Add F2 intersection

Author: hitonanode

linear_algebra_matrix/f2_linear_space.hpp

@@ -0,0 +1,37 @@
+#pragma once
+#include <algorithm>
+#include <utility>
+#include <vector>
+
+template <class Int> struct f2_vector_space {
+    std::vector<Int> basis;
+
+    f2_vector_space() = default;
+
+    Int add(Int x) {
+        for (const Int &b : basis) x = std::min(x, x ^ b);
+
+        if (x) {
+            basis.push_back(x);
+            return x;
+        } else {
+            return Int(0);
+        }
+    }
+};
+
+std::vector<int> f2_intersection(const std::vector<int> &A, const std::vector<int> &B) {
+    f2_vector_space<long long> tmp;
+    for (int a : A) tmp.add(((long long)a << 32) + a);
+
+    std::vector<int> ret;
+
+    for (int b : B) {
+        long long v = (long long)b << 32;
+
+        auto u = tmp.add(v);
+        if (u < (1LL << 32)) ret.push_back(u);
+    }
+
+    return ret;
+}

linear_algebra_matrix/f2_linear_space.md

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+---
+title: $\mathbb{F}_{2}$ linear space ($\mathbb{F}_{2}$ 線形空間)
+documentation_of: ./f2_linear_space.hpp
+---
+
+$\mathbb{F}_{2}$ 線形空間に関する各種演算．
+
+## 使用方法
+
+`A` の元で張られる線形空間と `B` の元で張られる線形空間の共通部分の基底を一つ求める関数方法．
+
+```cpp
+int n, m;
+vector<int> A(n), B(m);
+
+vector<int> C = f2_intersection(A, B);
+```
+
+## 問題例
+
+- [Library Checker: Intersection of F_2 vector spaces](https://judge.yosupo.jp/problem/intersection_of_f2_vector_spaces)

linear_algebra_matrix/test/f2_intersection.test.cpp

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+#define PROBLEM "https://judge.yosupo.jp/problem/intersection_of_f2_vector_spaces"
+#include "../f2_vector_space.hpp"
+
+#include <iostream>
+using namespace std;
+
+int main() {
+    cin.tie(nullptr);
+    ios::sync_with_stdio(false);
+
+    int T;
+    cin >> T;
+
+    while (T--) {
+        int n;
+        cin >> n;
+        vector<int> A(n);
+        for (int &x : A) cin >> x;
+
+        int m;
+        cin >> m;
+        vector<int> B(m);
+        for (int &x : B) cin >> x;
+
+        auto C = f2_intersection(A, B);
+
+        cout << C.size();
+        for (int x : C) cout << ' ' << x;
+        cout << '\n';
+    }
+}