Fix F2 bitset linalg

Author: hitonanode

linear_algebra_matrix/linalg_bitset.hpp

@@ -9,7 +9,7 @@
 // Complexity: O(nm + nm rank(M) / 64)
 // Verified: abc276_h (2000 x 8000)
 template <int Wmax>
-std::vector<std::bitset<Wmax>> gauss_jordan(int W, std::vector<std::bitset<Wmax>> M) {
+std::vector<std::bitset<Wmax>> f2_gauss_jordan(int W, std::vector<std::bitset<Wmax>> M) {
     assert(W <= Wmax);
     int H = M.size(), c = 0;
     for (int h = 0; h < H and c < W; ++h, ++c) {
@@ -33,7 +33,7 @@ std::vector<std::bitset<Wmax>> gauss_jordan(int W, std::vector<std::bitset<Wmax>
 }
 
 // Rank of Gauss-Jordan eliminated matrix
-template <int Wmax> int rank_gauss_jordan(int W, const std::vector<std::bitset<Wmax>> &M) {
+template <int Wmax> int f2_rank_gauss_jordan(int W, const std::vector<std::bitset<Wmax>> &M) {
     assert(W <= Wmax);
     for (int h = (int)M.size() - 1; h >= 0; h--) {
         int j = 0;
@@ -72,25 +72,25 @@ template <int Wmax> int f2_determinant(const std::vector<std::bitset<Wmax>> &M)
 
 template <int W1, int W2>
 std::vector<std::bitset<W2>>
-matmul(const std::vector<std::bitset<W1>> &A, const std::vector<std::bitset<W2>> &B) {
+f2_matmul(const std::vector<std::bitset<W1>> &A, const std::vector<std::bitset<W2>> &B) {
     int H = A.size(), K = B.size();
     std::vector<std::bitset<W2>> C(H);
     for (int i = 0; i < H; i++) {
         for (int j = 0; j < K; j++) {
-            if (A[i][j]) C[i] ^= B[j];
+            if (A.at(i).test(j)) C.at(i) ^= B.at(j);
         }
     }
     return C;
 }
 
 template <int Wmax>
-std::vector<std::bitset<Wmax>> matpower(std::vector<std::bitset<Wmax>> X, long long n) {
+std::vector<std::bitset<Wmax>> f2_matpower(std::vector<std::bitset<Wmax>> X, long long n) {
     int D = X.size();
     std::vector<std::bitset<Wmax>> ret(D);
     for (int i = 0; i < D; i++) ret[i][i] = 1;
     while (n) {
-        if (n & 1) ret = matmul<Wmax, Wmax>(ret, X);
-        X = matmul<Wmax, Wmax>(X, X), n >>= 1;
+        if (n & 1) ret = f2_matmul<Wmax, Wmax>(ret, X);
+        X = f2_matmul<Wmax, Wmax>(X, X), n >>= 1;
     }
     return ret;
 }
@@ -101,7 +101,7 @@ std::vector<std::bitset<Wmax>> matpower(std::vector<std::bitset<Wmax>> X, long l
 // Complexity: O(HW + HW rank(A) / 64 + W^2 len(freedoms))
 template <int Wmax, class Vec>
 std::tuple<bool, std::bitset<Wmax>, std::vector<std::bitset<Wmax>>>
-system_of_linear_equations(std::vector<std::bitset<Wmax>> A, Vec b, int W) {
+f2_system_of_linear_equations(std::vector<std::bitset<Wmax>> A, Vec b, int W) {
     int H = A.size();
     assert(W <= Wmax);
     assert(A.size() == b.size());
@@ -111,7 +111,7 @@ system_of_linear_equations(std::vector<std::bitset<Wmax>> A, Vec b, int W) {
         for (int j = 0; j < W; ++j) M[i][j] = A[i][j];
         M[i][W] = b[i];
     }
-    M = gauss_jordan<Wmax + 1>(W + 1, M);
+    M = f2_gauss_jordan<Wmax + 1>(W + 1, M);
     std::vector<int> ss(W, -1);
     std::vector<int> ss_nonneg_js;
     for (int i = 0; i < H; i++) {

linear_algebra_matrix/linalg_bitset.md

@@ -15,7 +15,7 @@ vector<bitset<Wmax>> A;
 vector<bool> b;
 
 // Solve Ax = b (x: F_2^W)
-auto [feasible, x0, freedoms] = system_of_linear_equations<Wmax, vector<bool>>(A, b, W);
+auto [feasible, x0, freedoms] = f2_system_of_linear_equations<Wmax, vector<bool>>(A, b, W);
 
 // Calc determinant (or check whether A is regular)
 int det = f2_determinant<dim>(mat);

linear_algebra_matrix/test/linalg_bitset.test.cpp

@@ -26,9 +26,9 @@ int main() {
     }
 
     cin >> T;
-    A = matpower<Wmax>(A, T);
+    A = f2_matpower<Wmax>(A, T);
     for (int i = 0; i < N; i++) A[i][N] = v[i];
-    A = gauss_jordan<Wmax>(N + 1, A);
+    A = f2_gauss_jordan<Wmax>(N + 1, A);
 
     for (int i = 0; i < N; i++) {
         if (A[i].count() == 1 and A[i][N]) {

linear_algebra_matrix/test/linalg_bitset.yuki1421.test.cpp

@@ -59,7 +59,7 @@ int main() {
             }
             A.emplace_back(a);
         }
-        auto [ok, solution, freedoms] = system_of_linear_equations<Wmax, vector<bool>>(A, b, N);
+        auto [ok, solution, freedoms] = f2_system_of_linear_equations<Wmax, vector<bool>>(A, b, N);
         if (!ok) bad();
         for (int i = 0; i < N; ++i) ret[i] += int(solution[i]) << d;
     }

linear_algebra_matrix/test/linalg_bitset_mul.test.cpp

@@ -0,0 +1,43 @@
+#define PROBLEM "https://judge.yosupo.jp/problem/matrix_product_mod_2"
+#include "../linalg_bitset.hpp"
+
+#include <algorithm>
+#include <bitset>
+#include <iostream>
+#include <string>
+#include <vector>
+using namespace std;
+
+int main() {
+    cin.tie(nullptr);
+    ios::sync_with_stdio(false);
+
+    constexpr int dim = 1 << 12;
+
+    using BS = bitset<dim>;
+
+    int N, M, K;
+    cin >> N >> M >> K;
+
+    vector<BS> A(N), B(M);
+    for (auto &v : A) {
+        string s;
+        cin >> s;
+        std::reverse(s.begin(), s.end()); // bitset に文字列 s を与えると s[0] が最高位になるので反転
+        v = BS(s);
+    }
+
+    for (auto &v : B) {
+        string s;
+        cin >> s;
+        std::reverse(s.begin(), s.end());
+        v = BS(s);
+    }
+
+    auto C = f2_matmul<dim, dim>(A, B);
+    for (const auto &v : C) {
+        auto tmp = v.to_string();
+        std::reverse(tmp.begin(), tmp.end());
+        cout << tmp.substr(0, K) << '\n';
+    }
+}