Add C# code for the chapter Heap and Graph (#324)

* add : C# heap ,graph, fix type "sift"=>"shift"

* chore: rename "shift" to "sift"

* add: heap,graph C# sample code ,fix format

* fix md format

* fix md intend foramt

* fix basic_operation_of_graph.md format

* fix md format

* fix md format

* fix indentation format

* chore: fix my_heap.cs test

* fix: test and doc typo

* fix bug for commit 5eae708 (#317)

* Add Zig code blocks.

* fix: resolve build error for commit 5eae708 (#318)

* Unify the function naming of
queue from `offer()` to `push()`

* Update TypeScript codes.

* Update binary_search_tree

* Update graph operations.

* Fix code indentation.

* Update worst_best_time_complexity,
leetcode_two_sum

* Update avl_tree

* copy zig codes of chapter_array_and_linkedlist and chapter_computatio… (#319)

* copy zig codes of chapter_array_and_linkedlist and chapter_computational_complexity to markdown files

* Update time_complexity.md

---------

Co-authored-by: Yudong Jin <krahets@163.com>

* Fix Python code styles.
Update hash_map.

* chore: fix heap logic

* Update graph_adjacency_matrix.cs

* Update graph_adjacency_matrix.cs

* Update my_heap.cs

* fix: heap test

* fix naming format

* merge markdown

* fix markdown format

* Update graph_adjacency_list.cs

* Update graph_adjacency_matrix.cs

* Update PrintUtil.cs

* Create Vertex.cs

* Update heap.cs

---------

Co-authored-by: zjkung1123 <zjkung1123@fugle.tw>
Co-authored-by: sjinzh <99076655+sjinzh@users.noreply.github.com>
Co-authored-by: Yudong Jin <krahets@163.com>
Co-authored-by: nuomi1 <nuomi1@qq.com>

codes/csharp/chapter_graph/graph_adjacency_list.cs

@@ -0,0 +1,132 @@
+/**
+ * File: graph_adjacency_list.cs
+ * Created Time: 2023-02-06
+ * Author: zjkung1123 (zjkung1123@gmail.com)
+ */
+
+using hello_algo.include;
+using NUnit.Framework;
+
+namespace hello_algo.chapter_graph;
+
+/* 基于邻接表实现的无向图类 */
+class GraphAdjList
+{
+    // 邻接表 adjList 中的元素是 Vertex 对象
+    Dictionary<Vertex, List<Vertex>> adjList;
+
+    /* 构造函数 */
+    public GraphAdjList(Vertex[][] edges)
+    {
+        this.adjList = new Dictionary<Vertex, List<Vertex>>();
+        // 添加所有顶点和边
+        foreach (Vertex[] edge in edges)
+        {
+            addVertex(edge[0]);
+            addVertex(edge[1]);
+            addEdge(edge[0], edge[1]);
+        }
+    }
+
+    /* 获取顶点数量 */
+    public int size()
+    {
+        return adjList.Count;
+    }
+
+    /* 添加边 */
+    public void addEdge(Vertex vet1, Vertex vet2)
+    {
+        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)
+            throw new InvalidOperationException();
+        // 添加边 vet1 - vet2
+        adjList[vet1].Add(vet2);
+        adjList[vet2].Add(vet1);
+    }
+
+    /* 删除边 */
+    public void removeEdge(Vertex vet1, Vertex vet2)
+    {
+        if (!adjList.ContainsKey(vet1) || !adjList.ContainsKey(vet2) || vet1 == vet2)
+            throw new InvalidOperationException();
+        // 删除边 vet1 - vet2
+        adjList[vet1].Remove(vet2);
+        adjList[vet2].Remove(vet1);
+    }
+
+    /* 添加顶点 */
+    public void addVertex(Vertex vet)
+    {
+        if (adjList.ContainsKey(vet))
+            return;
+        // 在邻接表中添加一个新链表
+        adjList.Add(vet, new List<Vertex>());
+    }
+
+    /* 删除顶点 */
+    public void removeVertex(Vertex vet)
+    {
+        if (!adjList.ContainsKey(vet))
+            throw new InvalidOperationException();
+        // 在邻接表中删除顶点 vet 对应的链表
+        adjList.Remove(vet);
+        // 遍历其它顶点的链表，删除所有包含 vet 的边
+        foreach (List<Vertex> list in adjList.Values)
+        {
+            list.Remove(vet);
+        }
+    }
+
+    /* 打印邻接表 */
+    public void print()
+    {
+        Console.WriteLine("邻接表 =");
+        foreach (KeyValuePair<Vertex, List<Vertex>> entry in adjList)
+        {
+            List<int> tmp = new List<int>();
+            foreach (Vertex vertex in entry.Value)
+                tmp.Add(vertex.Val);
+            Console.WriteLine(entry.Key.Val + ": [" + string.Join(", ", tmp) + "],");
+        }
+    }
+}
+
+public class graph_adjacency_list
+{
+    [Test]
+    public void Test()
+    {
+        /* 初始化无向图 */
+        Vertex[] v = Vertex.valsToVets(new int[] { 1, 3, 2, 5, 4 });
+        Vertex[][] edges = new Vertex[][] { new Vertex[] { v[0], v[1] }, new Vertex[] { v[0], v[3] },
+                                            new Vertex[] { v[1], v[2] }, new Vertex[] { v[2], v[3] },
+                                            new Vertex[] { v[2], v[4] }, new Vertex[] { v[3], v[4] } };
+        GraphAdjList graph = new GraphAdjList(edges);
+        Console.WriteLine("\n初始化后，图为");
+        graph.print();
+
+        /* 添加边 */
+        // 顶点 1, 2 即 v[0], v[2]
+        graph.addEdge(v[0], v[2]);
+        Console.WriteLine("\n添加边 1-2 后，图为");
+        graph.print();
+
+        /* 删除边 */
+        // 顶点 1, 3 即 v[0], v[1]
+        graph.removeEdge(v[0], v[1]);
+        Console.WriteLine("\n删除边 1-3 后，图为");
+        graph.print();
+
+        /* 添加顶点 */
+        Vertex v5 = new Vertex(6);
+        graph.addVertex(v5);
+        Console.WriteLine("\n添加顶点 6 后，图为");
+        graph.print();
+
+        /* 删除顶点 */
+        // 顶点 3 即 v[1]
+        graph.removeVertex(v[1]);
+        Console.WriteLine("\n删除顶点 3 后，图为");
+        graph.print();
+    }
+}

codes/csharp/chapter_graph/graph_adjacency_matrix.cs

@@ -0,0 +1,149 @@
+/**
+ * File: graph_adjacency_list.cs
+ * Created Time: 2023-02-06
+ * Author: zjkung1123 (zjkung1123@gmail.com)
+ */
+
+using hello_algo.include;
+using NUnit.Framework;
+
+namespace hello_algo.chapter_graph;
+
+/* 基于邻接矩阵实现的无向图类 */
+class GraphAdjMat
+{
+    List<int> vertices;     // 顶点列表，元素代表“顶点值”，索引代表“顶点索引”
+    List<List<int>> adjMat; // 邻接矩阵，行列索引对应“顶点索引”
+
+    /* 构造函数 */
+    public GraphAdjMat(int[] vertices, int[][] edges)
+    {
+        this.vertices = new List<int>();
+        this.adjMat = new List<List<int>>();
+        // 添加顶点
+        foreach (int val in vertices)
+        {
+            addVertex(val);
+        }
+        // 添加边
+        // 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
+        foreach (int[] e in edges)
+        {
+            addEdge(e[0], e[1]);
+        }
+    }
+
+    /* 获取顶点数量 */
+    public int size()
+    {
+        return vertices.Count;
+    }
+
+    /* 添加顶点 */
+    public void addVertex(int val)
+    {
+        int n = size();
+        // 向顶点列表中添加新顶点的值
+        vertices.Add(val);
+        // 在邻接矩阵中添加一行
+        List<int> newRow = new List<int>(n);
+        for (int j = 0; j < n; j++)
+        {
+            newRow.Add(0);
+        }
+        adjMat.Add(newRow);
+        // 在邻接矩阵中添加一列
+        foreach (List<int> row in adjMat)
+        {
+            row.Add(0);
+        }
+    }
+
+    /* 删除顶点 */
+    public void removeVertex(int index)
+    {
+        if (index >= size())
+            throw new IndexOutOfRangeException();
+        // 在顶点列表中移除索引 index 的顶点
+        vertices.RemoveAt(index);
+        // 在邻接矩阵中删除索引 index 的行
+        adjMat.RemoveAt(index);
+        // 在邻接矩阵中删除索引 index 的列
+        foreach (List<int> row in adjMat)
+        {
+            row.RemoveAt(index);
+        }
+    }
+
+    /* 添加边 */
+    // 参数 i, j 对应 vertices 元素索引
+    public void addEdge(int i, int j)
+    {
+        // 索引越界与相等处理
+        if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
+            throw new IndexOutOfRangeException();
+        // 在无向图中，邻接矩阵沿主对角线对称，即满足 (i, j) == (j, i)
+        adjMat[i][j] = 1;
+        adjMat[j][i] = 1;
+    }
+
+    /* 删除边 */
+    // 参数 i, j 对应 vertices 元素索引
+    public void removeEdge(int i, int j)
+    {
+        // 索引越界与相等处理
+        if (i < 0 || j < 0 || i >= size() || j >= size() || i == j)
+            throw new IndexOutOfRangeException();
+        adjMat[i][j] = 0;
+        adjMat[j][i] = 0;
+    }
+    
+    /* 打印邻接矩阵 */
+    public void print()
+    {
+        Console.Write("顶点列表 = ");
+        PrintUtil.PrintList(vertices);
+        Console.WriteLine("邻接矩阵 =");
+        PrintUtil.printMatrix(adjMat);
+    }
+}
+
+public class graph_adjacency_matrix
+{
+    [Test]
+    public void Test()
+    {
+        /* 初始化无向图 */
+        // 请注意，edges 元素代表顶点索引，即对应 vertices 元素索引
+        int[] vertices = { 1, 3, 2, 5, 4 };
+        int[][] edges = new int[][] { new int[] { 0, 1 }, new int[] { 0, 3 },
+                                      new int[] { 1, 2 }, new int[] { 2, 3 },
+                                      new int[] { 2, 4 }, new int[] { 3, 4 } };
+        GraphAdjMat graph = new GraphAdjMat(vertices, edges);
+        Console.WriteLine("\n初始化后，图为");
+        graph.print();
+
+        /* 添加边 */
+        // 顶点 1, 2 的索引分别为 0, 2
+        graph.addEdge(0, 2);
+        Console.WriteLine("\n添加边 1-2 后，图为");
+        graph.print();
+
+        /* 删除边 */
+        // 顶点 1, 3 的索引分别为 0, 1
+        graph.removeEdge(0, 1);
+        Console.WriteLine("\n删除边 1-3 后，图为");
+        graph.print();
+
+        /* 添加顶点 */
+        graph.addVertex(6);
+        Console.WriteLine("\n添加顶点 6 后，图为");
+        graph.print();
+
+        /* 删除顶点 */
+        // 顶点 3 的索引为 1
+        graph.removeVertex(1);
+        Console.WriteLine("\n删除顶点 3 后，图为");
+        graph.print();
+    }
+}

codes/csharp/chapter_heap/heap.cs

@@ -0,0 +1,70 @@
+/**
+ * File: heap.cs
+ * Created Time: 2023-02-06
+ * Author: zjkung1123 (zjkung1123@gmail.com)
+ */
+
+using hello_algo.include;
+using NUnit.Framework;
+
+namespace hello_algo.chapter_heap;
+
+public class heap
+{
+    public void testPush(PriorityQueue<int, int> heap, int val)
+    {
+        heap.Enqueue(val, val); // 元素入堆
+        Console.WriteLine($"\n元素 {val} 入堆后\n");
+        PrintUtil.printHeap(heap);
+    }
+
+    public void testPoll(PriorityQueue<int, int> heap)
+    {
+        int val = heap.Dequeue(); // 堆顶元素出堆
+        Console.WriteLine($"\n堆顶元素 {val} 出堆后\n");
+        PrintUtil.printHeap(heap);
+    }
+    [Test]
+    public void Test()
+    {
+        /* 初始化堆 */
+        // 初始化小顶堆
+        PriorityQueue<int, int> minHeap = new PriorityQueue<int, int>();
+        // 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）
+        PriorityQueue<int, int> maxHeap = new PriorityQueue<int, int>(Comparer<int>.Create((x, y) => y - x));
+        Console.WriteLine("以下测试样例为大顶堆");
+
+        /* 元素入堆 */
+        testPush(maxHeap, 1);
+        testPush(maxHeap, 3);
+        testPush(maxHeap, 2);
+        testPush(maxHeap, 5);
+        testPush(maxHeap, 4);
+
+        /* 获取堆顶元素 */
+        int peek = maxHeap.Peek();
+        Console.WriteLine($"堆顶元素为 {peek}");
+
+        /* 堆顶元素出堆 */
+        // 出堆元素会形成一个从大到小的序列
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+        testPoll(maxHeap);
+
+        /* 获取堆大小 */
+        int size = maxHeap.Count;
+        Console.WriteLine($"堆元素数量为 {size}");
+
+        /* 判断堆是否为空 */
+        bool isEmpty = maxHeap.Count == 0;
+        Console.WriteLine($"堆是否为空 {isEmpty}");
+
+        /* 输入列表并建堆 */
+        var list = new int[] { 1, 3, 2, 5, 4 };
+        minHeap = new PriorityQueue<int, int>(list.Select(x => (x, x)));
+        Console.WriteLine("输入列表并建立小顶堆后");
+        PrintUtil.printHeap(minHeap);
+    }
+}

codes/csharp/chapter_heap/my_heap.cs

@@ -0,0 +1,183 @@
+/**
+ * File: my_heap.cs
+ * Created Time: 2023-02-06
+ * Author: zjkung1123 (zjkung1123@gmail.com)
+ */
+
+using hello_algo.include;
+using NUnit.Framework;
+
+namespace hello_algo.chapter_heap;
+
+/* 大顶堆 */
+class MaxHeap
+{
+    // 使用列表而非数组，这样无需考虑扩容问题
+    private readonly List<int> maxHeap;
+
+    /* 构造函数，建立空堆 */
+    public MaxHeap()
+    {
+        maxHeap = new List<int>();
+    }
+
+    /* 构造函数，根据输入列表建堆 */
+    public MaxHeap(IEnumerable<int> nums)
+    {
+        // 将列表元素原封不动添加进堆
+        maxHeap = new List<int>(nums);
+        // 堆化除叶结点以外的其他所有结点
+        var size = parent(this.size() - 1);
+        for (int i = size; i >= 0; i--)
+        {
+            siftDown(i);
+        }
+    }
+
+    /* 获取左子结点索引 */
+    int left(int i)
+    {
+        return 2 * i + 1;
+    }
+
+    /* 获取右子结点索引 */
+    int right(int i)
+    {
+        return 2 * i + 2;
+    }
+
+    /* 获取父结点索引 */
+    int parent(int i)
+    {
+        return (i - 1) / 2; // 向下整除
+    }
+
+    /* 访问堆顶元素 */
+    public int peek()
+    {
+        return maxHeap[0];
+    }
+
+    /* 元素入堆 */
+    public void push(int val)
+    {
+        // 添加结点
+        maxHeap.Add(val);
+        // 从底至顶堆化
+        siftUp(size() - 1);
+    }
+
+    /* 获取堆大小 */
+    public int size()
+    {
+        return maxHeap.Count;
+    }
+
+    /* 判断堆是否为空 */
+    public bool isEmpty()
+    {
+        return size() == 0;
+    }
+
+    /* 从结点 i 开始，从底至顶堆化 */
+    void siftUp(int i)
+    {
+        while (true)
+        {
+            // 获取结点 i 的父结点
+            int p = parent(i);
+            // 若“越过根结点”或“结点无需修复”，则结束堆化
+            if (p < 0 || maxHeap[i] <= maxHeap[p])
+                break;
+            // 交换两结点
+            swap(i, p);
+            // 循环向上堆化
+            i = p;
+        }
+    }
+
+    /* 元素出堆 */
+    public int poll()
+    {
+        // 判空处理
+        if (isEmpty())
+            throw new IndexOutOfRangeException();
+        // 交换根结点与最右叶结点（即交换首元素与尾元素）
+        swap(0, size() - 1);
+        // 删除结点
+        int val = maxHeap.Last();
+        maxHeap.RemoveAt(size() - 1);
+        // 从顶至底堆化
+        siftDown(0);
+        // 返回堆顶元素
+        return val;
+    }
+
+    /* 从结点 i 开始，从顶至底堆化 */
+    void siftDown(int i)
+    {
+        while (true)
+        {
+            // 判断结点 i, l, r 中值最大的结点，记为 ma
+            int l = left(i), r = right(i), ma = i;
+            if (l < size() && maxHeap[l] > maxHeap[ma])
+                ma = l;
+            if (r < size() && maxHeap[r] > maxHeap[ma])
+                ma = r;
+            // 若“结点 i 最大”或“越过叶结点”，则结束堆化
+            if (ma == i) break;
+            // 交换两结点
+            swap(i, ma);
+            // 循环向下堆化
+            i = ma;
+        }
+    }
+
+    /* 交换元素 */
+    void swap(int i, int p)
+    {
+        (maxHeap[i], maxHeap[p]) = (maxHeap[p], maxHeap[i]);
+    }
+
+    /* 打印堆（二叉树） */
+    public void print()
+    {
+        var queue = new Queue<int>(maxHeap);
+        PrintUtil.printHeap(queue);
+    }
+}
+
+public class my_heap
+{
+    [Test]
+    public void Test()
+    {
+        /* 初始化大顶堆 */
+        MaxHeap maxHeap = new MaxHeap(new int[] { 9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2 });
+        Console.WriteLine("\n输入列表并建堆后");
+        maxHeap.print();
+
+        /* 获取堆顶元素 */
+        int peek = maxHeap.peek();
+        Console.WriteLine($"堆顶元素为 {peek}");
+
+        /* 元素入堆 */
+        int val = 7;
+        maxHeap.push(val);
+        Console.WriteLine($"元素 {val} 入堆后");
+        maxHeap.print();
+
+        /* 堆顶元素出堆 */
+        peek = maxHeap.poll();
+        Console.WriteLine($"堆顶元素 {peek} 出堆后");
+        maxHeap.print();
+
+        /* 获取堆大小 */
+        int size = maxHeap.size();
+        Console.WriteLine($"堆元素数量为 {size}");
+
+        /* 判断堆是否为空 */
+        bool isEmpty = maxHeap.isEmpty();
+        Console.WriteLine($"堆是否为空 {isEmpty}");
+    }
+}

codes/csharp/include/PrintUtil.cs

@@ -1,8 +1,8 @@
-/**
- * File: PrintUtil.cs
- * Created Time: 2022-12-23
- * Author: haptear (haptear@hotmail.com)
- */
+/**
+* File: PrintUtil.cs
+* Created Time: 2022-12-23
+* Author: haptear (haptear@hotmail.com), krahets (krahets@163.com)
+*/
 
 namespace hello_algo.include;
 
@@ -20,6 +20,15 @@ public class Trunk
 
 public class PrintUtil
 {
+    /**
+     * Print a list
+     * @param list
+     */
+    public static void PrintList(List<int> list)
+    {
+        Console.WriteLine("[" + string.Join(", ", list) + "]");
+    }
+
     /**
      * Print a linked list
      * @param head
@@ -119,4 +128,39 @@ public class PrintUtil
             Console.WriteLine(kv.ToString() + " -> " + map[kv]?.ToString());
         }
     }
+
+    public static void printHeap(Queue<int> queue)
+    {
+        Console.Write("堆的数组表示：");
+        List<int> list = queue.ToList();
+        Console.WriteLine(string.Join(',', list));
+        Console.WriteLine("堆的树状表示：");
+        TreeNode tree = TreeNode.ArrToTree(list.Cast<int?>().ToArray());
+        PrintTree(tree);
+    }
+
+    public static void printHeap(PriorityQueue<int, int> queue)
+    {
+        var newQueue = new PriorityQueue<int, int>(queue.UnorderedItems, queue.Comparer);
+        Console.Write("堆的数组表示：");    
+        List<int> list = new List<int>();
+        while (newQueue.TryDequeue(out int element, out int priority))
+        {
+            list.Add(element);
+        }
+        Console.WriteLine("堆的树状表示：");
+        Console.WriteLine(string.Join(',', list.ToList()));
+        TreeNode tree = TreeNode.ArrToTree(list.Cast<int?>().ToArray());
+        PrintTree(tree);
+    }
+
+    public static void printMatrix(List<List<int>> matrix)
+    {
+        Console.WriteLine("[");
+        foreach (List<int> row in matrix)
+        {
+            Console.WriteLine("  [" + string.Join(", ", row.Select(r => $"{r}")) + "],");
+        }
+        Console.WriteLine("]");
+    }
 }

codes/csharp/include/Vertex.cs

@@ -0,0 +1,37 @@
+/**
+ * File: graph_adjacency_list.cs
+ * Created Time: 2023-02-06
+ * Author: zjkung1123 (zjkung1123@gmail.com), krahets (krahets@163.com)
+ */
+
+/* 顶点类 */
+class Vertex
+{
+    public int Val { get; init; }
+    public Vertex(int val)
+    {
+        Val = val;
+    }
+
+    /* 输入值列表 vals ，返回顶点列表 vets */
+    public static Vertex[] valsToVets(int[] vals)
+    {
+        Vertex[] vets = new Vertex[vals.Length];
+        for (int i = 0; i < vals.Length; i++)
+        {
+            vets[i] = new Vertex(vals[i]);
+        }
+        return vets;
+    }
+
+    /* 输入顶点列表 vets ，返回值列表 vals */
+    public static List<int> vetsToVals(List<Vertex> vets)
+    {
+        List<int> vals = new List<int>();
+        foreach (Vertex vet in vets)
+        {
+            vals.Add(vet.Val);
+        }
+        return vals;
+    }
+}

docs/chapter_heap/heap.md

@@ -226,7 +226,39 @@ comments: true
 === "C#"
 
     ```csharp title="heap.cs"
+    /* 初始化堆 */
+    // 初始化小顶堆
+    PriorityQueue<int, int> minHeap = new PriorityQueue<int, int>();
+    // 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）
+    PriorityQueue<int, int> maxHeap = new PriorityQueue<int, int>(Comparer<int>.Create((x, y) => y - x));
+
+    /* 元素入堆 */
+    maxHeap.Enqueue(1, 1);
+    maxHeap.Enqueue(3, 3);
+    maxHeap.Enqueue(2, 2);
+    maxHeap.Enqueue(5, 5);
+    maxHeap.Enqueue(4, 4);
+
+    /* 获取堆顶元素 */
+    int peek = maxHeap.Peek();//5
+
 
+    /* 堆顶元素出堆 */
+    // 出堆元素会形成一个从大到小的序列
+    peek = maxHeap.Dequeue();  // 5
+    peek = maxHeap.Dequeue();  // 4
+    peek = maxHeap.Dequeue();  // 3
+    peek = maxHeap.Dequeue();  // 2
+    peek = maxHeap.Dequeue();  // 1
+
+    /* 获取堆大小 */
+    int size = maxHeap.Count;
+
+    /* 判断堆是否为空 */
+    bool isEmpty = maxHeap.Count == 0;
+
+    /* 输入列表并建堆 */
+    minHeap = new PriorityQueue<int, int>(new List<(int, int)> { (1, 1), (3, 3), (2, 2), (5, 5), (4, 4), });
     ```
 
 === "Swift"