mapped monozkw;

old-yan · Feb 9, 2025 · f58da5b · f58da5b
1 parent edf99bf
commit f58da5b
Show file tree

Hide file tree

Showing 13 changed files with 326 additions and 10 deletions.
diff --git a/DS/LichaoSegTree.md b/DS/LichaoSegTree.md
@@ -6,8 +6,9 @@
 
 1. [P4097 【模板】李超线段树 / [HEOI2013] Segment](https://www.luogu.com.cn/problem/P4097)
 2. [P4655 [CEOI2017] Building Bridges](https://www.luogu.com.cn/problem/P4655)
-3. [Line Add Get Min](https://judge.yosupo.jp/problem/line_add_get_min)(https://github.com/yosupo06/library-checker-problems/issues/174)
-4. [Segment Add Get Min](https://judge.yosupo.jp/problem/segment_add_get_min)(https://github.com/yosupo06/library-checker-problems/issues/211)
+3. [智乃的直线](https://ac.nowcoder.com/acm/problem/226924)
+4. [Line Add Get Min](https://judge.yosupo.jp/problem/line_add_get_min)(https://github.com/yosupo06/library-checker-problems/issues/174)
+5. [Segment Add Get Min](https://judge.yosupo.jp/problem/segment_add_get_min)(https://github.com/yosupo06/library-checker-problems/issues/211)
 
 ### 二、模板功能
 

diff --git a/DS/LichaoSegTree_ex.h b/DS/LichaoSegTree_ex.h
@@ -29,10 +29,6 @@ namespace OY {
             bool is_ascending() const { return m_k > 0; }
             bool is_horizontal() const { return m_k == 0; }
         };
-        struct BaseLess {
-            template <typename Tp>
-            bool operator()(const Tp &x, const Tp &y) const { return x < y; }
-        };
         template <typename Tp, Tp BackGroundValue>
         struct BaseJudger {
             template <typename Line>

diff --git a/DS/LichaoSegTree_ex.md b/DS/LichaoSegTree_ex.md
@@ -5,6 +5,7 @@
 	练习题目：
 
 1. [P4069 [SDOI2016] 游戏](https://www.luogu.com.cn/problem/P4069)
+2. [智乃的直线](https://ac.nowcoder.com/acm/problem/226924)
 
 ### 二、模板功能
 

diff --git a/DS/LichaoZkwTree.md b/DS/LichaoZkwTree.md
@@ -7,6 +7,7 @@
 1. [P4097 【模板】李超线段树 / [HEOI2013] Segment](https://www.luogu.com.cn/problem/P4097)
 2. [P4254 [JSOI2008] Blue Mary 开公司](https://www.luogu.com.cn/problem/P4254)
 3. [P4655 [CEOI2017] Building Bridges](https://www.luogu.com.cn/problem/P4655)
+4. [智乃的直线](https://ac.nowcoder.com/acm/problem/226924)
 
 ### 二、模板功能
 

diff --git a/DS/LichaoZkwTree_ex.h b/DS/LichaoZkwTree_ex.h
@@ -32,10 +32,6 @@ namespace OY {
             bool is_ascending() const { return m_k > 0; }
             bool is_horizontal() const { return m_k == 0; }
         };
-        struct BaseLess {
-            template <typename Tp>
-            bool operator()(const Tp &x, const Tp &y) const { return x < y; }
-        };
         template <typename Tp, Tp BackGroundValue>
         struct BaseJudger {
             template <typename Line>

diff --git a/DS/LichaoZkwTree_ex.md b/DS/LichaoZkwTree_ex.md
@@ -5,6 +5,7 @@
 	练习题目：
 
 1. [P4069 [SDOI2016] 游戏](https://www.luogu.com.cn/problem/P4069)
+2. [智乃的直线](https://ac.nowcoder.com/acm/problem/226924)
 
 ### 二、模板功能
 

diff --git a/DS/MappedMonoZkwTree.h b/DS/MappedMonoZkwTree.h
@@ -0,0 +1,59 @@
+/*
+最后修改:
+20250209
+测试环境:
+gcc11.2,c++11
+clang22.0,C++11
+msvc14.2,C++14
+*/
+#ifndef __OY_MAPPEDMONOZKWTREE__
+#define __OY_MAPPEDMONOZKWTREE__
+
+#include <queue>
+
+#include "MonoZkwTree.h"
+
+namespace OY {
+    namespace MMZKW {
+        using size_type = MONOZKW::size_type;
+        template <typename Tp, typename Compare, Tp Identity>
+        struct PqMapping {
+            using container_type = std::priority_queue<Tp, std::vector<Tp>, Compare>;
+            static Tp get(const container_type &bucket) {
+                if (bucket.empty()) return Identity;
+                return bucket.top();
+            }
+        };
+        template <typename Monoid, typename Mapping>
+        class Tree {
+            using inner_type = MONOZKW::Tree<Monoid>;
+            using container_type = typename Mapping::container_type;
+            inner_type m_zkw;
+            std::vector<container_type> m_buckets;
+        public:
+            Tree() = default;
+            Tree(size_type n) { resize(n); }
+            void resize(size_type n) {
+                m_buckets.clear(), m_buckets.reserve(n);
+                for(size_type i=0;i!=n;i++)m_buckets.emplace_back();
+                m_zkw.resize(n, [&](size_type i) { return Mapping::get(m_buckets[i]); });
+            }
+            container_type &operator[](size_type i) { return m_buckets[i]; }
+            const container_type &operator[](size_type i) const { return m_buckets[i]; }
+            void update(size_type i) { m_zkw.modify(i, Mapping::get(m_buckets[i])); }
+            auto query(size_type i) const -> decltype(m_zkw.query(i)) { return m_zkw.query(i); }
+            auto query(size_type left, size_type right) const -> decltype(m_zkw.query(left, right)) { return m_zkw.query(left, right); }
+            auto query_all() const -> decltype(m_zkw.query_all()) { return m_zkw.query_all(); }
+            template <typename Judger>
+            size_type max_right(size_type left, Judger &&judge) const { return m_zkw.max_right(left, judge); }
+            template <typename Judger>
+            size_type min_left(size_type right, Judger &&judge) const { return m_zkw.min_left(right, judge); }
+        };
+    }
+    template <typename Monoid, typename Tp, Tp Minimum = std::numeric_limits<Tp>::min()>
+    using MaxPqMonoZkwTree = MMZKW::Tree<Monoid, MMZKW::PqMapping<Tp, std::less<Tp>, Minimum>>;
+    template <typename Monoid, typename Tp, Tp Maximum = std::numeric_limits<Tp>::max()>
+    using MinPqMonoZkwTree = MMZKW::Tree<Monoid, MMZKW::PqMapping<Tp, std::greater<Tp>, Maximum>>;
+}
+
+#endif
diff --git a/DS/MappedMonoZkwTree.md b/DS/MappedMonoZkwTree.md
@@ -0,0 +1,55 @@
+### 一、模板类别
+
+	数据结构： `MappedMonoZkw` 线段树。
+
+	练习题目：
+
+1. [弩蚊怒夏](https://ac.nowcoder.com/acm/problem/226861)
+2. [小红的数组操作](https://ac.nowcoder.com/acm/problem/277952)
+
+### 二、模板功能
+
+
+		本模板基本类似 `MonoZkwTree` 。区别在于， `MonoZkw` 的叶结点处，只有一个普普通通的元素值；而 `MappedMonoZkw` 的叶结点处，可能并非一个普通元素值。可能是一个容器，由这个容器推出一个代表元素作为此叶结点处的值；也可能是一些别的类型的东西，经过计算得到元素值。
+
+		通过 `Mapping` 模板参数，可以控制叶结点处的数据类型，以及计算叶结点的值的方法。默认的提供了 `MaxPqMonoZkwTree` 和 `MinPqMonoZkwTree` ，表示每个叶结点处有一个堆，由堆顶作为代表元素充当线段树的叶结点处的值。
+
+### 三、模板示例
+
+```c++
+#include "DS/MappedMonoZkwTree.h"
+#include "IO/FastIO.h"
+
+void test() {
+    // 假如，有 10 个桶
+    // 查询 query(l, r) 表示查询 bucket[l~r] 这些桶的最大值的和
+    // 空桶的贡献是 0
+    using monoid = OY::MonoSumTree<int>::group;
+    OY::MaxPqMonoZkwTree<monoid, int, 0> S(10);
+    // 记得对桶做修改之后，要调用 S.update
+    S[2].push(25), S[2].push(50);
+    S.update(2);
+
+    S[4].push(30);
+    S.update(4);
+
+    S[5].push(100), S[5].push(8);
+    S.update(5);
+
+    S[8].push(88);
+    S.update(8);
+
+    cout << "S.query(4, 6) = " << S.query(4, 6) << endl;
+}
+
+int main() {
+    test();
+}
+```
+
+```
+#输出如下
+S.query(4, 6) = 130
+
+```
+
diff --git a/TEST/local/MappedMonoZkwTree_test.cpp b/TEST/local/MappedMonoZkwTree_test.cpp
@@ -0,0 +1,33 @@
+#include "DS/MappedMonoZkwTree.h"
+#include "IO/FastIO.h"
+
+void test() {
+    // 假如，有 10 个桶
+    // 查询 query(l, r) 表示查询 bucket[l~r] 这些桶的最大值的和
+    // 空桶的贡献是 0
+    using monoid = OY::MonoSumTree<int>::group;
+    OY::MaxPqMonoZkwTree<monoid, int, 0> S(10);
+    // 记得对桶做修改之后，要调用 S.update
+    S[2].push(25), S[2].push(50);
+    S.update(2);
+
+    S[4].push(30);
+    S.update(4);
+
+    S[5].push(100), S[5].push(8);
+    S.update(5);
+
+    S[8].push(88);
+    S.update(8);
+
+    cout << "S.query(4, 6) = " << S.query(4, 6) << endl;
+}
+
+int main() {
+    test();
+}
+/*
+#输出如下
+S.query(4, 6) = 130
+
+*/
diff --git a/TEST/oj/nc_226861.cpp b/TEST/oj/nc_226861.cpp
@@ -0,0 +1,42 @@
+#include "DS/MappedMonoZkwTree.h"
+#include "IO/FastIO.h"
+
+/*
+[弩蚊怒夏](https://ac.nowcoder.com/acm/problem/226861)
+*/
+/**
+ * 上面的链接打不开
+ * 请换用这个链接 https://ac.nowcoder.com/acm/contest/19917/B
+ * 本题使用单点修改线段树可以解决，每个叶子节点处有一个堆，堆的最大值作为叶子处的值
+ */
+
+void solve_mmzkw() {
+    uint32_t n, m, k;
+    cin >> n >> m >> k;
+    using monoid = OY::MonoMaxTree<uint32_t>::group;
+    OY::MaxPqMonoZkwTree<monoid, uint32_t> S(n);
+    while (m--) {
+        uint32_t pos, a;
+        cin >> pos >> a, pos--;
+        // S[pos] 是一个叶子处的堆
+        S[pos].push(a);
+        S.update(pos);
+    }
+    while (k--) {
+        uint32_t l, r, p;
+        cin >> l >> r >> p, l--, r--;
+        uint64_t ans = 0;
+        while (S.query_all() >= p) {
+            auto pos = S.max_right(l, [&](auto v) { return v < p; }) + 1;
+            if (pos > r) break;
+            do ans += S[pos].top(), S[pos].pop();
+            while (!S[pos].empty() && S[pos].top() >= p);
+            S.update(pos);
+        }
+        cout << ans << endl;
+    }
+}
+
+int main() {
+    solve_mmzkw();
+}
diff --git a/TEST/oj/nc_226924.cpp b/TEST/oj/nc_226924.cpp
@@ -0,0 +1,73 @@
+#include "DS/LichaoSegTree.h"
+#include "DS/LichaoSegTree_ex.h"
+#include "DS/LichaoZkwTree.h"
+#include "DS/LichaoZkwTree_ex.h"
+#include "IO/FastIO.h"
+
+#include <climits>
+
+/*
+[智乃的直线](https://ac.nowcoder.com/acm/problem/226924)
+*/
+/**
+ * 上面的链接打不开
+ * 请换用这个链接 https://ac.nowcoder.com/acm/contest/19917/A
+ * 本题使用单点修改线段树可以解决，每个叶子节点处有一个堆，堆的最大值作为叶子处的值
+ */
+
+void solve_lc() {
+    uint32_t n, m;
+    cin >> n >> m;
+    struct Line {
+        int m_k, m_b;
+        Line() = default;
+        Line(int k, int b) : m_k(k), m_b(b) {}
+        int64_t calc(int i) const { return int64_t(m_k) * i + m_b; }
+    };
+    OY::LCSEG::Tree<Line, std::less<>> S_max(n + 1, {-10000, INT_MIN});
+    // OY::LCZKW::Tree<Line, std::less<>> S_max(n + 1, {-10000, INT_MIN});
+    OY::LCSEG::Tree<Line, std::greater<>> S_min(n + 1, {10000, INT_MAX});
+    // OY::LCZKW::Tree<Line, std::greater<>> S_min(n + 1, {10000, INT_MAX});
+    while (m--) {
+        char op;
+        cin >> op;
+        if (op == '0') {
+            int k, b;
+            cin >> k >> b;
+            S_max.add(0, n, {k, b});
+            S_min.add(0, n, {k, b});
+        } else {
+            uint32_t x;
+            cin >> x;
+            cout << S_max.query(x).calc(x) << ' ' << S_min.query(x).calc(x) << endl;
+        }
+    }
+}
+
+void solve_lcex() {
+    uint32_t n, m;
+    cin >> n >> m;
+    OY::VectorLichaoSlopeChmaxSegTree_ex<int64_t, INT64_MIN, false, OY::LCSEGEX::BaseLine<int64_t>, uint32_t> S_max(n + 1);
+    // OY::LichaoSlopeChmaxZkwTree_ex<int64_t, INT64_MIN, false, OY::LCZKWEX::BaseLine<int64_t>> S_max(n + 1);
+    OY::VectorLichaoSlopeChminSegTree_ex<int64_t, INT64_MAX, false, OY::LCSEGEX::BaseLine<int64_t>, uint32_t> S_min(n + 1);
+    // OY::LichaoSlopeChminZkwTree_ex<int64_t, INT64_MAX, false, OY::LCZKWEX::BaseLine<int64_t>> S_min(n + 1);
+    while (m--) {
+        char op;
+        cin >> op;
+        if (op == '0') {
+            int k, b;
+            cin >> k >> b;
+            S_max.add_line(0, n, {k, b});
+            S_min.add_line(0, n, {k, b});
+        } else {
+            uint32_t x;
+            cin >> x;
+            cout << S_max.query(x) << ' ' << S_min.query(x) << endl;
+        }
+    }
+}
+
+int main() {
+    solve_lc();
+    // solve_lcex();
+}
diff --git a/TEST/oj/nc_277952.cpp b/TEST/oj/nc_277952.cpp
@@ -0,0 +1,46 @@
+#include "DS/MappedMonoZkwTree.h"
+#include "IO/FastIO.h"
+
+/*
+[小红的数组操作](https://ac.nowcoder.com/acm/problem/277952)
+*/
+/**
+ * 上面的链接打不开
+ * 请换用这个链接 https://ac.nowcoder.com/acm/contest/88888/F
+ * 本题使用单点修改线段树可以解决，每个叶子节点处有一个 multiset，multiset 的最小值作为叶子处的值
+ * multiset 还可以进一步优化为一个懒删除堆
+ * 
+ * 当然，简便起见，也可以直接用一个子线段树当 multiset 
+ */
+
+void solve_mmzkw() {
+    auto read = [](auto...) {
+        uint32_t x;
+        cin >> x;
+        return x;
+    };
+    using inner_tree = OY::MonoMinTree<uint32_t>;
+    using monoid = inner_tree::group;
+    struct Mapping {
+        using container_type = inner_tree;
+        static uint32_t get(const container_type &bucket) { return bucket.size() ? bucket.query_all() : monoid::identity(); }
+    };
+    uint32_t n = read();
+    OY::MMZKW::Tree<monoid, Mapping> S(n);
+    for (uint32_t i = 0; i != n; i++) S[i].resize(read(), read), S.update(i);
+    uint32_t q = read();
+    while (q--) {
+        char op;
+        cin >> op;
+        if (op == '1') {
+            uint32_t i = read() - 1, j = read() - 1, x = read();
+            S[i].modify(j, x);
+            S.update(i);
+        } else
+            cout << S.query(0, read() - 1) << endl;
+    }
+}
+
+int main() {
+    solve_mmzkw();
+}
diff --git a/TREE/HeavyLightDecomposition.h b/TREE/HeavyLightDecomposition.h
@@ -83,6 +83,18 @@ namespace OY {
                 else if (a != b)
                     call(info[a].m_dfn + 1, info[b].m_dfn);
             }
+            template <bool LCA, typename Callback>
+            void do_for_off_path(size_type a, size_type b, Callback &&call) const {
+                std::pair<size_type, size_type> ranges[32];
+                size_type cnt = 0;
+                do_for_path<LCA>(a, b, [&](size_type l, size_type r) { ranges[cnt++] = {l, r}; });
+                if (!cnt) return;
+                std::sort(ranges, ranges + cnt);
+                if (ranges[0].first) call(0, ranges[0].first - 1);
+                for (size_type i = 1; i != cnt; i++)
+                    if (ranges[i - 1].second + 1 != ranges[i].first) call(ranges[i - 1].second + 1, ranges[i].first - 1);
+                if (ranges[cnt - 1].second + 1 != m_rooted_tree->vertex_cnt()) call(ranges[cnt - 1].second + 1, m_rooted_tree->vertex_cnt() - 1);
+            }
             template <typename Callback>
             void do_for_directed_path(size_type from, size_type to, Callback &&call) const {
                 auto info = m_info.data();