Merge pull request yosupo06#1248 from maspypy/solve_linear

問題追加 system of linear equations (mod 2)

linear_algebra/system_of_linear_equations_mod_2/checker.cpp

@@ -0,0 +1,89 @@
+#include <algorithm>
+#include <vector>
+#include <string>
+#include <bitset>
+#include "testlib.h"
+
+using namespace std;
+using BS = bitset<4096>;
+
+int N, M;
+BS A[4096];
+BS b;
+
+BS evaluate(BS x) {
+  BS y;
+  for (int i = 0; i < N; ++i) {
+    int cnt = (x & A[i]).count();
+    y[i] = cnt % 2;
+  }
+  return y;
+}
+
+int matrix_rank(vector<BS> a) {
+  int N = a.size();
+  int rk = 0;
+  for (int j = 0; j < M; ++j) {
+    if (rk == N) break;
+    if (!a[rk][j]) {
+      for (int i = rk + 1; i < N; ++i) {
+        if (a[i][j]) {
+          swap(a[rk], a[i]);
+          break;
+        }
+      }
+    }
+    if (!a[rk][j]) continue;
+    for (int i = rk + 1; i < N; ++i) {
+      if (a[i][j]) { a[i] ^= a[rk]; }
+    }
+    ++rk;
+  }
+  return rk;
+}
+
+int get_rank(InStream& stream) {
+  int r = stream.readInt(-1, M);
+  if (r == -1) return -1;
+  vector<BS> mat;
+
+  for (int k = 0; k < r + 1; ++k) {
+    string S = stream.readToken();
+    stream.ensure(int(S.size()) == M);
+    for (auto& ch: S) stream.ensure(ch == '0' || ch == '1');
+    BS x;
+    for (int j = 0; j < M; ++j) x[j] = (S[j] - '0');
+    BS y = evaluate(x);
+    if (k == 0) {
+      for (int i = 0; i < N; ++i) { stream.ensure(y[i] == b[i]); }
+    } else {
+      for (int i = 0; i < N; ++i) { stream.ensure(y[i] == false); }
+      mat.emplace_back(x);
+    }
+  }
+  stream.ensure(matrix_rank(mat) == r);
+  return r;
+}
+
+int main(int argc, char* argv[]) {
+  registerTestlibCmd(argc, argv);
+  // read input
+  N = inf.readInt();
+  M = inf.readInt();
+  for (int i = 0; i < N; ++i) {
+    string S = inf.readToken();
+    for (int j = 0; j < M; ++j) A[i][j] = (S[j] - '0');
+  }
+  string S = inf.readToken();
+  for (int i = 0; i < N; ++i) b[i] = (S[i] - '0');
+
+  int k_ans = get_rank(ans);
+  int k_ouf = get_rank(ouf);
+
+  if (k_ans == -1 && k_ouf == -1) { quitf(_ok, "OK No solution"); }
+  if (k_ans != -1 && k_ouf == -1) { quitf(_wa, "WA you cannot find solution"); }
+  if (k_ans == -1 && k_ouf != -1) { quitf(_fail, "Judge cannot find solution"); }
+  if (k_ans > k_ouf) { quitf(_wa, "There are more solutions"); }
+  if (k_ans < k_ouf) { quitf(_fail, "What happened?"); }
+  quitf(_ok, "OK");
+}

linear_algebra/system_of_linear_equations_mod_2/gen/base.hpp

@@ -0,0 +1,73 @@
+#include <bitset>
+#include <vector>
+#include "random.h"
+
+using namespace std;
+using BS = bitset<4096>;
+
+void out(int n, int m, vector<BS> A, BS b) {
+  auto out_BS = [&](int n, BS x) -> void {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = (x[i] ? '1' : '0');
+    printf("%s\n", S.c_str());
+  };
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; ++i) out_BS(m, A[i]);
+  out_BS(n, b);
+}
+
+void gen_yes(int n, int m, int r, Random &gen) {
+  assert(r <= m && r <= n);
+  vector<BS> a(n);
+  for (int i = 0; i < r; ++i) {
+    for (int j = 0; j < m; ++j) { a[i][j] = gen.uniform_bool(); }
+  }
+  for (int i = r; i < n; ++i) {
+    for (int k = 0; k < r; ++k) {
+      if (gen.uniform_bool()) a[i] ^= a[k];
+    }
+  }
+  // shuffle
+  gen.shuffle(a.begin(), a.end());
+
+  BS x;
+  for (int i = 0; i < m; ++i) x[i] = gen.uniform_bool();
+  BS y;
+  for (int i = 0; i < n; ++i) { y[i] = (a[i] & x).count() % 2; }
+  out(n, m, a, y);
+}
+
+void gen_no(int n, int m, int r, Random &gen) {
+  assert(r <= m && r < n);
+  vector<BS> a(n);
+  for (int i = 0; i < r; ++i) {
+    for (int j = 0; j < m; ++j) { a[i][j] = gen.uniform_bool(); }
+  }
+
+  BS y;
+  for (int i = 0; i < n; ++i) { y[i] = gen.uniform_bool(); }
+  // at least one 1
+  y[gen.uniform<int>(r, n - 1)] = 1;
+
+  for (int i = r; i < n; ++i) {
+    for (int k = 0; k < r; ++k) {
+      if (gen.uniform_bool()) {
+        a[i] ^= a[k];
+        y[i] = y[i] ^ y[k];
+      }
+    }
+  }
+
+  // shuffle
+  vector<int> new_idx(n);
+  for (int i = 0; i < n; ++i) new_idx[i] = i;
+  gen.shuffle(new_idx.begin(), new_idx.end());
+  vector<BS> new_a(n);
+  BS new_y;
+  for (int i = 0; i < n; ++i) {
+    new_a[new_idx[i]] = a[i];
+    new_y[new_idx[i]] = y[i];
+  }
+
+  out(n, m, new_a, new_y);
+}

linear_algebra/system_of_linear_equations_mod_2/gen/example_00.in

@@ -0,0 +1,5 @@
+3 3
+101
+011
+110
+011

linear_algebra/system_of_linear_equations_mod_2/gen/example_01.in

@@ -0,0 +1,5 @@
+3 3
+101
+011
+110
+111

linear_algebra/system_of_linear_equations_mod_2/gen/example_02.in

@@ -0,0 +1,3 @@
+1 3
+111
+1

linear_algebra/system_of_linear_equations_mod_2/gen/max_lowrank.cpp

@@ -0,0 +1,20 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+#include "base.hpp"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int rs[] = {1, 10, 100, 1000, 4000};
+
+  int n = N_MAX;
+  int m = M_MAX;
+  int r = rs[seed % 5];
+  if (seed % 2 == 0) gen_yes(n, m, r, gen);
+  if (seed % 2 == 1) gen_no(n, m, r, gen);
+  return 0;
+}

linear_algebra/system_of_linear_equations_mod_2/gen/max_random.cpp

@@ -0,0 +1,27 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MAX;
+  int m = M_MAX;
+  auto random_01_str = [&](int n) -> string {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = '0' + gen.uniform(0, 1);
+    return S;
+  };
+
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; i++) {
+    string S = random_01_str(m);
+    printf("%s\n", S.c_str());
+  }
+  string S = random_01_str(n);
+  printf("%s\n", S.c_str());
+  return 0;
+}

linear_algebra/system_of_linear_equations_mod_2/gen/max_small.cpp

@@ -0,0 +1,18 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+#include "base.hpp"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = N_MAX;
+  int m = gen.uniform<int>(2, 10);
+  int r = gen.uniform<int>(1, min(n, m) - 1);
+  if (seed % 2 == 0) gen_yes(n, m, r, gen);
+  if (seed % 2 == 1) gen_no(n, m, r, gen);
+  return 0;
+}

linear_algebra/system_of_linear_equations_mod_2/gen/random.cpp

@@ -0,0 +1,27 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(1, N_MAX);
+  int m = gen.uniform<int>(1, M_MAX);
+  auto random_01_str = [&](int n) -> string {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = '0' + gen.uniform(0, 1);
+    return S;
+  };
+
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; i++) {
+    string S = random_01_str(m);
+    printf("%s\n", S.c_str());
+  }
+  string S = random_01_str(n);
+  printf("%s\n", S.c_str());
+  return 0;
+}

linear_algebra/system_of_linear_equations_mod_2/gen/small_max.cpp

@@ -0,0 +1,18 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+#include "base.hpp"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(2, 10);
+  int m = M_MAX;
+  int r = gen.uniform<int>(1, min(n, m) - 1);
+  if (seed % 2 == 0) gen_yes(n, m, r, gen);
+  if (seed % 2 == 1) gen_no(n, m, r, gen);
+  return 0;
+}

linear_algebra/system_of_linear_equations_mod_2/gen/small_random.cpp

@@ -0,0 +1,27 @@
+#include <iostream>
+#include "random.h"
+#include "../params.h"
+
+using namespace std;
+
+int main(int, char* argv[]) {
+  long long seed = atoll(argv[1]);
+  auto gen = Random(seed);
+
+  int n = gen.uniform<int>(1, 3);
+  int m = gen.uniform<int>(1, 3);
+  auto random_01_str = [&](int n) -> string {
+    string S(n, '?');
+    for (int i = 0; i < n; ++i) S[i] = '0' + gen.uniform(0, 1);
+    return S;
+  };
+
+  printf("%d %d\n", n, m);
+  for (int i = 0; i < n; i++) {
+    string S = random_01_str(m);
+    printf("%s\n", S.c_str());
+  }
+  string S = random_01_str(n);
+  printf("%s\n", S.c_str());
+  return 0;
+}

linear_algebra/system_of_linear_equations_mod_2/gen/smallest_00.in

@@ -0,0 +1,3 @@
+1 1
+0
+0

linear_algebra/system_of_linear_equations_mod_2/gen/smallest_01.in

@@ -0,0 +1,3 @@
+1 1
+0
+1

linear_algebra/system_of_linear_equations_mod_2/gen/smallest_02.in

@@ -0,0 +1,3 @@
+1 1
+1
+0

linear_algebra/system_of_linear_equations_mod_2/gen/smallest_03.in

@@ -0,0 +1,3 @@
+1 1
+1
+1