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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#150596#6380. LaLa and Divination MagicLeticiaFCSRE 1ms3580kbC++208.7kb2023-08-25 21:21:322023-08-25 21:21:33

Judging History

你现在查看的是最新测评结果

  • [2023-08-25 21:21:33]
  • 评测
  • 测评结果:RE
  • 用时:1ms
  • 内存:3580kb
  • [2023-08-25 21:21:32]
  • 提交

answer

#include"bits/stdc++.h"

using lint = int64_t;

constexpr int MOD = int(1e9) + 7;
constexpr int INF = 0x63636363;
constexpr int NINF = 0xcfcfcfcf;
constexpr lint LINF = 0x6363636363636363;

using namespace std;

struct scc_t {
    int n, t, scc_num;
    vector<vector<int>> adj;
    vector<int> low, id, stk, in_stk, cc_id;
    scc_t(const vector<vector<int>>& g) : n(int(g.size())), t(0), scc_num(0),
    adj(g), low(n,-1), id(n,-1), in_stk(n, false), cc_id(n) {}
    template<class F> void dfs(int cur, F f) {
        id[cur] = low[cur] = t++;
        stk.push_back(cur);
        in_stk[cur] = true;
        for (int nxt : adj[cur]) {
            if (id[nxt] == -1) {
                dfs(nxt, f);
                low[cur] = min(low[cur], low[nxt]);
            } else if (in_stk[nxt])
                low[cur] = min(low[cur], id[nxt]);
        }
        if (low[cur] == id[cur]) {
            vector<int> cc; cc.reserve(stk.size());
            while (true) {
                int v = stk.back(); stk.pop_back();
                in_stk[v] = false;
                cc.push_back(v);
                cc_id[v] = scc_num;
                if (v == cur) break;
            } f(cc); scc_num ++;
        }
    }
    template<class F> void solve(F f) {
        stk.reserve(n);
        for (int r = 0; r < n; ++r)
            if (id[r] == -1) dfs(r, f);
    }
};


const int M = 2002;
using B = bitset<M>;
B mat[M], matRev[M];
int always[M];


struct TwoSat {
    int N;
    vector<vector<int>> gr;
    vector<int> values; // 0 = false, 1 = true
    TwoSat(int n = 0) : N(n), gr(2*n) {}
    int add_var() { // (optional)
        gr.emplace_back();
        gr.emplace_back();
        return N++;
    }
    void either(int f, int j) {
        f = max(2*f, -1-2*f);
        j = max(2*j, -1-2*j);
        gr[f].push_back(j^1);
        gr[j].push_back(f^1);
    }
    void implies(int f, int j) { either(~f, j); }
    void set_value(int x) { either(x, x); }
    void at_most_one(const vector<int>& li) { // (optional)
        if (int(li.size()) <= 1) return;
        int cur = ~li[0];
        for (int i = 2; i < int(li.size()); ++i) {
            int next = add_var();
            either(cur, ~li[i]);
            either(cur, next);
            either(~li[i], next);
            cur = ~next;
        }
        either(cur, ~li[1]);
    }
    int solve() {
        scc_t s(gr);
        vector<int> ordem; ordem.reserve(2*N);
        s.solve([&ordem](const vector<int> &v){ 
            ordem.insert(ordem.end(), v.begin(), v.end());
        } );
        values.assign(N, -1);
        for (int i = 0; i < N; ++i) if (s.cc_id[2*i] == s.cc_id[2*i+1]) return 0;
        for (int i = 0; i < N; ++i){
            if (s.cc_id[2*i] < s.cc_id[2*i+1]) values[i] = false;
            else values[i] = true;
        }
        reverse(ordem.begin(), ordem.end());
        vector<B> adj(2*N);
        vector<B> alcanca(2*N);
        for(int o =0; o<2*N; o++){
            int u = ordem[o];
            for(int v : gr[u]){
                adj[u][v] = true;
                alcanca[u][v] = true;
            }
        }
        for(int o = 2*N-1; o >= 0; o--){
            int u = ordem[o];
            for(int v : gr[u])
                alcanca[u] |= alcanca[v];
        }
        vector<bool> settado(2*N);
        vector<bool> valor(2*N);
        for(int u =0; u<2*N; u++){
            int x = 2*u, notx = 2*u+1;
            if(alcanca[x][notx]){
                settado[x] = true;
                settado[notx] = true;
                valor[x] = false;
                valor[notx] = true;
                for(int v = 0; v < 2*N; v++)
                    if(alcanca[notx][v]){
                        settado[v] = true;
                        valor[v] = true;
                    }
            } else if(alcanca[notx][x]){
                settado[x] = true;
                settado[notx] = true;
                valor[x] = true;
                valor[notx] = false;
                for(int v = 0; v < 2*N; v++)
                    if(alcanca[x][v]){
                        settado[v] = true;
                        valor[v] = true;
                    }
            }
        }
        int ans = 0;
        auto count_sol = [&](int o, auto &&self) -> void {
            if(o == 2*N){
                ans++;
                // cout<<"SOL \n";
                // for(int u=0; u<N; u++){
                //     cout<<u<<" "<<valor[2*u]<<" "<<valor[2*u+1]<<"\n";
                // }
                return;
            }
            int u = ordem[o];
            if(settado[u]){
                self(o+1, self);
            } else {
                vector<int> alc;
                bool ok = true;
                if(ok)
                    for(int v : gr[u]){
                        if(settado[v] && valor[v] == false){
                            ok = false;
                            break;
                        }
                        if(!settado[v]){
                            settado[v] = true;
                            valor[v] = true;
                            settado[v^1] = true;
                            valor[v^1] = false;
                            alc.push_back(v);
                        }
                    }
                settado[u] = true;
                settado[u^1] = true;
                if(ok){
                    valor[u] = true;
                    valor[u^1] = false;
                    self(o+1, self);
                } 
                
                for(int v : alc){
                    settado[v] = settado[v^1] = false;
                }
                valor[u] = false;
                valor[u^1] = true;
                self(o+1, self);
                settado[u] = false;
                settado[u^1] = false;            
            }
        };
        count_sol(0, count_sol);
        return ans;
    }
};

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n, m;
    cin>>n>>m;
    for(int j=0; j<m; j++){
        always[j] = -1;
    }
    for(int i =0; i<n; i++){
        string s; cin>>s;
        for(int j=0; j<m; j++){
            mat[j][i] = int(s[j] - '0');
            matRev[j][i] = !mat[j][i];
        }
    }
    TwoSat sat(m);
    vector<tuple<int, int, int>> op;
    op.reserve(2*m);

    for(int u =0; u<m; u++){
        if(int c = mat[u].count(); c == n){
            sat.either(u, u);
            op.emplace_back(u, u, 4);
            always[u] = 1;
        } else if(c == 0){
            sat.either(~u, ~u);
            op.emplace_back(u, u, 1);
            always[u] = 0;
        }
    }
    for(int u =0; u<m; u++){
        for(int v=u+1; v<m; v++){
            if((~always[u]) && (~always[v])) continue;
            vector<vector<int>> ok(2, vector<int>(2));
            
            int cnt = 0;

            if(( matRev[u] & matRev[v]).count() ){
                ok[0][0] = true;
                cnt++;
            }
            if(( matRev[u] & mat[v]).count() ){
                ok[0][1] = true;
                cnt++;
            }
            if(( mat[u] & matRev[v]).count() ){
                ok[1][0] = true;
                cnt++;
            }
            if(( mat[u] & mat[v]).count() ){
                ok[1][1] = true;
                cnt++;
            }
            
            if(cnt == 4) continue;
            
            if(!ok[0][0]){
                sat.implies(~u, v);
                sat.implies(~v, u);
                op.emplace_back(u, v, 4);
            }
            if(!ok[0][1]){ 
                sat.implies(~u, ~v);
                sat.implies(v, u);
                op.emplace_back(u, v, 2);
            }
            if(!ok[1][0]){
                sat.implies(u, v);
                sat.implies(~v, ~u);
                op.emplace_back(u, v, 3);
            }
            if(!ok[1][1]){
                sat.implies(u, ~v);
                sat.implies(v, ~u);
                op.emplace_back(u, v, 1);
            }           
            // cout<<"u "<<u<<" v "<<v<<"\n";
            // for(int i=0;i<2; i++){ 
            //     for(int j=0;j<2; j++){
            //         if(ok[i][j])
            //             cout<<" "<<i<<" "<<j<<"\n"; 
            //     } 
            // }
        }
    }
    if(int count_sol = sat.solve(); count_sol == n){
        cout<<op.size()<<'\n';
        for(const auto &[u,v,t] : op)
            cout<<u<<' '<<v<<' '<<t<<'\n';
    } else {
        cout<<"-1\n";
    }
    return 0;
}


/*
1-either(~x, ~y): x -> ~y, y -> ~x 
2-either(x, ~y): ~x -> ~y, y -> x
3-either(~x, y): x -> y, ~y -> ~x
4-either(x, y): ~x -> y, ~y -> x
*/

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 3456kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #2:

score: 0
Accepted
time: 0ms
memory: 3504kb

input:

3 3
101
011
111

output:

6
2 2 4
0 1 4
0 2 4
0 2 3
1 2 4
1 2 3

result:

ok Kout = 6, Kans = 6

Test #3:

score: 0
Accepted
time: 1ms
memory: 3560kb

input:

2 1
0
1

output:

0

result:

ok Kout = 0, Kans = 0

Test #4:

score: 0
Accepted
time: 0ms
memory: 3504kb

input:

2 1
0
1

output:

0

result:

ok Kout = 0, Kans = 0

Test #5:

score: 0
Accepted
time: 0ms
memory: 3488kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #6:

score: 0
Accepted
time: 1ms
memory: 3496kb

input:

2 1
0
1

output:

0

result:

ok Kout = 0, Kans = 0

Test #7:

score: 0
Accepted
time: 1ms
memory: 3416kb

input:

2 1
0
1

output:

0

result:

ok Kout = 0, Kans = 0

Test #8:

score: 0
Accepted
time: 1ms
memory: 3444kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #9:

score: 0
Accepted
time: 1ms
memory: 3564kb

input:

1 1
1

output:

1
0 0 4

result:

ok Kout = 1, Kans = 1

Test #10:

score: 0
Accepted
time: 0ms
memory: 3416kb

input:

1 1
0

output:

1
0 0 1

result:

ok Kout = 1, Kans = 1

Test #11:

score: 0
Accepted
time: 0ms
memory: 3452kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #12:

score: 0
Accepted
time: 1ms
memory: 3416kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #13:

score: 0
Accepted
time: 1ms
memory: 3456kb

input:

2 4
0111
0010

output:

12
0 0 1
2 2 4
0 1 3
0 1 1
0 3 3
0 3 1
1 2 4
1 2 3
1 3 2
1 3 3
2 3 4
2 3 2

result:

ok Kout = 12, Kans = 15

Test #14:

score: 0
Accepted
time: 0ms
memory: 3508kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #15:

score: 0
Accepted
time: 1ms
memory: 3452kb

input:

4 2
10
11
01
00

output:

0

result:

ok Kout = 0, Kans = 0

Test #16:

score: 0
Accepted
time: 1ms
memory: 3492kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #17:

score: 0
Accepted
time: 0ms
memory: 3496kb

input:

2 4
0010
1000

output:

12
1 1 1
3 3 1
0 1 2
0 1 1
0 2 4
0 2 1
0 3 2
0 3 1
1 2 3
1 2 1
2 3 2
2 3 1

result:

ok Kout = 12, Kans = 15

Test #18:

score: 0
Accepted
time: 1ms
memory: 3564kb

input:

2 5
11101
00000

output:

21
3 3 1
0 1 2
0 1 3
0 2 2
0 2 3
0 3 2
0 3 1
0 4 2
0 4 3
1 2 2
1 2 3
1 3 2
1 3 1
1 4 2
1 4 3
2 3 2
2 3 1
2 4 2
2 4 3
3 4 3
3 4 1

result:

ok Kout = 21, Kans = 21

Test #19:

score: 0
Accepted
time: 1ms
memory: 3444kb

input:

5 4
0010
1001
0011
0101
1011

output:

-1

result:

ok Kout = -1, Kans = -1

Test #20:

score: 0
Accepted
time: 1ms
memory: 3500kb

input:

3 2
01
00
10

output:

1
0 1 1

result:

ok Kout = 1, Kans = 1

Test #21:

score: 0
Accepted
time: 1ms
memory: 3424kb

input:

3 2
10
11
00

output:

1
0 1 2

result:

ok Kout = 1, Kans = 1

Test #22:

score: 0
Accepted
time: 0ms
memory: 3440kb

input:

2 1
0
1

output:

0

result:

ok Kout = 0, Kans = 0

Test #23:

score: 0
Accepted
time: 1ms
memory: 3532kb

input:

3 27
111010110011101010011110110
010001110100000110100101101
000011111000000010011111001

output:

-1

result:

ok Kout = -1, Kans = -1

Test #24:

score: 0
Accepted
time: 1ms
memory: 3456kb

input:

3 7
1000100
0001100
0101111

output:

36
2 2 1
4 4 4
0 1 1
0 2 2
0 2 1
0 3 4
0 3 1
0 4 4
0 4 3
0 5 1
0 6 1
1 2 2
1 2 1
1 3 3
1 4 4
1 4 3
1 5 2
1 5 3
1 6 2
1 6 3
2 3 3
2 3 1
2 5 3
2 5 1
2 6 3
2 6 1
3 4 4
3 4 3
3 5 2
3 6 2
4 5 4
4 5 2
4 6 4
4 6 2
5 6 2
5 6 3

result:

ok Kout = 36, Kans = 39

Test #25:

score: 0
Accepted
time: 1ms
memory: 3452kb

input:

1 19
1010110011001101000

output:

19
0 0 4
1 1 1
2 2 4
3 3 1
4 4 4
5 5 4
6 6 1
7 7 1
8 8 4
9 9 4
10 10 1
11 11 1
12 12 4
13 13 4
14 14 1
15 15 4
16 16 1
17 17 1
18 18 1

result:

ok Kout = 19, Kans = 532

Test #26:

score: 0
Accepted
time: 1ms
memory: 3568kb

input:

5 32
10101101001001001101111100100110
00110110010111010101011000011010
01010101110100000110001000010100
11010011000110101101110001011111
00111001110011110000000010000111

output:

-1

result:

ok Kout = -1, Kans = -1

Test #27:

score: 0
Accepted
time: 1ms
memory: 3580kb

input:

3 12
110010101000
110001011000
110101011001

output:

100
0 0 4
1 1 4
2 2 1
8 8 4
9 9 1
10 10 1
0 3 4
0 3 2
0 4 4
0 4 2
0 5 4
0 5 2
0 6 4
0 6 2
0 7 4
0 7 2
0 11 4
0 11 2
1 3 4
1 3 2
1 4 4
1 4 2
1 5 4
1 5 2
1 6 4
1 6 2
1 7 4
1 7 2
1 11 4
1 11 2
2 3 3
2 3 1
2 4 3
2 4 1
2 5 3
2 5 1
2 6 3
2 6 1
2 7 3
2 7 1
2 11 3
2 11 1
3 4 1
3 5 3
3 6 1
3 7 3
3 8 4
3 8 3
...

result:

ok Kout = 100, Kans = 145

Test #28:

score: 0
Accepted
time: 1ms
memory: 3556kb

input:

3 25
1110100100011100101100111
0100000001011101101010101
0111110111111001001110111

output:

-1

result:

ok Kout = -1, Kans = -1

Test #29:

score: 0
Accepted
time: 1ms
memory: 3420kb

input:

1 5
10110

output:

5
0 0 4
1 1 1
2 2 4
3 3 4
4 4 1

result:

ok Kout = 5, Kans = 35

Test #30:

score: 0
Accepted
time: 1ms
memory: 3496kb

input:

5 17
01011100010100110
01001101111011001
00100111001101010
10101000001010110
00101011010010001

output:

-1

result:

ok Kout = -1, Kans = -1

Test #31:

score: 0
Accepted
time: 1ms
memory: 3504kb

input:

3 30
010100010011100011010001010100
011111100101001100010101010010
011000010111111111000101101110

output:

-1

result:

ok Kout = -1, Kans = -1

Test #32:

score: 0
Accepted
time: 1ms
memory: 3536kb

input:

5 30
110010101001001100010110010000
011011111000011001101000100000
110101010111000000100100111000
001111011110101101101001101011
101100001101011110101010110000

output:

-1

result:

ok Kout = -1, Kans = -1

Test #33:

score: 0
Accepted
time: 0ms
memory: 3452kb

input:

10 10
0110101111
1100100000
1000101100
1000010101
1001011101
1011101101
1011111011
0101010000
0111011010
1111010110

output:

-1

result:

ok Kout = -1, Kans = -1

Test #34:

score: 0
Accepted
time: 1ms
memory: 3512kb

input:

9 10
1000001101
0110010110
1011101111
1010001110
1110001000
1001110110
1101010010
0001011111
1000010100

output:

-1

result:

ok Kout = -1, Kans = -1

Test #35:

score: 0
Accepted
time: 1ms
memory: 3420kb

input:

3 5
11111
01000
01100

output:

18
1 1 4
0 1 4
0 1 3
0 2 3
0 3 2
0 3 3
0 4 2
0 4 3
1 2 4
1 2 2
1 3 4
1 3 2
1 4 4
1 4 2
2 3 2
2 4 2
3 4 2
3 4 3

result:

ok Kout = 18, Kans = 18

Test #36:

score: 0
Accepted
time: 1ms
memory: 3512kb

input:

7 9
000010100
101001100
110010111
000000110
100010101
101000100
101101100

output:

-1

result:

ok Kout = -1, Kans = -1

Test #37:

score: 0
Accepted
time: 1ms
memory: 3452kb

input:

1 4
0000

output:

4
0 0 1
1 1 1
2 2 1
3 3 1

result:

ok Kout = 4, Kans = 22

Test #38:

score: 0
Accepted
time: 1ms
memory: 3508kb

input:

9 8
10011110
10111101
11001010
01000101
10110011
00101001
00101100
11010110
01000000

output:

-1

result:

ok Kout = -1, Kans = -1

Test #39:

score: 0
Accepted
time: 0ms
memory: 3468kb

input:

3 10
0000000111
1011011111
0101111010

output:

-1

result:

ok Kout = -1, Kans = -1

Test #40:

score: 0
Accepted
time: 0ms
memory: 3452kb

input:

2 1
1
0

output:

0

result:

ok Kout = 0, Kans = 0

Test #41:

score: 0
Accepted
time: 1ms
memory: 3552kb

input:

1 5
00110

output:

5
0 0 1
1 1 1
2 2 4
3 3 4
4 4 1

result:

ok Kout = 5, Kans = 35

Test #42:

score: 0
Accepted
time: 0ms
memory: 3580kb

input:

6 9
100101111
100001110
100101010
001101000
101100010
010101110

output:

-1

result:

ok Kout = -1, Kans = -1

Test #43:

score: -100
Runtime Error

input:

6 836
001111110001001001101010101010011100010100100100111110110100101000100100000000011101110001011100111111111001101111111101101110010011000100100111111101011010101101011101010000100011100011000011111011011110000001010101001101110100001111111001000110111000010110001100110010010000101011001010101100...

output:


result: