changes

Author: lrvideckis

library/math/matrix_related/walk.hpp

@@ -0,0 +1,6 @@
+bitset<B> walk(bitset<B>& k) {
+  bitset<B> res;
+  for (int i = B, j = npivot; i--;)
+    if (basis[i][i] && res[i] ^ k[--j]) res ^= basis[i];
+  return res;
+}

library/math/matrix_related/xor_basis_ordered.hpp

@@ -5,34 +5,24 @@
 //!   basis_ordered<int> b1;
 //!   basis_ordered<ll> b2;
 //!   basis_ordered<bitset<lg>> b3;
-//!   b2.insert(x); // 0 <= x < (1LL<<lg)
+//!   b2.insert(x); // 0 <= x < (1LL<<B)
 //! @endcode
-//! @time O(lg)
-//! @space O(lg)
-const int lg = 60;
-template<class T> struct basis_ordered {
-  int siz = 0;
-  T b[lg]{};
-  int shrink(T& v) {
-    for (int i = lg - 1; i >= 0; i--)
-      if (((v >> i) & T(1)) != T(0)) {
-        if (b[i] == T(0)) return i;
-        v ^= b[i];
+//! @time O(q * B^2/32)
+//! @space O(B^2/32)
+template<int B> struct xor_basis {
+  bitset<B> basis[B];
+  int npivot = 0, nfree = 0;
+  int shrink(bitset<B>& v) {
+    for (int i = B; i--;)
+      if (v[i]) {
+        if (basis[i][i]) return i;
+        v ^= basis[i];
       }
     return -1;
   }
-  bool insert(T v) {
+  bool insert(bitset<B>& v) {
     int i = shrink(v);
-    return i >= 0 ? b[i] = v, ++siz : 0;
-  }
-  T walk(T k) {
-    T res{};
-    for (int i = lg - 1, j = siz - 1; i >= 0; i--)
-      if (b[i] != T(0)) {
-        if ((((res >> i) ^ (k >> j)) & T(1)) != T(0))
-          res ^= b[i];
-        j--;
-      }
-    return res;
+    return i >= 0 ? basis[i] = v, ++npivot : !++nfree;
   }
+#include "walk.hpp"
 };

tests/library_checker_aizu_tests/handmade_tests/xor_basis_walk.test.cpp

@@ -0,0 +1,41 @@
+#define PROBLEM \
+  "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ITP1_1_A"
+#include "../template.hpp"
+#include "../../../library/contest/random.hpp"
+#include "../../../library/math/matrix_related/xor_basis_ordered.hpp"
+const int B = 18;
+vector<bitset<B>> get_all(const vector<bitset<B>>& basis) {
+  int n = ssize(basis);
+  vector<bitset<B>> span;
+  for (int mask = 0; mask < (1 << n); mask++) {
+    bitset<B> curr_xor;
+    assert(curr_xor.none());
+    for (int bit = 0; bit < n; bit++)
+      if ((mask >> bit) & 1) curr_xor ^= basis[bit];
+    span.push_back(curr_xor);
+  }
+  ranges::sort(span, {}, [&](const bitset<B>& x) -> long {
+    return x.to_ulong();
+  });
+  return span;
+}
+int main() {
+  cin.tie(0)->sync_with_stdio(0);
+  for (int num_tests = 0; num_tests < 10000; num_tests++) {
+    xor_basis<B> b;
+    int n = rnd(1, 18);
+    vector<bitset<B>> naive_basis;
+    for (int i = 0; i < n; i++) {
+      bitset<B> val = rnd(0, (1 << n) - 1);
+      if (b.insert(val)) naive_basis.push_back(val);
+    }
+    vector<bitset<B>> fast_basis;
+    for (int i = 0; i < B; i++)
+      if (b.basis[i].any())
+        fast_basis.push_back(b.basis[i]);
+    vector<bitset<B>> naive_span = get_all(naive_basis);
+    vector<bitset<B>> fast_span = get_all(fast_basis);
+    assert(naive_span == fast_span);
+  }
+  cout << "Hello World\n";
+}