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完善所以c#相关的文档和代码

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zhuzhiqing
2022-12-23 15:42:02 +08:00
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264
codes/csharp/chapter_tree/avl_tree.cs Normal file
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using hello_algo.include;
using NUnit.Framework;
using System.Collections.Generic;
namespace hello_algo.chapter_tree
{
// Tree class
class AVLTree
{
public TreeNode? root; // 根节点
/* 获取结点高度 */
public int height(TreeNode? node)
{
// 空结点高度为 -1 ，叶结点高度为 0
return node == null ? -1 : node.height;
}
/* 更新结点高度 */
private void updateHeight(TreeNode node)
{
// 结点高度等于最高子树高度 + 1
node.height = Math.Max(height(node.left), height(node.right)) + 1;
}
/* 获取平衡因子 */
public int balanceFactor(TreeNode? node)
{
// 空结点平衡因子为 0
if (node == null) return 0;
// 结点平衡因子 = 左子树高度 - 右子树高度
return height(node.left) - height(node.right);
}
/* 右旋操作 */
TreeNode? rightRotate(TreeNode? node)
{
if (node == null)
return null;
TreeNode? child = node.left;
TreeNode? grandChild = child?.right;
// 以 child 为原点，将 node 向右旋转
child.right = node;
node.left = grandChild;
// 更新结点高度
updateHeight(node);
updateHeight(child);
// 返回旋转后子树的根节点
return child;
}
/* 左旋操作 */
TreeNode? leftRotate(TreeNode? node)
{
if (node == null)
return null;
TreeNode? child = node.right;
TreeNode? grandChild = child?.left;
// 以 child 为原点，将 node 向左旋转
child.left = node;
node.right = grandChild;
// 更新结点高度
updateHeight(node);
updateHeight(child);
// 返回旋转后子树的根节点
return child;
}
/* 执行旋转操作，使该子树重新恢复平衡 */
private TreeNode? rotate(TreeNode? node)
{
if (node == null)
return node;
// 获取结点 node 的平衡因子
int balanceFactorInt = balanceFactor(node);
// 左偏树
if (balanceFactorInt > 1)
{
if (balanceFactor(node.left) >= 0)
{
// 右旋
return rightRotate(node);
}
else
{
// 先左旋后右旋
node.left = leftRotate(node?.left);
return rightRotate(node);
}
}
// 右偏树
if (balanceFactorInt < -1)
{
if (balanceFactor(node.right) <= 0)
{
// 左旋
return leftRotate(node);
}
else
{
// 先右旋后左旋
node.right = rightRotate(node?.right);
return leftRotate(node);
}
}
// 平衡树，无需旋转，直接返回
return node;
}
/* 插入结点 */
public TreeNode? insert(int val)
{
root = insertHelper(root, val);
return root;
}
/* 递归插入结点（辅助函数） */
private TreeNode? insertHelper(TreeNode? node, int val)
{
if (node == null) return new TreeNode(val);
/* 1. 查找插入位置，并插入结点 */
if (val < node.val)
node.left = insertHelper(node.left, val);
else if (val > node.val)
node.right = insertHelper(node.right, val);
else
return node; // 重复结点不插入，直接返回
updateHeight(node); // 更新结点高度
/* 2. 执行旋转操作，使该子树重新恢复平衡 */
node = rotate(node);
// 返回子树的根节点
return node;
}
/* 删除结点 */
public TreeNode? remove(int val)
{
root = removeHelper(root, val);
return root;
}
/* 递归删除结点（辅助函数） */
private TreeNode? removeHelper(TreeNode? node, int? val)
{
if (node == null) return null;
/* 1. 查找结点，并删除之 */
if (val < node.val)
node.left = removeHelper(node.left, val);
else if (val > node.val)
node.right = removeHelper(node.right, val);
else
{
if (node.left == null || node.right == null)
{
TreeNode? child = node.left != null ? node.left : node.right;
// 子结点数量 = 0 ，直接删除 node 并返回
if (child == null)
return null;
// 子结点数量 = 1 ，直接删除 node
else
node = child;
}
else
{
// 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点
TreeNode? temp = minNode(node.right);
node.right = removeHelper(node.right, temp?.val);
node.val = temp?.val;
}
}
updateHeight(node); // 更新结点高度
/* 2. 执行旋转操作，使该子树重新恢复平衡 */
node = rotate(node);
// 返回子树的根节点
return node;
}
/* 获取最小结点 */
private TreeNode? minNode(TreeNode? node)
{
if (node == null) return node;
// 循环访问左子结点，直到叶结点时为最小结点，跳出
while (node.left != null)
{
node = node.left;
}
return node;
}
/* 查找结点 */
public TreeNode? search(int val)
{
TreeNode? cur = root;
// 循环查找，越过叶结点后跳出
while (cur != null)
{
// 目标结点在 root 的右子树中
if (cur.val < val)
cur = cur.right;
// 目标结点在 root 的左子树中
else if (cur.val > val)
cur = cur.left;
// 找到目标结点，跳出循环
else
break;
}
// 返回目标结点
return cur;
}
}
public class avl_tree
{
static void testInsert(AVLTree tree, int val)
{
tree.insert(val);
Console.WriteLine("\n插入结点 " + val + " 后，AVL 树为");
PrintUtil.printTree(tree.root);
}
static void testRemove(AVLTree tree, int val)
{
tree.remove(val);
Console.WriteLine("\n删除结点 " + val + " 后，AVL 树为");
PrintUtil.printTree(tree.root);
}
[Test]
public void Test()
{
/* 初始化空 AVL 树 */
AVLTree avlTree = new AVLTree();
/* 插入结点 */
// 请关注插入结点后，AVL 树是如何保持平衡的
testInsert(avlTree, 1);
testInsert(avlTree, 2);
testInsert(avlTree, 3);
testInsert(avlTree, 4);
testInsert(avlTree, 5);
testInsert(avlTree, 8);
testInsert(avlTree, 7);
testInsert(avlTree, 9);
testInsert(avlTree, 10);
testInsert(avlTree, 6);
/* 插入重复结点 */
testInsert(avlTree, 7);
/* 删除结点 */
// 请关注删除结点后，AVL 树是如何保持平衡的
testRemove(avlTree, 8); // 删除度为 0 的结点
testRemove(avlTree, 5); // 删除度为 1 的结点
testRemove(avlTree, 4); // 删除度为 2 的结点
/* 查询结点 */
TreeNode? node = avlTree.search(7);
Console.WriteLine("\n查找到的结点对象为 " + node + "，结点值 = " + node?.val);
}
}
}

181
codes/csharp/chapter_tree/binary_search_tree.cs Normal file
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using hello_algo.include;
using NUnit.Framework;
using System.Collections.Generic;
namespace hello_algo.chapter_tree
{
internal class binary_search_tree
{
TreeNode? root;
/// <summary>
/// 查找结点
/// </summary>
/// <param name="num"></param>
/// <returns></returns>
TreeNode? search(int num)
{
TreeNode? cur = root;
// 循环查找，越过叶结点后跳出
while (cur != null)
{
// 目标结点在 root 的右子树中
if (cur.val < num) cur = cur.right;
// 目标结点在 root 的左子树中
else if (cur.val > num) cur = cur.left;
// 找到目标结点，跳出循环
else break;
}
// 返回目标结点
return cur;
}
/// <summary>
/// 插入结点
/// </summary>
/// <param name="num"></param>
/// <returns></returns>
TreeNode? insert(int num)
{
// 若树为空，直接提前返回
if (root == null) return null;
TreeNode? cur = root, pre = null;
// 循环查找，越过叶结点后跳出
while (cur != null)
{
// 找到重复结点，直接返回
if (cur.val == num) return null;
pre = cur;
// 插入位置在 root 的右子树中
if (cur.val < num) cur = cur.right;
// 插入位置在 root 的左子树中
else cur = cur.left;
}
// 插入结点 val
TreeNode node = new TreeNode(num);
if (pre != null)
{
if (pre.val < num) pre.right = node;
else pre.left = node;
}
return node;
}
/* 删除结点 */
TreeNode? remove(int? num)
{
// 若树为空，直接提前返回
if (root == null) return null;
TreeNode? cur = root, pre = null;
// 循环查找，越过叶结点后跳出
while (cur != null)
{
// 找到待删除结点，跳出循环
if (cur.val == num) break;
pre = cur;
// 待删除结点在 root 的右子树中
if (cur.val < num) cur = cur.right;
// 待删除结点在 root 的左子树中
else cur = cur.left;
}
// 若无待删除结点，则直接返回
if (cur == null || pre == null) return null;
// 子结点数量 = 0 or 1
if (cur.left == null || cur.right == null)
{
// 当子结点数量 = 0 / 1 时， child = null / 该子结点
TreeNode? child = cur.left != null ? cur.left : cur.right;
// 删除结点 cur
if (pre.left == cur)
{
pre.left = child;
}
else
{
pre.right = child;
}
}
// 子结点数量 = 2
else
{
// 获取中序遍历中 cur 的下一个结点
TreeNode? nex = min(cur.right);
if (nex != null)
{
int? tmp = nex.val;
// 递归删除结点 nex
remove(nex.val);
// 将 nex 的值复制给 cur
cur.val = tmp;
}
}
return cur;
}
/* 获取最小结点 */
TreeNode? min(TreeNode? root)
{
if (root == null) return root;
// 循环访问左子结点，直到叶结点时为最小结点，跳出
while (root.left != null)
{
root = root.left;
}
return root;
}
[Test]
public void Test()
{
// 初始化结点
TreeNode n1 = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
TreeNode n6 = new TreeNode(6);
TreeNode n7 = new TreeNode(7);
TreeNode n8 = new TreeNode(8);
TreeNode n9 = new TreeNode(9);
TreeNode n10 = new TreeNode(10);
TreeNode n11 = new TreeNode(11);
TreeNode n12 = new TreeNode(12);
TreeNode n13 = new TreeNode(13);
TreeNode n14 = new TreeNode(14);
TreeNode n15 = new TreeNode(15);
root = n8;
root.left = n4;
root.right = n12;
n4.left = n2;
n4.right = n6;
n12.left = n10;
n12.right = n14;
n2.left = n1;
n2.right = n3;
n6.left = n5;
n6.right = n7;
n10.left = n9;
n10.right = n11;
n14.left = n13;
n14.right = n15;
var cur = search(7);
Console.WriteLine("查找结点 结果 = " + cur?.val);
var node = insert(16);
Console.WriteLine("插入结点 结果 = " + node?.val);
node = remove(1);
Console.WriteLine("删除结点 结果 = " + node?.val);
node = remove(2);
Console.WriteLine("删除结点 结果 = " + node?.val);
node = remove(4);
Console.WriteLine("删除结点 结果 = " + node?.val);
}
}
}

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codes/csharp/chapter_tree/binary_tree.cs Normal file
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using hello_algo.include;
using NUnit.Framework;
using System.Collections.Generic;
namespace hello_algo.chapter_tree
{
public class binary_tree
{
[Test]
public void Test()
{
/* 初始化二叉树 */
// 初始化结点
TreeNode n1 = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
// 构建引用指向（即指针）
n1.left = n2;
n1.right = n3;
n2.left = n4;
n2.right = n5;
Console.WriteLine("\n初始化二叉树\n");
PrintUtil.printTree(n1);
/* 插入与删除结点 */
TreeNode P = new TreeNode(0);
// 在 n1 -> n2 中间插入结点 P
n1.left = P;
P.left = n2;
Console.WriteLine("\n插入结点 P 后\n");
PrintUtil.printTree(n1);
// 删除结点 P
n1.left = n2;
Console.WriteLine("\n删除结点 P 后\n");
PrintUtil.printTree(n1);
}
}
}

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codes/csharp/chapter_tree/binary_tree_bfs.cs Normal file
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using hello_algo.include;
using NUnit.Framework;
namespace hello_algo.chapter_tree
{
public class binary_tree_bfs
{
/// <summary>
/// 层序遍历
/// </summary>
/// <param name="root"></param>
/// <returns></returns>
public List<int?> hierOrder(TreeNode root)
{
// 初始化队列，加入根结点
Queue<TreeNode> queue = new();
queue.Enqueue(root);
// 初始化一个列表，用于保存遍历序列
List<int?> list = new();
while (queue.Count != 0)
{
TreeNode node = queue.Dequeue(); // 队列出队
list.Add(node.val); // 保存结点值
if (node.left != null)
queue.Enqueue(node.left); // 左子结点入队
if (node.right != null)
queue.Enqueue(node.right); // 右子结点入队
}
return list;
}
List<int?> list = new();
/// <summary>
/// 前序遍历
/// </summary>
/// <param name="root"></param>
void preOrder(TreeNode? root)
{
if (root == null) return;
// 访问优先级：根结点 -> 左子树 -> 右子树
list.Add(root.val);
preOrder(root.left);
preOrder(root.right);
}
/// <summary>
/// 中序遍历
/// </summary>
/// <param name="root"></param>
void inOrder(TreeNode? root)
{
if (root == null) return;
// 访问优先级：左子树 -> 根结点 -> 右子树
inOrder(root.left);
list.Add(root.val);
inOrder(root.right);
}
/// <summary>
/// 后序遍历
/// </summary>
/// <param name="root"></param>
void postOrder(TreeNode? root)
{
if (root == null) return;
// 访问优先级：左子树 -> 右子树 -> 根结点
postOrder(root.left);
postOrder(root.right);
list.Add(root.val);
}
/// <summary>
/// 辅助函数,数组转字符串
/// </summary>
public static string ToString(int?[] nums)
{
return string.Join(",", nums);
}
[Test]
public void Test()
{
// 初始化结点
TreeNode root = new TreeNode(1);
TreeNode n2 = new TreeNode(2);
TreeNode n3 = new TreeNode(3);
TreeNode n4 = new TreeNode(4);
TreeNode n5 = new TreeNode(5);
TreeNode n6 = new TreeNode(6);
TreeNode n7 = new TreeNode(7);
// 构建引用指向（即指针）
root.left = n2;
root.right = n3;
n2.left = n4;
n2.right = n5;
n3.left = n6;
n3.right = n7;
list = hierOrder(root);
Console.WriteLine("层序遍历 结果 = " + ToString(list.ToArray()));
list = new List<int?>();
preOrder(root);
Console.WriteLine("前序遍历 结果 = " + ToString(list.ToArray()));
list = new List<int?>();
inOrder(root);
Console.WriteLine("中序遍历 结果 = " + ToString(list.ToArray()));
list = new List<int?>();
postOrder(root);
Console.WriteLine("后序遍历 结果 = " + ToString(list.ToArray()));
}
}
}