending & m) && i+j<n )
4fd800b3a8 2011-02-23        kinaba: 			{
4fd800b3a8 2011-02-23        kinaba: 				int p2 = ((pending^m)<<1) | 1;
4fd800b3a8 2011-02-23        kinaba: 				if( p2 >= (1<<k+1+k) ) // 0b100000
4fd800b3a8 2011-02-23        kinaba: 					continue;
4fd800b3a8 2011-02-23        kinaba: 				sum = add(sum, rec(p2, i+1, n, k));
4fd800b3a8 2011-02-23        kinaba: 			}
4fd800b3a8 2011-02-23        kinaba: 		return memo[key]=sum;
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(); }
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 string &Expected, const string &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 = 3; int Arg1 = 1; string Arg2 = "3"; verify_case(0, Arg2, countPermutations(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_1() { int Arg0 = 3; int Arg1 = 2; string Arg2 = "6"; verify_case(1, Arg2, countPermutations(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_2() { int Arg0 = 10; int Arg1 = 3; string Arg2 = "19708"; verify_case(2, Arg2, countPermutations(Arg0, Arg1)); }
4fd800b3a8 2011-02-23        kinaba: 	void test_case_3() { int Arg0 = 100; int Arg1 = 1; string Arg2 = "573147844013817084101"; verify_case(3, Arg2, countPermutations(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() {
4fd800b3a8 2011-02-23        kinaba: 	FairTournament().run_test(-1);
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE