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Submission #539024

# Submission time Handle Problem Language Result Execution time Memory
539024 2022-03-18T09:48:00 Z amunduzbaev L-triominoes (CEOI21_ltriominoes) C++17
28 / 100
 117 ms 6468 KB 
#include "bits/stdc++.h"
using namespace std;

#define ar array

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;
	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]--;
	}
	
	if(n <= 7){
		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;
			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;
								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";
	} else {
		vector<vector<mtx>> pw(7, vector<mtx>(30, mtx(0)));
		for(int t=0;t<7;t++){
			int n = t + 1;
			mtx dp(1 << n);
			for(int i=0;i < (1 << n);i++){
				for(int j=0;j < (1 << n);j++){
					int mask = 0, mm = i;
					for(int l=0;l<n;l++){
						if(mm >> l & 1) continue;
						if(l + 1 < n && !(mm >> (l + 1) & 1) && !(mask >> (l + (j >> l & 1)) & 1) && 
						(j >> l & 1) == (j >> (l + 1) & 1)){
							mm |= (1 << l);
							mm |= (1 << (l + 1));
							mask |= (1 << (l + (j >> l & 1)));
						} else if((j >> l & 1) && l + 1 < n && !(mask >> (l + 1) & 1) && !(mask >> l & 1)){
							mm |= (1 << l);
							mask |= (1 << l);
							mask |= (1 << (l + 1));
						} else if(!(j >> l & 1) && l && !(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[t][0] = dp;
			for(int j=1;j<30;j++){
				pw[t][j] = pw[t][j-1] * pw[t][j-1];
			}
		}
		
		sort(a.begin(), a.end(), [&](auto& a, auto& b){
			return (a[1] < b[1]);
		});
		
		auto solve = [&](int l, int r, vector<int>& dp, vector<int>& t1, int& d, int& I, int rev){
			int t = (r - l);
			vector<int> d1(1 << t);
			for(int mask=0;mask<(1 << n);mask++){
				int m = (mask >> l) & ((1 << t) - 1);
				d1[m] |= dp[mask];
			} rev = (rev >> l) & ((1 << t) - 1);
			
			for(int mask=0;mask < (1 << t);mask++){
				for(int j=0;j < (1 << t);j++){
					if(d){
						t1[j] |= (d1[mask] & pw[I][t - 1].t[mask][j]);
					} else {
						if(rev & j) continue;
						t1[rev | j] |= (d1[mask] & pw[I][t - 1].t[mask][j]);
					}
				}
			}
		};
		
		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;
			for(int l=29;~l;l--){
				if(d >> l & 1){
					d ^= (1 << l);
					vector<int> tp(1 << n);
					for(int t=1;t<=7;t++){
						int r = n - t;
						if(r > 7) continue;
						
						vector<int> t1(1 << t), t2(1 << r);
						solve(0, t, dp, t1, d, l, rev);
						solve(t, n, dp, t2, d, l, rev);
						for(int mask=0;mask < (1 << n);mask++){
							tp[mask] |= (t1[mask & ((1 << t) -1 )] & t2[mask >> t]);
						}
					}
					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 t=1;t<=7;t++){
					int r = n - t;
					if(r > 7) continue;
					
					vector<int> t1(1 << t), t2(1 << r);
					solve(0, t, dp, t1, d, l, d);
					solve(t, n, dp, t2, d, l, d);
					for(int mask=0;mask < (1 << n);mask++){
						tp[mask] |= (t1[mask & ((1 << t) -1 )] & t2[mask >> t]);
					}
				}
				swap(tp, dp);
			}
		}
		
		if(dp[(1 << n) - 1]) cout<<"YES\n";
		else cout<<"NO\n";
	}
}

Subtask #1
0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 3 ms 468 KB Output is correct
7 Correct 100 ms 2512 KB Output is correct
8 Runtime error 72 ms 6332 KB Execution killed with signal 11
9 Halted 0 ms 0 KB -

Subtask #2
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 102 ms 2512 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Runtime error 71 ms 6468 KB Execution killed with signal 11
6 Halted 0 ms 0 KB -

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 0 ms 272 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 0 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 0 ms 212 KB Output is correct
12 Correct 0 ms 212 KB Output is correct
13 Correct 0 ms 212 KB Output is correct
14 Correct 1 ms 212 KB Output is correct
15 Correct 1 ms 212 KB Output is correct
16 Correct 1 ms 212 KB Output is correct
17 Correct 1 ms 340 KB Output is correct
18 Correct 0 ms 340 KB Output is correct
19 Correct 1 ms 212 KB Output is correct
20 Correct 1 ms 340 KB Output is correct
21 Correct 0 ms 212 KB Output is correct
22 Correct 1 ms 212 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 1 ms 212 KB Output is correct
25 Correct 1 ms 212 KB Output is correct
26 Correct 1 ms 340 KB Output is correct
27 Correct 1 ms 212 KB Output is correct
28 Correct 0 ms 212 KB Output is correct
29 Correct 1 ms 212 KB Output is correct
30 Correct 1 ms 212 KB Output is correct
31 Correct 1 ms 212 KB Output is correct
32 Correct 0 ms 212 KB Output is correct
33 Correct 1 ms 340 KB Output is correct
34 Correct 1 ms 212 KB Output is correct
35 Correct 1 ms 340 KB Output is correct
36 Correct 1 ms 340 KB Output is correct
37 Correct 1 ms 212 KB Output is correct
38 Correct 1 ms 212 KB Output is correct
39 Correct 1 ms 212 KB Output is correct
40 Correct 1 ms 212 KB Output is correct
41 Correct 1 ms 340 KB Output is correct
42 Correct 1 ms 212 KB Output is correct
43 Correct 1 ms 340 KB Output is correct
44 Correct 0 ms 212 KB Output is correct
45 Correct 1 ms 340 KB Output is correct
46 Correct 1 ms 212 KB Output is correct
47 Correct 1 ms 212 KB Output is correct
48 Correct 1 ms 340 KB Output is correct
49 Correct 0 ms 212 KB Output is correct

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 5 ms 468 KB Output is correct
4 Correct 3 ms 468 KB Output is correct
5 Correct 16 ms 900 KB Output is correct
6 Correct 2 ms 468 KB Output is correct
7 Correct 2 ms 468 KB Output is correct
8 Correct 2 ms 468 KB Output is correct
9 Correct 3 ms 596 KB Output is correct
10 Correct 2 ms 340 KB Output is correct
11 Correct 6 ms 468 KB Output is correct
12 Correct 27 ms 912 KB Output is correct
13 Correct 2 ms 340 KB Output is correct
14 Correct 2 ms 340 KB Output is correct
15 Correct 6 ms 468 KB Output is correct
16 Correct 24 ms 916 KB Output is correct
17 Correct 5 ms 468 KB Output is correct
18 Correct 5 ms 468 KB Output is correct
19 Correct 21 ms 916 KB Output is correct
20 Correct 17 ms 896 KB Output is correct
21 Correct 3 ms 468 KB Output is correct
22 Correct 16 ms 916 KB Output is correct
23 Correct 1 ms 340 KB Output is correct
24 Correct 6 ms 468 KB Output is correct
25 Correct 24 ms 852 KB Output is correct
26 Correct 2 ms 340 KB Output is correct
27 Correct 5 ms 468 KB Output is correct
28 Correct 3 ms 468 KB Output is correct
29 Correct 5 ms 468 KB Output is correct
30 Correct 3 ms 468 KB Output is correct
31 Correct 5 ms 492 KB Output is correct
32 Correct 24 ms 852 KB Output is correct
33 Correct 24 ms 912 KB Output is correct
34 Correct 16 ms 900 KB Output is correct
35 Correct 15 ms 852 KB Output is correct
36 Correct 3 ms 468 KB Output is correct
37 Correct 16 ms 924 KB Output is correct

Subtask #5
0 / 35.0

# Verdict Execution time Memory Grader output
1 Correct 113 ms 2452 KB Output is correct
2 Correct 117 ms 2512 KB Output is correct
3 Runtime error 98 ms 6408 KB Execution killed with signal 11
4 Halted 0 ms 0 KB -

Subtask #6
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 3 ms 468 KB Output is correct
7 Correct 100 ms 2512 KB Output is correct
8 Runtime error 72 ms 6332 KB Execution killed with signal 11
9 Halted 0 ms 0 KB -