添加了若干内容，修复了若干内容

Author: lr580

README.md

@@ -1,4 +1,4 @@
-**当前最新普通版发布版本为 `v1.2.0`** ，  **最新打印版发布版本为 `v1.2.0` (总词数约10.0w(含代码))**
+**当前最新普通版发布版本为 `v1.2.2`** ，  **最新打印版发布版本为 `v1.2.0` (总词数约10.0w(含代码))**
 
 成品为 `template.pdf` (移步 [releases](https://github.com/lr580/algorithm_template/releases) 查看/下载)
 
@@ -293,15 +293,31 @@ lr580's 算法模板
 
 ## 更新日志
 
+- 23/10-27 - 24/06/05 (`v1.2.2`)
+
+  - 添加了动态开点线段树模板
+  
+  - 微加了位运算语法应用
+  - 添加了暴力 LCA
+  - 微修了 Dijkstra 最短路应用例子表述错误、朴素法代码等
+  - 添加了调试输出版本的语法
+  - 添加了枚举组合 Gosper's Hack 模板
+  - 修正了整数三分模板
+  - 增加了树上 k 级祖先倍增法
+  - 增加了背包方案数模板
+  - 修正了 Miller Rabin 素性测试复杂度
+  - 微加了差分约束内容
+  - 微修了 STL vector 语法表述错误
+  
 - 23/10/22 - 23/10/26 (`v1.2.1`)
 
   - 重制了匹配问题等目录排版
-  
+
   - 微加了 STL 内容
   - 添加了树状数组上倍增、线段树上二分、pb_ds 哈希表
   - 修正了整数三分模板
   - 添加了立体计算几何公式
-  
+
 - 23/10/19 - 23/10/21 (`v1.2.0`)
 
   - 添加了快速矩阵前 n 项和模板

code/gospers_hack.cpp

@@ -0,0 +1,38 @@
+#include <iostream>
+#include <vector>
+
+// Function to generate the next subset
+unsigned int nextSubset(unsigned int subset) {
+    unsigned int u = subset & -subset;
+    unsigned int v = subset + u;
+    return v | (((v ^ subset) / u) >> 2);
+}
+
+// Function to generate all k-subsets of a set of size n
+void gospersHack(int k, int n) {
+    unsigned int subset = (1 << k) - 1;
+    unsigned int limit = (1 << n);
+
+    while (subset < limit) {
+        // Process the subset here
+        // For example, printing it out
+        for (int i = 0; i < n; ++i) {
+            if (subset & (1 << i)) {
+                std::cout << i + 1 << " ";
+            }
+        }
+        std::cout << std::endl;
+
+        subset = nextSubset(subset);
+    }
+}
+
+int main() {
+    int k = 3; // Size of subsets
+    int n = 5; // Size of the set
+
+    std::cout << "All " << k << "-subsets of a " << n << "-element set:\n";
+    gospersHack(k, n);
+
+    return 0;
+}

code/lca_tarjan.cpp

@@ -0,0 +1,97 @@
+#include <algorithm>
+#include <cstring>
+#include <iostream>
+using namespace std;
+
+class Edge {
+ public:
+  int toVertex, fromVertex;
+  int next;
+  int LCA;
+  Edge() : toVertex(-1), fromVertex(-1), next(-1), LCA(-1){};
+  Edge(int u, int v, int n) : fromVertex(u), toVertex(v), next(n), LCA(-1){};
+};
+
+const int MAX = 100;
+int head[MAX], queryHead[MAX];
+Edge edge[MAX], queryEdge[MAX];
+int parent[MAX], visited[MAX];
+int vertexCount, queryCount;
+
+void init() {
+  for (int i = 0; i <= vertexCount; i++) {
+    parent[i] = i;
+  }
+}
+
+int find(int x) {
+  if (parent[x] == x) {
+    return x;
+  } else {
+    return find(parent[x]);
+  }
+}
+
+void tarjan(int u) {
+  parent[u] = u;
+  visited[u] = 1;
+
+  for (int i = head[u]; i != -1; i = edge[i].next) {
+    Edge& e = edge[i];
+    if (!visited[e.toVertex]) {
+      tarjan(e.toVertex);
+      parent[e.toVertex] = u;
+    }
+  }
+
+  for (int i = queryHead[u]; i != -1; i = queryEdge[i].next) {
+    Edge& e = queryEdge[i];
+    if (visited[e.toVertex]) {
+      queryEdge[i ^ 1].LCA = e.LCA = find(e.toVertex);
+    }
+  }
+}
+
+int main() {
+  memset(head, 0xff, sizeof(head));
+  memset(queryHead, 0xff, sizeof(queryHead));
+
+  cin >> vertexCount >> queryCount;
+  int count = 0;
+  for (int i = 0; i < vertexCount - 1; i++) {
+    int start = 0, end = 0;
+    cin >> start >> end;
+
+    edge[count] = Edge(start, end, head[start]);
+    head[start] = count;
+    count++;
+
+    edge[count] = Edge(end, start, head[end]);
+    head[end] = count;
+    count++;
+  }
+
+  count = 0;
+  for (int i = 0; i < queryCount; i++) {
+    int start = 0, end = 0;
+    cin >> start >> end;
+
+    queryEdge[count] = Edge(start, end, queryHead[start]);
+    queryHead[start] = count;
+    count++;
+
+    queryEdge[count] = Edge(end, start, queryHead[end]);
+    queryHead[end] = count;
+    count++;
+  }
+
+  init();
+  tarjan(1);
+
+  for (int i = 0; i < queryCount; i++) {
+    Edge& e = queryEdge[i * 2];
+    cout << "(" << e.fromVertex << "," << e.toVertex << ") " << e.LCA << endl;
+  }
+
+  return 0;
+}

code/segment_tree_lazy.cpp

@@ -0,0 +1,102 @@
+#include <bits/stdc++.h> // https://leetcode.cn/problems/range-module
+using namespace std;
+using ll = long long;
+class RangeModule
+{
+    constexpr static ll inf = 1e9;
+    constexpr static ll maxn = 60 * 1e4; // log(inf)*q
+    struct node
+    {
+        ll ls, rs, sum, laz;
+    } t[maxn] = {};
+    int cnt = 1;
+#define cll const ll &
+#define mkcf ll cf = (lf + rf) >> 1
+    void pushdown(int r, cll lf, cll rf)
+    {
+        if (!t[r].ls)
+            t[r].ls = ++cnt;
+        if (!t[r].rs)
+            t[r].rs = ++cnt;
+        if (!t[r].laz)
+            return;
+        if (t[r].laz == 1)
+        {
+            mkcf;
+            t[t[r].ls].sum = (cf - lf + 1); // len-len/2
+            t[t[r].rs].sum = rf - cf;       // len/2
+        }
+        else
+        {
+            t[t[r].ls].sum = t[t[r].rs].sum = 0;
+        }
+        t[t[r].ls].laz = t[t[r].rs].laz = t[r].laz;
+        t[r].laz = 0;
+    }
+    void pushup(int r)
+    {
+        t[r].sum = t[t[r].ls].sum + t[t[r].rs].sum;
+    }
+    void update(int r, ll lf, ll rf, cll lc, cll rc, cll v)
+    {
+        if (lc <= lf && rf <= rc)
+        {
+            t[r].sum += (v == 1) * (rf - lf + 1);
+            t[r].laz = v;
+            return;
+        }
+        pushdown(r, lf, rf);
+        mkcf;
+        if (lc <= cf)
+            update(t[r].ls, lf, cf, lc, rc, v);
+        if (rc >= cf + 1)
+            update(t[r].rs, cf + 1, rf, lc, rc, v);
+        pushup(r);
+    }
+    ll query(int r, ll lf, ll rf, cll lc, cll rc)
+    {
+        if (lc <= lf && rf <= rc)
+            return t[r].sum;
+        pushdown(r, lf, rf);
+        ll res = 0;
+        mkcf;
+        if (lc <= cf)
+            res += query(t[r].ls, lf, cf, lc, rc);
+        if (rc >= cf + 1)
+            res += query(t[r].rs, cf + 1, rf, lc, rc);
+        return res;
+    }
+
+public:
+    RangeModule() {}
+
+    void addRange(int left, int right)
+    {
+        update(1, 1, inf, left, right - 1, 1);
+    }
+
+    bool queryRange(int left, int right)
+    {
+        return query(1, 1, inf, left, right - 1) == right - left;
+    }
+
+    void removeRange(int left, int right)
+    {
+        update(1, 1, inf, left, right - 1, -1);
+    }
+};
+
+signed main()
+{
+    ios::sync_with_stdio(false), cin.tie(0);
+
+    return 0;
+}
+
+/**
+ * Your RangeModule object will be instantiated and called as such:
+ * RangeModule* obj = new RangeModule();
+ * obj->addRange(left,right);
+ * bool param_2 = obj->queryRange(left,right);
+ * obj->removeRange(left,right);
+ */