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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#113704#6644. Red Black Gridhos_lyricAC ✓10ms9008kbC++147.0kb2023-06-19 04:38:402023-06-19 04:38:41

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-19 04:38:41]
  • 评测
  • 测评结果:AC
  • 用时:10ms
  • 内存:9008kb
  • [2023-06-19 04:38:40]
  • 提交

answer

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


constexpr int LIM_SMALL = 9;

void experiment() {
  /*
  for (int N = 1; N <= 5; ++N) {
    vector<int> brt(2*N*(N-1) + 1, 0);
    for (int p = 0; p < 1 << (N*N); ++p) {
      int cnt = 0;
      for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) {
        if (x + 1 < N && (p >> (x*N+y) & 1) != (p >> ((x+1)*N+y) & 1)) ++cnt;
        if (y + 1 < N && (p >> (x*N+y) & 1) != (p >> (x*N+(y+1)) & 1)) ++cnt;
      }
      brt[cnt] = 1;
    }
    if (N <= 10) {
      cerr << N << ": ";
      for (int x = 0; x <= 2*N*(N-1); ++x) cerr << brt[x];
      cerr << endl;
    }
  }
  //*/
  for (int N = 1; N <= 100; ++N) {
    vector<int> can(2*N*(N-1) + 1, 0);
    for (int a = 1; a < N; ++a) for (int b = 1; b < N; ++b) {
      const int lim = (max(a - 2, 0) * max(b - 2, 0) + 1) / 2;
      for (int i = 0; i <= lim; ++i) {
        can[a + b + 4 * i] = 1;
      }
    }
    for (int x = 0; x <= 2*N*(N-1); ++x) if (can[x]) {
      can[2*N*(N-1) - x] = 1;
    }
    if (N <= 12) {
      cerr << N << ": ";
      for (int x = 0; x <= 2*N*(N-1); ++x) cerr << can[x];
      cerr << endl;
    }
    if (N > LIM_SMALL) {
      for (int x = 2; x <= 2*N*(N-1) - 2; ++x) {
        // assert(can[x]);
      }
    }
  }
}


int small[LIM_SMALL + 1][2*LIM_SMALL*(LIM_SMALL-1) + 1][LIM_SMALL + 1][LIM_SMALL + 1];

void pre() {
  for (int N = 1; N <= LIM_SMALL; ++N) {
    bitset<2*LIM_SMALL*(LIM_SMALL-1) + 1>
        dp[LIM_SMALL * LIM_SMALL + 1][1 << LIM_SMALL] = {};
    for (int p = 0; p < 1 << N; ++p) {
      dp[N * N][p][0] = true;
    }
    for (int z = N * N; --z >= 0; ) {
      const int x = z / N, y = z % N;
      for (int p = 0; p < 1 << N; ++p) {
        for (int a = 0; a < 2; ++a) {
          const int pp = (p & ~(1 << y)) | a << y;
          int d = 0;
          if (x > 0 && (p >> y & 1) != a) ++d;
          if (y > 0 && (p >> (y-1) & 1) != a) ++d;
          dp[z][p] |= dp[z + 1][pp] << d;
        }
      }
    }
    for (int K = 0; K <= 2*N*(N-1); ++K) {
      if (dp[0][0][K]) {
        int p = 0, k = K;
        for (int z = 0; z < N * N; ++z) {
          const int x = z / N, y = z % N;
          for (int a = 0; a < 2; ++a) {
            const int pp = (p & ~(1 << y)) | a << y;
            int d = 0;
            if (x > 0 && (p >> y & 1) != a) ++d;
            if (y > 0 && (p >> (y-1) & 1) != a) ++d;
            if (k >= d && dp[z + 1][pp][k - d]) {
              small[N][K][x][y] = a;
              p = pp;
              k -= d;
              goto found;
            }
          }
          assert(false);
         found:{}
        }
      } else {
        for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) {
          small[N][K][x][y] = -1;
        }
      }
    }
  }
}

int f[1010][1010];

void judge(int N, int K) {
  for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) {
    assert(f[x][y] == 0 || f[x][y] == 1);
  }
  int cnt = 0;
  for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) {
    if (x + 1 < N && f[x][y] != f[x + 1][y]) ++cnt;
    if (y + 1 < N && f[x][y] != f[x][y + 1]) ++cnt;
  }
  if (K != cnt) {
    cerr << "judge failed N = " << N << ", K = " << K << ", cnt = " << cnt << endl;
    for (int x = 0; x < N; ++x) {
      for (int y = 0; y < N; ++y) cerr << f[x][y];
      cerr << endl;
    }
  }
  assert(K == cnt);
}

bool solveDiff(int N, int K) {
  if (K == 0) {
    for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) f[x][y] = 0;
    return true;
  }
  for (int a = 1; a < N; ++a) for (int b = 1; b < N; ++b) {
    if (a + b <= K && (K - (a + b)) % 4 == 0) {
      const int lim = (max(a - 2, 0) * max(b - 2, 0) + 1) / 2;
      const int tar = (K - (a + b)) / 4;
      if (tar <= lim) {
        for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) f[x][y] = 0;
        for (int x = 0; x < a; ++x) for (int y = 0; y < b; ++y) f[x][y] = 1;
        int cnt = 0;
        for (int x = 1; x < a - 1; ++x) for (int y = 1; y < b - 1; ++y) if (!((x + y) & 1)) {
          if (cnt++ < tar) {
            f[x][y] = 0;
          }
        }
        return true;
      }
    }
  }
  return false;
}

bool solve(int N, int K) {
  if (N <= LIM_SMALL) {
    if (~small[N][K][0][0]) {
      for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) f[x][y] = small[N][K][x][y];
      return true;
    } else {
      return false;
    }
  } else if (solveDiff(N, K)) {
    return true;
  } else if (solveDiff(N, 2*N*(N-1) - K)) {
    for (int x = 0; x < N; ++x) for (int y = 0; y < N; ++y) if ((x + y) & 1) f[x][y] ^= 1;
    return true;
  } else {
    return false;
  }
}

void stress() {
  for (int N = 1; N <= 50; ++N) {
    vector<int> can(2*N*(N-1) + 1, 0);
    for (int K = 0; K <= 2*N*(N-1); ++K) {
      const bool res = solve(N, K);
      if (res) {
        if (N <= 15) {
          cerr << N << " " << K << endl;
          for (int x = 0; x < N; ++x) {
            for (int y = 0; y < N; ++y) cerr << f[x][y];
            cerr << endl;
          }
        }
        can[K] = 1;
        judge(N, K);
      }
    }
    if (N <= 10) {
      cerr << N << ": ";
      for (int x = 0; x <= 2*N*(N-1); ++x) cerr << can[x];
      cerr << endl;
    }
    for (int x = 2; x <= 2*N*(N-1) - 2; ++x) {
      assert(can[x]);
    }
  }
}

int main() {
  pre();
  
  // experiment();
  // stress();
  
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    int N, K;
    scanf("%d%d", &N, &K);
    
    const bool res = solve(N, K);
    if (res) {
#ifdef LOCAL
judge(N,K);
#endif
      puts("Possible");
      for (int x = 0; x < N; ++x) {
        for (int y = 0; y < N; ++y) {
          putchar("BR"[f[x][y]]);
        }
        puts("");
      }
    } else {
      puts("Impossible");
    }
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 2ms
memory: 4812kb

input:

2
3 6
3 1

output:

Possible
BBB
BBR
BRB
Impossible

result:

ok correct! (2 test cases)

Test #2:

score: 0
Accepted
time: 10ms
memory: 4832kb

input:

4424
1 0
2 4
2 3
2 2
2 1
2 0
3 12
3 11
3 10
3 9
3 8
3 7
3 6
3 5
3 4
3 3
3 2
3 1
3 0
4 24
4 23
4 22
4 21
4 20
4 19
4 18
4 17
4 16
4 15
4 14
4 13
4 12
4 11
4 10
4 9
4 8
4 7
4 6
4 5
4 4
4 3
4 2
4 1
4 0
5 40
5 39
5 38
5 37
5 36
5 35
5 34
5 33
5 32
5 31
5 30
5 29
5 28
5 27
5 26
5 25
5 24
5 23
5 22
5 21
5...

output:

Possible
B
Possible
BR
RB
Impossible
Possible
BB
BR
Impossible
Possible
BB
BB
Possible
BRB
RBR
BRB
Impossible
Possible
BBR
BRB
RBR
Possible
BBB
RBR
BRB
Possible
BBB
BRB
RBR
Possible
BBB
BRR
RBB
Possible
BBB
BBR
BRB
Possible
BBB
BBR
RBB
Possible
BBB
BBB
RBR
Possible
BBB
BBB
BRB
Possible
BBB
BBB
BBR
I...

result:

ok correct! (4424 test cases)

Test #3:

score: 0
Accepted
time: 2ms
memory: 8972kb

input:

1
1000 0

output:

Possible
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB...

result:

ok correct! (1 test case)

Test #4:

score: 0
Accepted
time: 4ms
memory: 6868kb

input:

1
1000 1

output:

Impossible

result:

ok correct! (1 test case)

Test #5:

score: 0
Accepted
time: 1ms
memory: 8804kb

input:

1
1000 1998000

output:

Possible
BRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRB...

result:

ok correct! (1 test case)

Test #6:

score: 0
Accepted
time: 4ms
memory: 6868kb

input:

1
1000 1997999

output:

Impossible

result:

ok correct! (1 test case)

Test #7:

score: 0
Accepted
time: 1ms
memory: 8772kb

input:

1
1000 1638091

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR...

result:

ok correct! (1 test case)

Test #8:

score: 0
Accepted
time: 2ms
memory: 8656kb

input:

1
1000 726743

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR...

result:

ok correct! (1 test case)

Test #9:

score: 0
Accepted
time: 9ms
memory: 8780kb

input:

1
1000 1159802

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR...

result:

ok correct! (1 test case)

Test #10:

score: 0
Accepted
time: 9ms
memory: 8776kb

input:

1
1000 1824691

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR...

result:

ok correct! (1 test case)

Test #11:

score: 0
Accepted
time: 3ms
memory: 8784kb

input:

1
1000 1606348

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR...

result:

ok correct! (1 test case)

Test #12:

score: 0
Accepted
time: 4ms
memory: 5152kb

input:

100
100 3588
100 16278
100 14222
100 3818
100 16278
100 2672
100 7447
100 5705
100 9385
100 19205
100 16362
100 14175
100 327
100 18201
100 3519
100 14923
100 5358
100 17389
100 8773
100 7611
100 2185
100 3314
100 2358
100 18271
100 9499
100 12584
100 8079
100 16954
100 12620
100 16333
100 7148
100 ...

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRBBBBB
RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBBBBB
RRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRB...

result:

ok correct! (100 test cases)

Test #13:

score: 0
Accepted
time: 3ms
memory: 7504kb

input:

10
280 56983
468 47999
111 964
346 192134
60 3108
348 98521
421 57292
24 310
29 1080
484 17366

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRBB
RBRBRBRBRB...

result:

ok correct! (10 test cases)

Test #14:

score: 0
Accepted
time: 0ms
memory: 9008kb

input:

13
44 3612
468 9437
171 34192
174 33316
121 15295
249 1231
84 9464
170 56598
358 183525
369 42656
29 595
226 74474
296 34671

output:

Possible
RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBBRBRBRBR
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBRRBRBRBRB
RBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBRBBRBRBRBR
BRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRRBRBRBRB
BRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBR
RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRB
BRBRBRBRBRBRBRBRBRBRB...

result:

ok correct! (13 test cases)

Test #15:

score: 0
Accepted
time: 9ms
memory: 5024kb

input:

792
43 1432
33 1687
39 1872
49 906
41 27
49 1140
41 2730
39 1350
33 1625
26 986
26 1079
29 377
50 2930
24 536
28 874
44 1659
36 46
26 1199
46 1289
50 1662
48 59
20 90
37 2025
40 1971
31 443
31 511
36 1940
29 1515
21 104
24 432
23 337
38 2222
36 1016
24 786
23 737
50 1728
45 2032
22 183
50 416
44 375...

output:

Possible
RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRBBBB
RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBBBB
RRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRRBBBB
RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBBBB
RRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRRBBBB
RBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBBBB
RRBRBRBRBRBRBRBRBRBRBRBRBRB...

result:

ok correct! (792 test cases)