Merge pull request #376 from hitonanode/add-method-hilbert-order-mos

add simple mo method to hilbert order mos

Author: hitonanode

other_algorithms/hilbert_order_mos.hpp

@@ -57,6 +57,7 @@ std::vector<int> sort_by_hilbert_order(const std::vector<std::pair<Int, Int>> &p
 // Mo's algorithm with Hilbert order
 // - add(x, y) : Add (x, y) as query.
 // - run(IncX, DecX, IncY, DecY, Query) : run Mo's algorithm.
+// - run(Add, Remove, Query) : run Mo's algorithm with Add, Remove, and Query functions. add(x, y) means [x, y).
 struct MosAlgorithmHilbertOrder {
     int cx, cy;
     std::vector<std::pair<int, int>> queries;
@@ -79,4 +80,9 @@ struct MosAlgorithmHilbertOrder {
             query(q);
         }
     }
+
+    template <typename F1, typename F3, typename F5> void run(F1 Add, F3 Remove, F5 Query) {
+        run([&](int x, int) { Remove(x); }, [&](int, int x) { Add(x); },
+            [&](int y, int) { Add(y); }, [&](int, int y) { Remove(y); }, Query);
+    }
 };

other_algorithms/hilbert_order_mos.md

@@ -7,6 +7,8 @@ Mo's algorithm の一種で，2 次元平面上の点として表現可能なク
 
 ## 使用方法
 
+### 一般の 2 次元平面上の点クエリの場合
+
 ```cpp
 vector<Result> ret(Q); // 答えを格納する領域
 int x_init = 0, y_init = 0;
@@ -26,9 +28,25 @@ mo.run(inc_x, dec_x, inc_y, dec_y, solve);
 for (auto ans : ret) cout << ans << '\n';
 ```
 
+### 特に半開区間 $[l, r)$ クエリで区間の左右の伸張・収縮が同一の関数で書ける場合
+
+```cpp
+MosAlgorithmHilbertOrder mos(0, 0);
+for (auto [l, r] : queries) {
+    mos.add(l, r);
+}
+
+mos.run(
+    [&](int i) { /* Add i */ },
+    [&](int i) { /* Remove i */ },
+    [&](int q) { /* ret.at(q) = get_solution(); */ }
+);
+```
+
 ## 問題例
 
 - [AtCoder Beginner Contest 384 G - Abs Sum](https://atcoder.jp/contests/abc384/tasks/abc384_g)
+- [AtCoder Beginner Contest 405 G - Range Shuffle Query](https://atcoder.jp/contests/abc405/tasks/abc405_g)
 
 ## Links