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算法设计与分析/复习文档/图搜索与NP复杂性.md

@@ -21,28 +21,52 @@ DFS 沿着一条路径**尽可能深地**搜索，走不通再回退。
 
 **实现方式**：使用**栈**（Stack）或**递归调用栈**
 
-```plaintext
-function DFS(graph, start):
-    visited = set()
-    stack = [start]
+```cpp
+#include <vector>
+#include <stack>
+#include <iostream>
+using namespace std;
 
-    while stack is not empty:
-        node = stack.pop()
-        if node not in visited:
-            visited.add(node)
-            for neighbor in graph[node]:
-                if neighbor not in visited:
-                    stack.push(neighbor)
+// DFS（栈实现）
+// graph: 邻接表, start: 起始顶点
+void DFS(vector<vector<int>>& graph, int start) {
+    int n = graph.size();
+    vector<bool> visited(n, false);
+    stack<int> st;
+    st.push(start);
+
+    while (!st.empty()) {
+        int node = st.top();
+        st.pop();
+        if (!visited[node]) {
+            visited[node] = true;
+            cout << node << " ";
+            for (int neighbor : graph[node]) {
+                if (!visited[neighbor])
+                    st.push(neighbor);
+            }
+        }
+    }
+}
 ```
 
 递归版本更直观：
 
-```plaintext
-function DFS_recursive(graph, node, visited):
-    visited.add(node)
-    for neighbor in graph[node]:
-        if neighbor not in visited:
-            DFS_recursive(graph, neighbor, visited)
+```cpp
+#include <vector>
+#include <iostream>
+using namespace std;
+
+// DFS（递归版本）
+// graph: 邻接表, node: 当前顶点, visited: 访问标记数组
+void DFS_recursive(vector<vector<int>>& graph, int node, vector<bool>& visited) {
+    visited[node] = true;
+    cout << node << " ";
+    for (int neighbor : graph[node]) {
+        if (!visited[neighbor])
+            DFS_recursive(graph, neighbor, visited);
+    }
+}
 ```
 
 ### 二、BFS（广度优先搜索）
@@ -51,18 +75,33 @@ BFS **按层遍历**，先访问所有距离为1的节点，再访问距离为2
 
 **实现方式**：使用**队列**（Queue）
 
-```plaintext
-function BFS(graph, start):
-    visited = set()
-    queue = [start]
-    visited.add(start)
+```cpp
+#include <vector>
+#include <queue>
+#include <iostream>
+using namespace std;
 
-    while queue is not empty:
-        node = queue.dequeue()
-        for neighbor in graph[node]:
-            if neighbor not in visited:
-                visited.add(neighbor)
-                queue.enqueue(neighbor)
+// BFS（队列实现）
+// graph: 邻接表, start: 起始顶点
+void BFS(vector<vector<int>>& graph, int start) {
+    int n = graph.size();
+    vector<bool> visited(n, false);
+    queue<int> q;
+    q.push(start);
+    visited[start] = true;
+
+    while (!q.empty()) {
+        int node = q.front();
+        q.pop();
+        cout << node << " ";
+        for (int neighbor : graph[node]) {
+            if (!visited[neighbor]) {
+                visited[neighbor] = true;
+                q.push(neighbor);
+            }
+        }
+    }
+}
 ```
 
 ### 三、BFS vs DFS 对比
@@ -112,13 +151,17 @@ flowchart TD
 
 **原理**：gcd(a, b) = gcd(b, a mod b)，直到 b = 0 时 a 即为答案。
 
-```plaintext
-function gcd(a, b):
-    while b != 0:
-        temp = b
-        b = a mod b
-        a = temp
-    return a
+```cpp
+// 欧几里得算法（辗转相除法）
+// 求两个正整数的最大公约数
+int gcd(int a, int b) {
+    while (b != 0) {
+        int temp = b;
+        b = a % b;
+        a = temp;
+    }
+    return a;
+}
 ```
 
 **示例**：gcd(2146, 8100)