Algorithm

Algorithm/BackTracking/readme.md

@@ -0,0 +1,80 @@
+回溯法（Backtracking）是一种**系统地枚举所有可能解**的方法，通常用于解决**组合、排列、约束满足等问题**。它的核心思想是：在搜索问题的解空间时，如果发现当前部分解无法得到最终解，就**立即放弃（回溯）**，避免无谓的计算。
+
+我给你拆开讲：
+
+---
+
+### 1️⃣ 基本思路
+
+1. 从问题的初始状态开始，尝试每一种可能的选择。
+2. 对于每一种选择：
+
+   * 判断是否符合条件（约束）。
+   * 如果符合，就继续尝试下一步。
+   * 如果不符合，直接放弃（剪枝）。
+3. 当到达最终状态时，把解记录下来。
+4. 搜索完当前选择后，撤销选择（回到上一步），尝试其他可能。
+
+这个“尝试→失败→撤销→尝试其他”过程就是“回溯”。
+
+---
+
+### 2️⃣ 典型问题
+
+回溯法适合解决这类问题：
+
+* **排列问题**：生成1\~n的所有排列。
+* **组合问题**：从n个元素中选出k个组合。
+* **子集问题**：生成所有子集。
+* **棋盘类问题**：N皇后、数独、填字游戏。
+* **约束满足问题**：图着色、八数码问题等。
+
+---
+
+### 3️⃣ 模板代码（C++示例）
+
+以**N皇后问题**为例：
+
+```cpp
+vector<int> queens; // queens[i] = 列号
+int n;
+
+bool isValid(int row, int col) {
+    for(int i = 0; i < row; i++) {
+        int c = queens[i];
+        if(c == col || abs(c - col) == row - i)
+            return false;
+    }
+    return true;
+}
+
+void backtrack(int row) {
+    if(row == n) {
+        // 找到一个解
+        for(int c : queens) cout << c << " ";
+        cout << endl;
+        return;
+    }
+    for(int col = 0; col < n; col++) {
+        if(isValid(row, col)) {
+            queens.push_back(col); // 选择
+            backtrack(row + 1);    // 递归
+            queens.pop_back();     // 回溯
+        }
+    }
+}
+```
+
+---
+
+### 4️⃣ 总结
+
+* 回溯法是一种**DFS+剪枝**的方法。
+* 核心是**选择、约束、递归、撤销**。
+* 常用于**枚举问题、组合问题和约束满足问题**。
+
+---
+
+如果你愿意，我可以给你画一张**回溯法搜索树的示意图**，直观理解它是怎么“尝试、失败、回退”的。
+
+你想让我画吗？

Algorithm/Graph/BFS/Maze.cpp

@@ -0,0 +1,66 @@
+#include <iostream>
+#include <utility>
+#include <deque>
+using namespace std;
+//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
+int dx[4] = {0, 0, -1, 1};
+int dy[4] = {1, -1, 0, 0};
+int dxx[8] = {-1, -1, -1, 0, 0, 1, 1, 1};
+int dyy[8] = {1, 0, -1, 1, -1, 1, 0, -1};
+int main(){
+	deque<pair<int, int>> q;
+	int n, m;
+	//<2F><><EFBFBD><EFBFBD> 
+	cin >> n >> m;
+	int startx, starty;
+	//<2F><><EFBFBD><EFBFBD> 
+	cin >> startx >> starty;
+	
+	deque<deque<int>> maze;
+	deque<deque<bool>> visited;
+	deque<deque<int>> dist(n, deque<int>(m, 0)); // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+	maze.resize(n);
+	visited.resize(n, deque<bool>(m, false));
+	int tmp;
+	//0<><30>ʾǽ<CABE><C7BD>1<EFBFBD><31>ʾ· 
+	for(int i = 0; i < n; i++){
+		for(int j = 0; j < m; j++){
+			cin >> tmp;
+			maze[i].push_back(tmp);
+		}
+	}
+	tmp = 0;
+	q.push_back(make_pair(startx, starty));
+	while(!q.empty()){
+		pair<int, int> u = q.front();
+		q.pop_front();
+		int x = u.first, y = u.second;
+		visited[x][y] = true;
+		
+		for(int i = 0; i < 4; i++){
+			if(x + dx[i] >= 0 && x + dx[i] < n && y + dy[i] >= 0 && y + dy[i] < m && !visited[x + dx[i]][y + dy[i]] && maze[x + dx[i]][y + dy[i]] == 1){
+				visited[x + dx[i]][y + dy[i]] = true;
+				dist[x + dx[i]][y + dy[i]] = dist[x][y] + 1; // <20><><EFBFBD>¾<EFBFBD><C2BE><EFBFBD>
+				q.push_back(make_pair(x + dx[i], y + dy[i]));
+			}
+		}
+	}
+	cout << endl;
+	for(int i = 0; i < n; i++){
+		for(int j = 0; j < m; j++){
+			cout << dist[i][j] << " ";
+		}
+		cout << endl;
+	}
+	return 0;
+}
+/*
+6 5
+0 0
+1 1 0 1 1
+1 0 1 1 1
+1 0 1 0 0
+1 0 1 1 1
+1 1 1 0 1
+1 1 1 1 1
+*/

Algorithm/Graph/DFS/UVa572-Oil-Deposits.cpp

@@ -0,0 +1,51 @@
+#include <iostream>
+#include <vector>
+using namespace std;
+int m = 5, n = 5;
+vector<vector<char>> s;
+vector<vector<bool>> visited;
+vector<vector<int>> ids;
+
+	
+void dfs(int x, int y, int id){
+	if(x < 0 || x >= m || y < 0 || y >=n) return;
+	if(s[x][y] != '@') return;
+	if(visited[x][y] == true) return;
+	visited[x][y] = true; 
+	ids[x][y] = id;
+	dfs(x - 1, y - 1, id + 1);
+	dfs(x - 1, y, id + 1);
+	dfs(x - 1, y + 1, id + 1);
+	dfs(x, y - 1, id + 1);
+	dfs(x, y + 1, id + 1);
+	dfs(x + 1, y - 1, id + 1);
+	dfs(x + 1, y, id + 1);
+	dfs(x + 1, y + 1, id + 1);
+	cout << id << " ";
+}
+
+int main(){
+	s.resize(m);
+	visited.assign(m, vector<bool>(n, false));
+	ids.assign(m, vector<int>(n, 0));
+	char tmp;
+	for(int i = 0; i < m; i++){
+		for(int j = 0; j < n; j++){
+			cin >> tmp;
+			s[i].push_back(tmp);
+		}
+	}
+	for(int i = 0; i < m; i++){
+		for(int j = 0; j < n; j++){
+			if(!visited[i][j] && s[i][j] == '@') dfs(i, j, 1);
+		}
+	}
+	cout << endl;
+	int max = -1;
+	for(int i = 0; i < m; i++){
+		for(int j = 0; j < n; j++){
+			if(ids[i][j] > max) max = ids[i][j];
+		}
+	}
+	cout << max << endl;
+}

Algorithm/Graph/EulerGraph/UVa-10129-PlayOnWords.cpp

@@ -0,0 +1,80 @@
+#include <iostream>
+#include <vector>
+#include <deque>
+#include <string>
+using namespace std;
+struct Graph{
+	int v;
+	int e;
+	vector<vector<int>> adj;
+	vector<bool> visited;
+	
+	Graph(int _v) : v(_v) {
+		adj.resize(v);
+		visited.assign(v, false);
+	}
+	bool validateV(int _v){
+		return ( _v >= 0 && _v < v);
+	}
+	void insert(int _a, int _b){
+		if(!validateV(_a) || !validateV(_b)) return;
+		
+		adj[_a].push_back(_b);
+	}
+	int degree(int _v){
+		if(!validateV(_v)) return 0;
+		return outDegree(_v) + inDegree(_v);
+	}
+	int outDegree(int _v){
+		if(!validateV(_v)) return 0;
+		return adj[_v].size();
+	}
+	int inDegree(int _v){
+		if(!validateV(_v)) return 0;
+		int js = 0;
+		for(auto x : adj){
+			for(int i = 0; i < x.size(); i++){
+				if(x[i] == _v) js++;
+			}
+		}
+		return js;
+	}
+	void dfs(int _v){
+		if(!validateV(_v)) return;
+		if(visited[_v]) return;
+		visited[_v] = true;
+		for(auto x : adj[_v]){
+			dfs(x);
+		}
+	}
+	bool isConnected(){
+		dfs(0);
+		for(auto x : visited){
+			if(!x) return false;
+		}
+		
+		int js = 0;
+		for(int i = 0; i < v; i++){
+			if(degree(i) % 2 == 1) js++;
+		}
+		return (js == 0) || (js == 2);
+	}
+};
+int main(){
+	int n;
+	cin >> n;
+	Graph g(n);
+	vector<string> s;
+	s.resize(n);
+	for(int i = 0; i < n; i++){
+		cin >> s[i];
+	}
+	for(int i = 0; i < n; i++){
+		for(int j = 0; j < n; j++){
+			if(i != j && s[i].back() == s[j].front()) g.insert(i, j);
+		}
+	}
+	g.isConnected() ? cout << "YES" << endl : cout << "NO" << endl;
+	system("pause");
+	return 0;
+}

Algorithm/List/UVA11988 破损的键盘 Broken Keyboard (a.k.a. Beiju Text).cpp

@@ -0,0 +1,30 @@
+#include <iostream>
+#include <list>
+#include <string>
+using namespace std;
+
+int main() {
+    string line;
+    while (getline(cin, line)) {   // һ<>ζ<EFBFBD>һ<EFBFBD><D2BB><EFBFBD>У<EFBFBD>ֱ<EFBFBD><D6B1> EOF
+        list<char> s;
+        auto it = s.begin();
+
+        for (char tmp : line) {
+            if (tmp == '[') {
+                it = s.begin();
+            }
+            else if (tmp == ']') {
+                it = s.end();
+            }
+            else {
+                it = s.insert(it, tmp);
+                ++it;
+            }
+        }
+
+        for (char c : s) cout << c;
+        cout << '\n';  // ÿ<><C3BF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>
+    }
+    return 0;
+}
+

Algorithm/Maths/P1102 A-B数对/P1102 A-B 数对 set不过.cpp

@@ -0,0 +1,19 @@
+#include <set>
+#include <iostream>
+using namespace std;
+int main(){
+	multiset<int> s;
+	int n, m;
+	cin >> n >> m;
+	int tmp;
+	for(int i = 0; i < n; i++){
+		cin >> tmp;
+		s.emplace(tmp);
+	}
+	int js = 0;
+	for(auto it = s.begin(); it != s.end(); it++){
+		js += s.count(*it - m);
+	} 
+	cout << js << endl;
+	return 0;
+}

Algorithm/Maths/P1102 A-B数对/P1102 A-B 数对 unordered_map.cpp

@@ -0,0 +1,26 @@
+#include <unordered_map>
+#include <vector> 
+#include <iostream>
+//<2F><> hash + map <20><>ԭ<EFBFBD><D4AD><EFBFBD>Dz<EFBFBD>ϣ<EFBFBD><CFA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD> O(n^2) 
+using namespace std;
+int main(){
+	unordered_map<long long, int> s;
+	vector<long long> arr;
+	long long n, m;
+	cin >> n >> m;
+	long long tmp;
+	for(int i = 0; i < n; i++){
+		cin >> tmp;
+		arr.push_back(tmp);
+		s[tmp]++; 
+	}
+	long long need;
+	long long js = 0;
+	for(int i = 0; i < n; i++){
+		need = arr[i] - m;
+		if(s.count(need)) js += s[need];//s[need]<5D><>ֵ<EFBFBD><D6B5> pair.seconds 
+		//s.emplace(make_pair(arr[i], 1));//<2F><><EFBFBD>У<EFBFBD><D0A3><EFBFBD><EFBFBD><EFBFBD>arr[i]<5D><><EFBFBD>ڣ<EFBFBD><DAA3><EFBFBD>ֱ<EFBFBD>ӷ<EFBFBD><D3B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
+	}
+	cout << js << endl;
+	return 0;
+}

Algorithm/Maths/P1102 A-B数对/P1102 A-B 数对 unordered_set不过 有重复.cpp

@@ -0,0 +1,19 @@
+#include <unordered_set>
+#include <iostream>
+using namespace std;
+int main(){
+	unordered_multiset<int> s;
+	int n, m;
+	cin >> n >> m;
+	int tmp;
+	for(int i = 0; i < n; i++){
+		cin >> tmp;
+		s.emplace(tmp);
+	}
+	int js = 0;
+	for(auto it = s.begin(); it != s.end(); it++){
+		js += s.count(*it - m);
+	} 
+	cout << js << endl;
+	return 0;
+}

Algorithm/Recursion/UVA699 下落的树叶 The Falling Leaves.cpp

@@ -0,0 +1,24 @@
+#include <iostream>
+#include <map>
+using namespace std;
+//<2F><><EFBFBD>Ƿ<EFBFBD><C7B7><EFBFBD>
+
+map<int, int> sum;
+void build(int p){
+	int tmp;
+	cin >> tmp;
+	if(tmp == -1) return;
+	sum[p] += tmp;
+	build(p - 1);
+	build(p + 1);
+}
+
+int main(){
+	build(0);
+	if(!sum.empty()){
+		for(auto it = sum.begin(); it != sum.end(); ++it){
+			cout << it->second << " ";
+		}
+	}
+	return 0;
+} 

Algorithm/Recursion/UVa839 天平Not_so_Mobile.cpp

@@ -0,0 +1,58 @@
+#include <iostream>
+//ǰ<><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20>ݹ<EFBFBD><DDB9><EFBFBD><EFBFBD>컨<EFBFBD><ECBBA8> 
+using namespace std;
+struct mobile{
+	double lw, ll, rw, rl;
+	double weight;
+	mobile* left;
+	mobile* right;
+
+	mobile(double a, double b, double c, double d) : lw(a), ll(b), rw(c), rl(d), left(nullptr), right(nullptr) {}
+};
+
+bool solve(mobile* &x){
+	double a, b, c, d;
+	bool b1 = true, b2 = true;
+	cin >> a >> b >> c >> d;
+	x = new mobile(a, b, c, d);
+	if(!x->lw) b1 = solve(x->left);
+	if(!x->rw) b2 = solve(x->right);
+	double leftWeight  = x->left  ? x->left->weight  : x->lw;
+	double rightWeight = x->right ? x->right->weight : x->rw;
+	x->weight = leftWeight + rightWeight;
+	//<2F><>עreturn<72><6E><EFBFBD><EFBFBD><EFBFBD><EFBFBD>solveһ<65><D2BB><EFBFBD>Ǿ<EFBFBD><C7BE>Ƕ<EFBFBD><C7B6>εݹ<CEB5><DDB9>ˣ<EFBFBD><CBA3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>solve<76><65> 
+	return b1 && b2 && (leftWeight * x->ll == rightWeight * x->rl);
+
+}
+
+
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n;
+    cin >> n;
+    string tmp;
+    getline(cin, tmp); // <20><>ȡ<EFBFBD><C8A1>һ<EFBFBD>к<EFBFBD><D0BA>Ļ<EFBFBD><C4BB><EFBFBD>
+
+    for (int i = 0; i < n; i++) {
+        mobile* root = nullptr;
+        bool ok = solve(root);
+        cout << (ok ? "YES" : "NO") << "\n";
+
+        if (i != n - 1) cout << "\n"; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ѯ֮<D1AF><D6AE><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>
+    }
+	/*
+	for(int i = 0; i < n - 1; i++){
+		cin >> a >> b >> c >> d;
+		mobile* tmp = new mobile(a, b, c, d);
+		if(a && !b){
+			
+		}
+	}
+	<09><><EFBFBD>Dz<EFBFBD><C7B2>õģ<C3B5>Ӧ<EFBFBD><D3A6><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ȼ<EFBFBD><C8BB>Ȼ<EFBFBD><C8BB><EFBFBD>γ<EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD> 
+	*/
+	
+	return 0;
+}