2012 TCO Algorithm - Round 1A

Links: http://community.topcoder.com/tco12/algorithm-schedule/

Score. 250

Simulation.

class EllysJuice
{
public:
	vector <string> getWinners(vector <string> players) {
		sort(players.begin(), players.end());
		
		vector <string> ans; ans.clear();
	
		do {
		//	for(int i = 0; i < (int)players.size(); ++i)
		//		cout << players[i] << " ; ";
		//	cout << endl;
		
			double x = 1.0, y = 1.0;
			map <string, double> g; g.clear();
			
			double maxv = -1.0;
			for(int i = 0; i < (int)players.size(); ++i) {
				if( i & 1 ) {
					x *= 0.5;
					g[ players[i] ] += x;
					maxv = max(maxv, g[ players[i] ] );
				} else {
					y *= 0.5;
					g[ players[i] ] += y;
					maxv = max(maxv, g[ players[i] ] );
				}
			}
			
			//cout << " maxv =  " << maxv << endl;
			
			int ip = -1;
			for(int i = 0; i < (int)players.size(); ++i)
				if( (g[ players[i] ] + 1e-9 > maxv) && (maxv + 1e-9 > g[ players[i] ]) ) {
					bool ok = 1;
					for(int j = i + 1; j < (int)players.size(); ++j)
						if( (g[ players[j] ] + 1e-9 > maxv) && (maxv + 1e-9 > g[ players[j] ]) && (players[i] != players[j]) ) {
							ok = 0; break;
						}
					if( ok ) ip = i;
					else break;
				}
			
			if( ip != -1 ) {
				//cout << " [ " << players[ip] << " ] " << endl;
				ans.push_back( players[ip] );
			}
			
		} while( next_permutation(players.begin(), players.end()) );
		
		sort(ans.begin(), ans.end());
		
		vector <string> ret; ret.clear();
		
		for(int i = 0; i < (int)ans.size(); ++i)
			if( i == 0 || ans[i] != ans[i - 1] )
				ret.push_back( ans[i] );
		
		return ret;
	}
};

Score. 500

Math.

typedef long long i64d;

class EllysFractions
{
public:

	bool isPrime(int N) {
		for(int i = 2; i * i <= N; ++i)
			if( N % i == 0 )
				return 0;
		return 1;
	}
	
	i64d getCount(int N) {
		i64d ans = 0LL;
		for(int i = 2; i <= N; ++i) {
			int tot = 0;
			for(int j = 2; j <= i; j++)
				if( isPrime(j) )
					++tot;
			ans += 1LL << (tot - 1);
		}
		return ans;
	}
};

Score. 1000

Search.

const int maxN = 50 + 2;

class EllysLights
{
public:

	vector<int> v1[maxN], v2[maxN];
	int sgn1[maxN], sgn2[maxN], Len;
	
	void dfs(int ip, int &ans, int dep) {
		if( ip == Len ) {
			if( ans == -1 || ans > dep ) ans = dep;
			return ;
		}
		
		if( ans != -1 && dep >= ans ) return ;
		
		if( sgn1[ip] == 1 ) {
			for(int i = 0; i < (int)v2[ip].size(); ++i) {
				int d = v2[ip][i];
				if( sgn2[ d ] ) continue;
				
				bool ok = 1;
				for(int j = 0; j < (int)v1[d].size(); ++j)
					if( v1[d][j] < ip ) {
						ok = 0; break;
					}
				if( !ok ) continue;
				
				for(int j = 0; j < (int)v1[d].size(); ++j)
					sgn1[ v1[d][j] ] ^= 1;
				
				sgn2[d] = 1;
				
				dfs(ip + 1, ans, dep + 1);
				
				sgn2[d] = 0;
				
				for(int j = 0; j < (int)v1[d].size(); ++j)
					sgn1[ v1[d][j] ] ^= 1;
			}
		}
		
		if( sgn1[ip] == 0 ) {
			dfs(ip + 1, ans, dep);
			for(int i = 0; i + 1 < (int)v2[ip].size(); ++i) {
				int d1 = v2[ip][i], d2 = v2[ip][i + 1];
				if( sgn2[d1] || sgn2[d2] ) continue;
				
				bool ok = 1;
				for(int j = 0; j < (int)v1[d1].size(); ++j)
					if( v1[d1][j] < ip ) {
						ok = 0; break;
					}
				if( !ok ) continue;
				for(int j = 0; j < (int)v1[d2].size(); ++j)
					if( v1[d2][j] < ip ) {
						ok = 0; break;
					}
				if( !ok ) continue;
				
				for(int j = 0; j < (int)v1[d1].size(); ++j)
					sgn1[ v1[d1][j] ] ^= 1;
				for(int j = 0; j < (int)v1[d2].size(); ++j)
					sgn1[ v1[d2][j] ] ^= 1;
					
				sgn2[ d1 ] = sgn2[ d2 ] = 1;
				
				dfs(ip + 1, ans, dep + 2);
				
				sgn2[ d1 ] = sgn2[ d2 ] = 0;
				
				for(int j = 0; j < (int)v1[d1].size(); ++j)
					sgn1[ v1[d1][j] ] ^= 1;
				for(int j = 0; j < (int)v1[d2].size(); ++j)
					sgn1[ v1[d2][j] ] ^= 1;
			}
		} 
	}

	int getMinimum(string initial, vector <string> switches) {
		int L1 = (int)initial.length(), L2 = (int)switches.size();
		Len = L1; 
		
		memset(sgn1, 0, sizeof(sgn1)); memset(sgn2, 0, sizeof(sgn2));
		
		for(int i = 0; i < L1; ++i) sgn1[i] = (initial[i] == 'Y') ? 1 : 0;
		
		for(int i = 0; i < maxN; ++i) { v1[i].clear(); v2[i].clear(); }
		
		for(int i = 0; i < L2; ++i) 
			for(int j = 0; j < L1; ++j)
				if( switches[i][j] == 'Y' ) {
					v1[i].push_back(j);
					v2[j].push_back(i);
				}
		
		bool ok = 1;
		
		for(int i = 0; i < L1; ++i)
			if( !sgn1[i] ) {
				ok = 0; break;
			}
	
		if( ok ) {
			for(int i = 0; i < L1 && ok; ++i)
				if( (int)v2[i].size() != 2 ) {
					ok = 0; break;
				}
			
			for(int i = 0; i < L2 && ok; ++i)
				if( (int)v1[i].size() != 2 ) {
					ok = 0; break;
				}
		}
		
		if( ok ) {
			return L2 >> 1;
		}
		
		int ans = -1;
		
		dfs(0, ans, 0);
		
		return ans;
	}

};

Author @ SWJTU @ 2012-04-01.