fix bit01 bug; add erasable_mono_pairheap; add lazymap/lazyumap/lazys…

…et/lazyuset;
old-yan · Oct 26, 2024 · 77a75dd · 77a75dd
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diff --git a/DS/AVL.md b/DS/AVL.md
@@ -11,8 +11,9 @@
 5. [P4070 [SDOI2016] 生成魔咒](https://www.luogu.com.cn/problem/P4070)
 6. [P5494 【模板】线段树分裂](https://www.luogu.com.cn/problem/P5494)
 7. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
-8. [数据结构](https://ac.nowcoder.com/acm/problem/276699)
-9. [Dynamic Sequence Range Affine Range Sum](https://judge.yosupo.jp/problem/dynamic_sequence_range_affine_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/242)
+8. [寿命修改](https://ac.nowcoder.com/acm/problem/275139)
+9. [数据结构](https://ac.nowcoder.com/acm/problem/276699)
+10. [Dynamic Sequence Range Affine Range Sum](https://judge.yosupo.jp/problem/dynamic_sequence_range_affine_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/242)
 
 
 ### 二、模板功能

diff --git a/DS/AdjDiff.md b/DS/AdjDiff.md
@@ -12,7 +12,8 @@
 6. [P4655 [CEOI2017] Building Bridges](https://www.luogu.com.cn/problem/P4655)
 7. [P10843 【MX-J2-T4】Turtle and Cycles](https://www.luogu.com.cn/problem/P10843)
 8. [fsl 的背包](https://ac.nowcoder.com/acm/problem/263978)
-9. [Static Range Sum](https://judge.yosupo.jp/problem/static_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/398)
+9. [k - 路径（hard vension）](https://ac.nowcoder.com/acm/problem/279411)
+10. [Static Range Sum](https://judge.yosupo.jp/problem/static_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/398)
 
 
 ### 二、模板功能

diff --git a/DS/BIT01.h b/DS/BIT01.h
@@ -71,7 +71,7 @@ namespace OY {
                 return res;
             }
             size_type query(size_type i) const { return m_bits[i >> MASK_WIDTH] >> (i & (MASK_SIZE - 1)) & 1; }
-            size_type query(size_type left, size_type right) const { return presum(right) - presum(left); }
+            size_type query(size_type left, size_type right) const { return presum(right) - presum(left - 1); }
             size_type kth(size_type k) const {
                 size_type cursor = -1;
                 for (size_type d = m_icap >> 1; d; d >>= 1)

diff --git a/DS/BIT01.md b/DS/BIT01.md
@@ -6,6 +6,7 @@
 
 1. [Hotaru's problem](https://acm.hdu.edu.cn/showproblem.php?pid=5371)
 2. [P4070 [SDOI2016] 生成魔咒](https://www.luogu.com.cn/problem/P4070)
+3. [寿命修改](https://ac.nowcoder.com/acm/problem/275139)
 
 ### 二、模板功能
 

diff --git a/DS/CompressedTree.md b/DS/CompressedTree.md
@@ -4,7 +4,8 @@
 
 	练习题目：
 
-1. [U311262 求区间后继](https://www.luogu.com.cn/problem/U311262)
+1. [P1801 黑匣子](https://www.luogu.com.cn/problem/P1801)
+2. [U311262 求区间后继](https://www.luogu.com.cn/problem/U311262)
 
 ### 二、模板功能
 

diff --git a/DS/ErasableMonoPairHeap.h b/DS/ErasableMonoPairHeap.h
@@ -0,0 +1,102 @@
+/*
+最后修改:
+20241020
+测试环境:
+gcc11.2,c++11
+clang22.0,C++11
+msvc14.2,C++14
+*/
+#ifndef __OY_ERASABLEMONOPAIRHEAP__
+#define __OY_ERASABLEMONOPAIRHEAP__
+
+#include "MonoPairHeap.h"
+
+namespace OY {
+    namespace EMONOPH {
+        using size_type = MONOPH::size_type;
+        template <typename Tp>
+        struct AddCommutativeGroup {
+            using value_type = Tp;
+            static Tp identity() { return Tp{}; }
+            static Tp op(const Tp &x, const Tp &y) { return x + y; }
+            static Tp inverse(const Tp &x) { return -x; }
+        };
+        template <typename Tp>
+        struct BitxorCommutativeGroup {
+            using value_type = Tp;
+            static Tp identity() { return Tp{}; }
+            static Tp op(const Tp &x, const Tp &y) { return x ^ y; }
+            static Tp inverse(const Tp &x) { return x; }
+        };
+        template <typename CommutativeGroup>
+        struct Trait {
+            using group = CommutativeGroup;
+            using value_type = typename group::value_type;
+            using sum_type = typename MONOPH::Has_Sum_Type<group, value_type>::type;
+            static constexpr bool has_op = MONOPH::Has_Op<group, sum_type>::value;
+        };
+        template <typename CommutativeGroup, bool HasOp = Trait<CommutativeGroup>::has_op>
+        struct HeapBase : Trait<CommutativeGroup> {
+            typename Trait<CommutativeGroup>::sum_type m_prod;
+            HeapBase() : m_prod(CommutativeGroup::identity()) {}
+        };
+        template <typename CommutativeGroup>
+        struct HeapBase<CommutativeGroup, false> : Trait<CommutativeGroup> {};
+        template <typename CommutativeGroup, typename Compare = std::less<typename CommutativeGroup::value_type>, template <typename> typename BufferType = VectorBufferWithCollect>
+        class Heap : HeapBase<CommutativeGroup> {
+        public:
+            using typename HeapBase<CommutativeGroup>::group;
+            using typename HeapBase<CommutativeGroup>::value_type;
+            using typename HeapBase<CommutativeGroup>::sum_type;
+            using HeapBase<CommutativeGroup>::has_op;
+            using heap_type = Heap<CommutativeGroup, Compare, BufferType>;
+            using inner_type = MONOPH::Heap<MONOPH::NoOp<value_type>, Compare, BufferType>;
+            using buffer_type = typename inner_type::buffer_type;
+            static void _reserve(size_type capacity) { inner_type::_reserve(capacity); }
+        private:
+            mutable inner_type m_data, m_lazy;
+            size_type m_sz;
+        public:
+            Heap() : m_sz() {}
+            void clear() {
+                m_data.clear(), m_lazy.clear(), m_sz = 0;
+                if constexpr (has_op) this->m_prod = group::identity();
+            }
+            size_type size() const { return m_sz; }
+            bool empty() const { return !m_sz; }
+            void push(const value_type &x) {
+                m_data.push(x), m_sz++;
+                if constexpr (has_op) this->m_prod = group::op(this->m_prod, x);
+            }
+            void erase(const value_type &x) {
+                m_lazy.push(x), m_sz--;
+                if constexpr (has_op) this->m_prod = group::op(this->m_prod, group::inverse(x));
+            }
+            void pop() {
+                while (!m_lazy.empty() && !Compare()(m_lazy.top(), m_data.top())) m_data.pop(), m_lazy.pop();
+                if constexpr (has_op) this->m_prod = group::op(this->m_prod, group::inverse(m_data.top()));
+                m_data.pop(), m_sz--;
+            }
+            const value_type &top() const {
+                while (!m_lazy.empty() && !Compare()(m_lazy.top(), m_data.top())) m_data.pop(), m_lazy.pop();
+                return m_data.top();
+            }
+            void join(heap_type &rhs) {
+                if (!rhs.empty()) {
+                    m_data.join(rhs.m_data), m_lazy.join(rhs.m_lazy), rhs.m_sz = 0;
+                    if constexpr (has_op) this->m_prod = group::op(this->m_prod, rhs.m_prod), rhs.m_prod = group::identity();
+                }
+            }
+            void join(heap_type &&rhs) { join(rhs); }
+            const sum_type &query_all() const { return this->m_prod; }
+        };
+    }
+    template <typename Tp, typename Compare = std::less<Tp>, template <typename> typename BufferType = VectorBufferWithCollect>
+    using ErasableMonoPairHeap = EMONOPH::Heap<MONOPH::NoOp<Tp>, Compare, BufferType>;
+    template <typename Tp, typename Compare = std::less<Tp>>
+    using VectorErasableMonoSumPairHeap = EMONOPH::Heap<EMONOPH::AddCommutativeGroup<Tp>, Compare>;
+    template <typename Tp, typename Compare = std::less<Tp>>
+    using VectorErasableMonoBitXorPairHeap = EMONOPH::Heap<EMONOPH::BitxorCommutativeGroup<Tp>, Compare>;
+}
+
+#endif
diff --git a/DS/ErasableMonoPairHeap.md b/DS/ErasableMonoPairHeap.md
@@ -0,0 +1,52 @@
+### 一、模板类别
+
+	数据结构：可删除元素的配对堆。
+
+	练习题目：
+
+1. [3321. 计算子数组的 x-sum II](https://leetcode.cn/problems/find-x-sum-of-all-k-long-subarrays-ii)
+
+
+### 二、模板功能
+
+		本模板为支持维护信息的堆。同时，借助懒删除技术，实现了堆中元素的删除。
+
+		与 `MonoPairHeap` 不同的是，本模板要求传入的代数结构为交换群，需要存在逆元。只有通过差分才可以实时维护堆的信息。
+
+		需要注意的是， `erase` 函数需要保证，每次传入的元素必须仍在堆中，未被删除。
+
+		在接口上，并无特殊之处。
+
+
+### 三、模板示例
+
+```c++
+#include "DS/ErasableMonoPairHeap.h"
+#include "IO/FastIO.h"
+
+void test() {
+    OY::VectorErasableMonoSumPairHeap<int> S;
+    S.push(100);
+    S.push(400);
+    S.push(200);
+    S.push(300);
+    S.push(500);
+    S.erase(200);
+    S.erase(400);
+    cout << "size = " << S.size() << endl;
+    S.pop();
+    cout << "sum = " << S.query_all() << endl;
+}
+
+int main() {
+    test();
+}
+```
+
+```
+#输出如下
+size = 3
+sum = 400
+
+```
+
diff --git a/DS/GlobalHashBIT.md b/DS/GlobalHashBIT.md
@@ -5,10 +5,11 @@
 	练习题目：
 
 1. [940. 不同的子序列 II](https://leetcode.cn/problems/distinct-subsequences-ii)
-2. [P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
-3. [P3372 【模板】线段树 1](https://www.luogu.com.cn/problem/P3372)
-4. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
-5. [U187320 【模板】树状数组 3](https://www.luogu.com.cn/problem/U187320)
+2. [P1801 黑匣子](https://www.luogu.com.cn/problem/P1801)
+3. [P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
+4. [P3372 【模板】线段树 1](https://www.luogu.com.cn/problem/P3372)
+5. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
+6. [U187320 【模板】树状数组 3](https://www.luogu.com.cn/problem/U187320)
 
 
 

diff --git a/DS/MaskRMQ.md b/DS/MaskRMQ.md
@@ -8,6 +8,8 @@
 2. [P1886 滑动窗口 /【模板】单调队列](https://www.luogu.com.cn/problem/P1886)
 3. [P3793 由乃救爷爷](https://www.luogu.com.cn/problem/P3793)
 4. [P3865 【模板】ST 表](https://www.luogu.com.cn/problem/P3865)
+5. [k - 路径（hard vension）](https://ac.nowcoder.com/acm/problem/279411)
+6. [小红的树上路径查询（hard）](https://ac.nowcoder.com/acm/problem/281352)
 
 
 ### 二、模板功能

diff --git a/DS/MergeSortTree.md b/DS/MergeSortTree.md
@@ -5,12 +5,13 @@
 	练习题目：
 
 1. [Minimum Sum](https://acm.hdu.edu.cn/showproblem.php?pid=3473)
-2. [P3834 【模板】可持久化线段树 2](https://www.luogu.com.cn/problem/P3834)
-3. [P4094 [HEOI2016/TJOI2016] 字符串](https://www.luogu.com.cn/problem/P4094)
-4. [P10814 【模板】离线二维数点](https://www.luogu.com.cn/problem/P10814)
-5. [U311262 求区间后继](https://www.luogu.com.cn/problem/U311262)
-6. [fsl 的背包](https://ac.nowcoder.com/acm/problem/263978)
-7. [Range Kth Smallest](https://judge.yosupo.jp/problem/range_kth_smallest)(https://github.com/yosupo06/library-checker-problems/issues/310)
+2. [P1801 黑匣子](https://www.luogu.com.cn/problem/P1801)
+3. [P3834 【模板】可持久化线段树 2](https://www.luogu.com.cn/problem/P3834)
+4. [P4094 [HEOI2016/TJOI2016] 字符串](https://www.luogu.com.cn/problem/P4094)
+5. [P10814 【模板】离线二维数点](https://www.luogu.com.cn/problem/P10814)
+6. [U311262 求区间后继](https://www.luogu.com.cn/problem/U311262)
+7. [fsl 的背包](https://ac.nowcoder.com/acm/problem/263978)
+8. [Range Kth Smallest](https://judge.yosupo.jp/problem/range_kth_smallest)(https://github.com/yosupo06/library-checker-problems/issues/310)
 
 
 ### 二、模板功能

diff --git a/DS/MonoAVL.md b/DS/MonoAVL.md
@@ -7,17 +7,18 @@
 
 1. [3321. 计算子数组的 x-sum II](https://leetcode.cn/problems/find-x-sum-of-all-k-long-subarrays-ii)
 2. [P1503 鬼子进村](https://www.luogu.com.cn/problem/P1503)
-3. [P1886 滑动窗口 /【模板】单调队列](https://www.luogu.com.cn/problem/P1886)
-4. [P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
-5. [P3391 【模板】文艺平衡树](https://www.luogu.com.cn/problem/P3391)
-6. [P4036 [JSOI2008] 火星人](https://www.luogu.com.cn/problem/P4036)
-7. [P4774 [NOI2018] 屠龙勇士](https://www.luogu.com.cn/problem/P4774)
-8. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
-9. [U361730 【模板】完全体·堆](https://www.luogu.com.cn/problem/U361730)
-10. [翻转排序](https://ac.nowcoder.com/acm/problem/275173)
-11. [旅途的终点](https://ac.nowcoder.com/acm/problem/275989)
-12. [正义从不打背身](https://ac.nowcoder.com/acm/problem/277862)
-13. [Range Reverse Range Sum](https://judge.yosupo.jp/problem/range_reverse_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/538)
+3. [P1801 黑匣子](https://www.luogu.com.cn/problem/P1801)
+4. [P1886 滑动窗口 /【模板】单调队列](https://www.luogu.com.cn/problem/P1886)
+5. [P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
+6. [P3391 【模板】文艺平衡树](https://www.luogu.com.cn/problem/P3391)
+7. [P4036 [JSOI2008] 火星人](https://www.luogu.com.cn/problem/P4036)
+8. [P4774 [NOI2018] 屠龙勇士](https://www.luogu.com.cn/problem/P4774)
+9. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
+10. [U361730 【模板】完全体·堆](https://www.luogu.com.cn/problem/U361730)
+11. [翻转排序](https://ac.nowcoder.com/acm/problem/275173)
+12. [旅途的终点](https://ac.nowcoder.com/acm/problem/275989)
+13. [正义从不打背身](https://ac.nowcoder.com/acm/problem/277862)
+14. [Range Reverse Range Sum](https://judge.yosupo.jp/problem/range_reverse_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/538)
 
 
 ### 二、模板功能

diff --git a/DS/MonoPairHeap.h b/DS/MonoPairHeap.h
@@ -103,7 +103,6 @@ namespace OY {
                 static_assert(buffer_type::is_vector_buffer, "Only In Vector Mode");
                 buffer_type::s_buf.reserve(capacity);
             }
-
         private:
             size_type m_rt{};
             static node *_ptr(size_type cur) { return buffer_type::data() + cur; }
@@ -140,7 +139,6 @@ namespace OY {
                 _pushup(p), _pushup(_ptr(a));
                 return b ? _merge(_merge(x, a), _merges(b)) : _merge(x, a);
             }
-
         public:
             Heap() { static Initializer _init; }
             Heap(const heap_type &rhs) = delete;

diff --git a/DS/MonoPairHeap.md b/DS/MonoPairHeap.md
@@ -4,9 +4,11 @@
 
 	练习题目：
 
-1. [P3377 【模板】左偏树（可并堆）](https://www.luogu.com.cn/problem/P3377)
-2. [P3378 【模板】堆](https://www.luogu.com.cn/problem/P3378)
-3. [U361730 【模板】完全体·堆](https://www.luogu.com.cn/problem/U361730)
+1. [P1801 黑匣子](https://www.luogu.com.cn/problem/P1801)
+2. [P3377 【模板】左偏树（可并堆）](https://www.luogu.com.cn/problem/P3377)
+3. [P3378 【模板】堆](https://www.luogu.com.cn/problem/P3378)
+4. [U361730 【模板】完全体·堆](https://www.luogu.com.cn/problem/U361730)
+5. [旅途的终点](https://ac.nowcoder.com/acm/problem/275989)
 
 
 ### 二、模板功能

diff --git a/DS/MonoSplay.md b/DS/MonoSplay.md
@@ -6,17 +6,18 @@
 
 1. [3321. 计算子数组的 x-sum II](https://leetcode.cn/problems/find-x-sum-of-all-k-long-subarrays-ii)
 2. [P1503 鬼子进村](https://www.luogu.com.cn/problem/P1503)
-3. [P1886 滑动窗口 /【模板】单调队列](https://www.luogu.com.cn/problem/P1886)
-4. [P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
-5. [P3391 【模板】文艺平衡树](https://www.luogu.com.cn/problem/P3391)
-6. [P4036 [JSOI2008] 火星人](https://www.luogu.com.cn/problem/P4036)
-7. [P4774 [NOI2018] 屠龙勇士](https://www.luogu.com.cn/problem/P4774)
-8. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
-9. [U361730 【模板】完全体·堆](https://www.luogu.com.cn/problem/U361730)
-10. [翻转排序](https://ac.nowcoder.com/acm/problem/275173)
-11. [旅途的终点](https://ac.nowcoder.com/acm/problem/275989)
-12. [正义从不打背身](https://ac.nowcoder.com/acm/problem/277862)
-13. [Range Reverse Range Sum](https://judge.yosupo.jp/problem/range_reverse_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/538)
+3. [P1801 黑匣子](https://www.luogu.com.cn/problem/P1801)
+4. [P1886 滑动窗口 /【模板】单调队列](https://www.luogu.com.cn/problem/P1886)
+5. [P3369 【模板】普通平衡树](https://www.luogu.com.cn/problem/P3369)
+6. [P3391 【模板】文艺平衡树](https://www.luogu.com.cn/problem/P3391)
+7. [P4036 [JSOI2008] 火星人](https://www.luogu.com.cn/problem/P4036)
+8. [P4774 [NOI2018] 屠龙勇士](https://www.luogu.com.cn/problem/P4774)
+9. [P6136 【模板】普通平衡树（数据加强版）](https://www.luogu.com.cn/problem/P6136)
+10. [U361730 【模板】完全体·堆](https://www.luogu.com.cn/problem/U361730)
+11. [翻转排序](https://ac.nowcoder.com/acm/problem/275173)
+12. [旅途的终点](https://ac.nowcoder.com/acm/problem/275989)
+13. [正义从不打背身](https://ac.nowcoder.com/acm/problem/277862)
+14. [Range Reverse Range Sum](https://judge.yosupo.jp/problem/range_reverse_range_sum)(https://github.com/yosupo06/library-checker-problems/issues/538)
 
 
 ### 二、模板功能

diff --git a/DS/MultiDimSegTree.h b/DS/MultiDimSegTree.h
@@ -197,10 +197,10 @@ namespace OY {
             }
         };
     }
-    template <typename SizeType, typename BaseMaxTable, size_t DIM, bool HasModify>
-    using MonoMaxMDSeg = MDSEG::Tree<SizeType, typename BaseMaxTable::group, BaseMaxTable, DIM, HasModify>;
-    template <typename SizeType, typename BaseMinTable, size_t DIM, bool HasModify>
-    using MonoMinMDSeg = MDSEG::Tree<SizeType, typename BaseMinTable::group, BaseMinTable, DIM, HasModify>;
+    template <typename SizeType, typename BaseMaxTable, size_t DIM, bool HasModify, typename CommutativeMonoid = typename BaseMaxTable::group>
+    using MonoMaxMDSeg = MDSEG::Tree<SizeType, CommutativeMonoid, BaseMaxTable, DIM, HasModify>;
+    template <typename SizeType, typename BaseMinTable, size_t DIM, bool HasModify, typename CommutativeMonoid = typename BaseMinTable::group>
+    using MonoMinMDSeg = MDSEG::Tree<SizeType, CommutativeMonoid, BaseMinTable, DIM, HasModify>;
     template <typename SizeType, typename Tp, size_t DIM>
     using MonoSumMDST = MDSEG::Tree<SizeType, MDSEG::BaseCommutativeMonoid<Tp, 0, std::plus<Tp>>, MDSEG::AdjTable<Tp>, DIM, false>;
     template <typename SizeType, typename Tp, size_t DIM>