Merge pull request #334 from hitonanode/f2-intersection

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

@@ -0,0 +1,21 @@
+---
+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/hafnian.md

@@ -13,4 +13,3 @@ documentation_of: ./hafnian.hpp
 
 - [1] A. Björklund, "Counting Perfect Matchings as Fast as Ryser,
   Proc. of 23rd ACM-SIAM symposium on Discrete Algorithms, pp.914–921, 2012.
-

linear_algebra_matrix/linalg_bitset.md

@@ -1,5 +1,5 @@
 ---
-title: Linear algebra on $\mathbb{F}_{2}$ using std::bitset ($\mathbb{F}_{2}$ 線形代数)
+title: Linear algebra on $\mathbb{F}_{2}$ using std::bitset (std::bitset を使用した $\mathbb{F}_{2}$ 線形代数)
 documentation_of: ./linalg_bitset.hpp
 ---
 

linear_algebra_matrix/test/f2_intersection.test.cpp

@@ -0,0 +1,31 @@
+#define PROBLEM "https://judge.yosupo.jp/problem/intersection_of_f2_vector_spaces"
+#include "../f2_linear_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';
+    }
+}