Submission #576762

#	Time	Username	Problem	Language	Result	Execution time	Memory
576762		amunduzbaev	L-triominoes (CEOI21_ltriominoes)	C++17	45 / 100	1430 ms	16248 KiB

ltrominoes

#include "bits/stdc++.h"
using namespace std;
 
#define ar array
#define int int64_t
const int N = 15;
const int M = 1005;
int dp[2][N][1 << N];
int is[N][M];


struct mtx{
	vector<vector<int>> t;
	int n;
	
	mtx (int sz){
		n = sz;
		t.resize(n, vector<int>(n, 0));
	}
	
	mtx operator * (mtx& b){
		mtx c(n);
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				for(int k=0;k<n;k++){
					c.t[i][j] |= (t[i][k] & b.t[k][j]);
				}
			}
		} return c;
	}
};
 
signed main(){
	ios::sync_with_stdio(0); cin.tie(0);
	
	int n, m, k; cin>>n>>m>>k;
	if(!k && m > 1000) {
		if(n == 3){
			if(m % 2 == 0) cout<<"YES\n";	
			else cout<<"NO\n";
			return 0;
		}
		
		if(n * m % 3 == 0) cout<<"YES\n"; 
		else cout<<"NO\n";
		return 0;
	}
	//~ if(m > 1000){
		//~ if(n < 6){
			//~ if((n * m) % 6 == 0) cout<<"YES\n";
			//~ else cout<<"NO\n";
		//~ } else {
			//~ if((n * m) % 3 == 0) cout<<"YES\n";
			//~ else cout<<"NO\n";
		//~ }
		//~ return 0;
	//~ }
	
	if(n <= 7){
		vector<ar<int, 2>> a(k);
		for(int i=0;i<k;i++){
			cin>>a[i][0]>>a[i][1];
			a[i][0]--, a[i][1]--;
		}
		
		vector<mtx> pw(30, mtx(1 << n));
		{
			mtx dp(1 << n);
			for(int i=0;i < (1 << n);i++){
				for(int j=0;j < (1 << (n + n));j++){
					int mask = 0, mm = i;
					for(int l=0;l<n;l++){
						if(mm >> l & 1) continue;
						int v = (j >> (2 * l)) & 3;
						if(v == 0){
							if(l + 1 < n && !(mm >> (l + 1) & 1) && !(mask >> (l + 1) & 1)){
								mm |= (1 << l);
								mm |= (1 << (l + 1));
								mask |= (1 << (l + 1));
							}
						}
						if(v == 1){
							if(l + 1 < n && !(mm >> (l + 1) & 1) && !(mask >> l & 1)){
								mm |= (1 << l);
								mm |= (1 << (l + 1));
								mask |= (1 << l);
							}
						}
						if(v == 2){
							if(l && !(mask >> (l - 1) & 1) && !(mask >> l & 1)){
								mm |= (1 << l);
								mask |= (1 << l);
								mask |= (1 << (l - 1));
							}
						}
						if(v == 3){
							if(l + 1 < n && !(mask >> (l + 1) & 1) && !(mask >> l & 1)){
								mm |= (1 << l);
								mask |= (1 << l);
								mask |= (1 << (l + 1));
							}
						}
					}
					
					if(mm == (1 << n) - 1 && !dp.t[i][mask]){
						//~ for(int j=0;j<n;j++) cout<<(i >> j & 1);
						//~ cout<<endl;
						//~ for(int j=0;j<n;j++) cout<<(mask >> j & 1);
						//~ cout<<endl<<endl;
						dp.t[i][mask] = 1;
					}
				}
			}
			
			pw[0] = dp;
			for(int j=1;j<30;j++){
				pw[j] = pw[j-1] * pw[j-1];
			}
		}
		
		sort(a.begin(), a.end(), [&](auto& a, auto& b){
			return (a[1] < b[1]);
		});
		
		vector<int> dp(1 << n);
		dp[(1 << n) - 1] = 1;
		int last = -1;
		for(int i=0;i<k;){
			int j = i, rev = 0;
			while(j<k && a[j][1] == a[i][1]) rev |= (1 << a[j][0]), j++;
			
			int d = a[i][1] - last;
			//~ cout<<d<<endl;
			//~ for(int i=0;i<n;i++) cout<<(rev >> i & 1);
			//~ cout<<endl;
			for(int l=29;~l;l--){
				if(d >> l & 1){
					d ^= (1 << l);
					vector<int> tp(1 << n);
					for(int mask=0;mask < (1 << n);mask++){
						for(int j=0;j < (1 << n);j++){
							if(d){
								tp[j] |= (dp[mask] & pw[l].t[mask][j]);
							} else {
								if(j & rev) continue;
								//~ if(dp[mask] && pw[l].t[mask][j]){
									//~ for(int i=0;i<n;i++) cout<<(mask >> i & 1);
									//~ cout<<endl;
									//~ for(int i=0;i<n;i++) cout<<(j >> i & 1);
									//~ cout<<endl;
								//~ }
								tp[j | rev] |= (dp[mask] & pw[l].t[mask][j]);
							}
						}
					}
					swap(tp, dp);
				}
			} last = a[i][1], i = j;
		}
		
		int d = m - last - 1;
		for(int l=29;~l;l--){
			if(d >> l & 1){
				vector<int> tp(1 << n);
				for(int mask=0;mask < (1 << n);mask++){
					for(int j=0;j < (1 << n);j++){
						tp[j] |= dp[mask] & pw[l].t[mask][j];
					}
				}
				
				swap(tp, dp);
			}
		}
		
		if(dp[(1 << n) - 1]) cout<<"YES\n";
		else cout<<"NO\n";
		return 0;
	}
	
	vector<int> x(k), y(k);
	for(int i=0;i<n;i++){
		for(int j=0;j<m;j++){
			is[i][j] = 1;
		}
	} 
	for(int i=0;i<k;i++){
		cin>>x[i]>>y[i]; x[i]--, y[i]--;
		is[x[i]][y[i]] = 0;
	}
	
	int ch[4][2] = {
		{0, 0},
		{-1, 0},
		{-1, 1},
		{0, 1}
	};
	int P[4] = {1, 0, -1, 0}, mas[4] = {14, 13, 11, 7};
	int mask = (!is[0][1]);
	for(int i=0;i<n;i++){
		if(!is[i][0]) mask |= (1 << (i + 1));
	}
	
	dp[0][1][mask] = 1;
	for(int i=0;i+1<m;i++){
		int c = i&1;
		memset(dp[!c], 0, sizeof dp[!c]);
		for(int j=1;j<n;j++){
			for(int mask=0;mask < (1 << (n + 1));mask++){
				if(!dp[c][j][mask]) continue;
				int us = 0;
				for(int t=0;t<4;t++){
					us |= (is[j + ch[t][0]][i + ch[t][1]] & (t < 3 ? !(mask >> (j + P[t]) & 1) : 1)) << t;
				}
				
				for(int t=0;t<4;t++){
					if((us & mas[t]) != mas[t]) continue;
					int m2 = mask;
					for(int l=0;l<4;l++){
						if(mas[t] >> l & 1){
							//~ assert(!(m2 >> (j + P[l]) & 1));
							m2 |= (1 << (j + P[l]));
						}
					}
					if(t == 1 && !(mask >> j & 1)) continue;
					if(t == 3){
						m2 ^= (1 << j);
						m2 |= (!is[j][i + 1]) << j;
					}
					
					if(j + 1 < n){
						dp[c][j + 1][m2] = 1;
					} else if(m2 >> n & 1) {
						m2 ^= (1 << n);
						m2 = m2 << 1 | (!is[0][i + 2]);
						dp[!c][1][m2] = 1;
					}
				}
				
				if(mask >> j & 1){
					int m2 = mask;
					if(j + 1 < n){
						m2 ^= (1 << j);
						m2 |= (!is[j][i+1]) << j;
						dp[c][j + 1][m2] = 1;
					} else if(m2 >> n & 1) {
						m2 ^= (1 << j) ^ (1 << n);
						m2 |= (!is[j][i+1]) << j;
						m2 = m2 << 1 | (!is[0][i + 2]);
						dp[!c][1][m2] = 1;
					}
				}
			}
		}
	}
	
	if(dp[(m-1)&1][1][(1 << (n + 1)) - 1]) cout<<"YES\n";
	else cout<<"NO\n";
}

• Subtask 1: 10 / 10
• Subtask 2: 7 / 7
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 0 / 35
• Subtask 6: 0 / 20