更新树的5道题

树与二叉树/二叉树的概念/P134.5.cpp

@@ -70,7 +70,7 @@ int main()
     CreatTree(t, input);
     PreOrder(t,1);
     cout << endl;
-    cout << "公共祖先为：" << FindCom_Ancestor(t, 10, 4);
+    cout << "公共祖先为：" << FindCom_Ancestor(t, 10, 4) << endl;
     return 0;
 }
 /* 

树与二叉树/二叉树的遍历和线索二叉树/P149.3.cpp

@@ -0,0 +1,111 @@
+#include <iostream>
+#include <stack>
+using namespace std;
+
+#pragma region 构造链式存储的二叉树
+
+#define MaxSize 100
+#define ElemType char
+#define _for(i,a,b) for(int i=(a);i<(b);i++)
+
+typedef struct node { //树的结点
+    ElemType val;
+    node* lchild;
+    node* rchild;
+}Node, *BiTree;
+
+void CreateBiTree(BiTree& T)//要改变指针，C++可以把指针的引用传进来
+{
+    ElemType ch;
+
+    cin >> ch;
+
+    if (ch == '#')
+        T = NULL;
+    else
+    {
+        T = new Node;
+        T->val = ch;
+        CreateBiTree(T->lchild);
+        CreateBiTree(T->rchild);
+    }
+}
+
+
+void visit(Node* BiNode) {
+    cout << BiNode->val << " ";
+}
+
+void InOrder(BiTree T){
+    if (T != NULL) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P149.3
+//编写后序遍历二叉树的非递归算法。
+
+stack<Node*> s;
+
+void PostOrder(BiTree T) {
+    BiTree p = T, r = NULL;
+    while (p || !s.empty()) {
+        if (p) {
+            s.push(p);
+            p = p->lchild;
+        }
+        else {
+            p = s.top();
+            if (p->rchild && p->rchild != r) {
+                p = p->rchild;
+                s.push(p);
+                p = p->lchild;
+            }
+            else {
+                Node* q = s.top();
+                s.pop();
+                visit(q);
+                r = q;
+                p = NULL;
+            }
+        }
+    }
+
+}
+
+
+
+
+int main()
+{
+    BiTree T;
+    cout << "请输入先序遍历顺序下各个结点的值,'#'表示没有结点:" << endl;
+//  input: A B D H # # I # # E # J # # C F # K # # G # #
+    CreateBiTree(T);
+    cout << "中序遍历：" << endl;
+    InOrder(T);
+    cout << endl;
+    cout << "非递归后序遍历：" << endl;
+    PostOrder(T);
+    cout << endl;
+    return 0;
+}
+
+
+
+
+/*
+
+                                            A
+                            B                               C
+                     D             E                 F             G
+               H           I Ø           J    Ø           K Ø           Ø 
+              Ø Ø        Ø Ø           Ø Ø              Ø Ø
+
+
+ 树的图片链接：https://s3.ax1x.com/2021/02/03/yKIbiq.png
+*/

树与二叉树/二叉树的遍历和线索二叉树/P149.4.cpp

@@ -0,0 +1,103 @@
+#include <iostream>
+#include <stack>
+#include <queue>
+using namespace std;
+
+#pragma region 构造链式存储的二叉树
+
+#define MaxSize 100
+#define ElemType char
+#define _for(i,a,b) for(int i=(a);i<(b);i++)
+
+typedef struct node { //树的结点
+    ElemType val;
+    node* lchild;
+    node* rchild;
+}Node, * BiTree;
+
+void CreateBiTree(BiTree& T)//要改变指针，C++可以把指针的引用传进来
+{
+    ElemType ch;
+
+    cin >> ch;
+
+    if (ch == '#')
+        T = NULL;
+    else
+    {
+        T = new Node;
+        T->val = ch;
+        CreateBiTree(T->lchild);
+        CreateBiTree(T->rchild);
+    }
+}
+
+
+void visit(Node* BiNode) {
+    cout << BiNode->val << " ";
+}
+
+void InOrder(BiTree T) {
+    if (T != NULL) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P149.4
+//试给出二叉树的自下而上、从右到左的层次遍历算法
+
+queue<Node*> q;
+stack<Node*> s;
+
+void LevelOrder(BiTree T) {
+    q.push(T);
+    while (!q.empty()) {
+        Node* t = q.front();
+        q.pop();
+        s.push(t);
+        if (t->lchild)
+            q.push(t->lchild);
+        if (t->rchild)
+            q.push(t->rchild);
+    }
+    while (!s.empty()) {
+        Node* x = s.top();
+        s.pop();
+        visit(x);
+    }
+}
+
+
+int main()
+{
+    BiTree T;
+    cout << "请输入先序遍历顺序下各个结点的值,'#'表示没有结点:" << endl;
+    //  input: A B D H # # I # # E # J # # C F # K # # G # #
+    CreateBiTree(T);
+    cout << "中序遍历：" << endl;
+    InOrder(T);
+    cout << endl;
+    cout << "层次遍历：" << endl;
+    LevelOrder(T);
+    cout << endl;
+    return 0;
+}
+
+
+
+
+/*
+
+                                            A
+                            B                               C
+                     D             E                 F             G
+               H           I Ø           J    Ø           K Ø           Ø
+              Ø Ø        Ø Ø           Ø Ø              Ø Ø
+
+
+ 树的图片链接：https://s3.ax1x.com/2021/02/03/yKIbiq.png
+*/

树与二叉树/二叉树的遍历和线索二叉树/P149.5.cpp

@@ -0,0 +1,112 @@
+#include <iostream>
+#include <stack>
+#include <queue>
+using namespace std;
+
+#pragma region 构造链式存储的二叉树
+
+#define MaxSize 100
+#define ElemType char
+#define _for(i,a,b) for(int i=(a);i<(b);i++)
+
+typedef struct node { //树的结点
+    ElemType val;
+    node* lchild;
+    node* rchild;
+}Node, * BiTree;
+
+void CreateBiTree(BiTree& T)//要改变指针，C++可以把指针的引用传进来
+{
+    ElemType ch;
+
+    cin >> ch;
+
+    if (ch == '#')
+        T = NULL;
+    else
+    {
+        T = new Node;
+        T->val = ch;
+        CreateBiTree(T->lchild);
+        CreateBiTree(T->rchild);
+    }
+}
+
+
+void visit(Node* BiNode) {
+    cout << BiNode->val << " ";
+}
+
+void InOrder(BiTree T) {
+    if (T != NULL) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P149.5
+//假设二叉树采用二叉链表存储结构,设计一个非递归算法求二叉树的高度
+
+queue<Node*> q;
+stack<Node*> s;
+//非递归
+int GetHeight(BiTree T) {
+    if (!T)
+        return 0;
+    int level = 0;
+    Node* front, * last;
+    last = front = T;
+    q.push(T);
+    while (!q.empty()) {
+        front = q.front();
+        if (front->lchild)
+            q.push(front->lchild);
+        if (front->rchild)
+            q.push(front->rchild);
+        if (front == last) {
+            level++;
+            last = q.back();
+        }
+        q.pop();
+    }
+    return level;
+}
+
+//递归
+int GetH(BiTree T) {
+    if (T == NULL)
+        return 0;
+    int Lh = GetH(T->lchild);
+    int Lr = GetH(T->rchild);
+    return Lh > Lr ? (Lh + 1) : (Lr + 1);
+}
+
+int main()
+{
+    BiTree T;
+    cout << "请输入先序遍历顺序下各个结点的值,'#'表示没有结点:" << endl;
+    //  input: A B D H # # I # # E # J # # C F # K # # G # #
+    CreateBiTree(T);
+    cout << "中序遍历：" << endl;
+    InOrder(T);
+    cout << endl;
+    //cout << "树的高度为：" << GetH(T) << endl;
+    cout << "树的高度为：" << GetHeight(T) << endl;
+    cout << endl;
+    return 0;
+}
+
+/*
+
+                                            A
+                            B                               C
+                     D             E                 F             G
+               H           I Ø           J    Ø           K Ø           Ø
+              Ø Ø        Ø Ø           Ø Ø              Ø Ø
+
+
+ 树的图片链接：https://s3.ax1x.com/2021/02/03/yKIbiq.png
+*/

树与二叉树/二叉树的遍历和线索二叉树/P149.6.cpp

@@ -0,0 +1,111 @@
+#include <iostream>
+#include <stack>
+#include <queue>
+#include <vector>
+#include <string>
+using namespace std;
+
+#pragma region 构造链式存储的二叉树
+
+#define MaxSize 100
+#define ElemType char
+#define _for(i,a,b) for(int i=(a);i<(b);i++)
+
+typedef struct node { //树的结点
+    ElemType val;
+    node* lchild;
+    node* rchild;
+}Node, * BiTree;
+
+void CreateBiTree(BiTree& T)//要改变指针，C++可以把指针的引用传进来
+{
+    ElemType ch;
+
+    cin >> ch;
+
+    if (ch == '#')
+        T = NULL;
+    else
+    {
+        T = new Node;
+        T->val = ch;
+        CreateBiTree(T->lchild);
+        CreateBiTree(T->rchild);
+    }
+}
+
+
+void visit(Node* BiNode) {
+    cout << BiNode->val << " ";
+}
+
+void InOrder(BiTree T) {
+    if (T != NULL) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+void PostOrder(BiTree T) {
+    if (T != NULL) {
+        PostOrder(T->lchild);
+        PostOrder(T->rchild);
+        visit(T);
+    }
+}
+
+#pragma endregion
+
+//P149.6
+//设一棵二又树中各结点的值互不相同,其先序遍历序列和中序遍历序列分别存于两个
+//维数组A[1…n]和B[1…n]中, 试编写算法建立该二叉树的二叉链表
+
+queue<Node*> q;
+stack<Node*> s;
+
+BiTree BuildTree(string A, string B, int l1, int h1, int l2, int h2) {
+
+    //  A = "ABDHIEJCFKG", B = "HDIBEJAFKCG";
+    BiTree root = new Node;
+    root->val = A[l1];
+    int i;
+    for (i = l2; B[i] != root->val; i++);
+    int llen = i - l2;
+    int rlen = h2 - i;
+    if (llen)
+        root->lchild = BuildTree(A, B, l1 + 1, l1 + llen, l2, l2 + llen - 1);
+    else
+        root->lchild = NULL;
+    if (rlen)
+        root->rchild = BuildTree(A, B, h1 - rlen + 1, h1, h2 - rlen + 1, h2);
+    else
+        root->rchild = NULL;
+    return root;
+}
+
+int main()
+{
+    BiTree T;
+//  cout << "请输入先序遍历顺序下各个结点的值,'#'表示没有结点:" << endl;
+    string Pre = "ABDHIEJCFKG", In = "HDIBEJAFKCG";
+//  input: A B D H # # I # # E # J # # C F # K # # G # #
+//  CreateBiTree(T);
+    T = BuildTree(Pre, In, 0, Pre.size() - 1, 0, In.size() - 1);
+    cout << "后序遍历验证：" << endl;
+    PostOrder(T);
+    cout << endl;
+    return 0;
+}
+
+/*
+
+                                            A
+                            B                               C
+                     D             E                 F             G
+               H           I Ø           J    Ø           K Ø           Ø
+              Ø Ø        Ø Ø           Ø Ø              Ø Ø
+
+
+ 树的图片链接：https://s3.ax1x.com/2021/02/03/yKIbiq.png
+*/

树与二叉树/二叉树的遍历和线索二叉树/P150.7.cpp

@@ -0,0 +1,126 @@
+#include <iostream>
+#include <stack>
+#include <queue>
+#include <vector>
+#include <string>
+using namespace std;
+
+#pragma region 构造链式存储的完全二叉树
+
+#define MaxSize 100
+#define ElemType char
+#define _for(i,a,b) for(int i=(a);i<(b);i++)
+
+typedef struct node { //树的结点
+    ElemType val;
+    node* lchild;
+    node* rchild;
+}Node, * BiTree;
+
+void CreateBiTree(BiTree& T)//要改变指针，C++可以把指针的引用传进来
+{
+    ElemType ch;
+
+    cin >> ch;
+
+    if (ch == '#')
+        T = NULL;
+    else
+    {
+        T = new Node;
+        T->val = ch;
+        CreateBiTree(T->lchild);
+        CreateBiTree(T->rchild);
+    }
+}
+
+
+void visit(Node* BiNode) {
+    cout << BiNode->val << " ";
+}
+
+void InOrder(BiTree T) {
+    if (T != NULL) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+void PostOrder(BiTree T) {
+    if (T != NULL) {
+        PostOrder(T->lchild);
+        PostOrder(T->rchild);
+        visit(T);
+    }
+}
+
+#pragma endregion
+
+//P150.7
+//二又树按二叉链表形式存储, 写一个判别给定二叉树是否是完全二叉树的算法
+
+queue<Node*> q;
+stack<Node*> s;
+
+bool Judge_Comtrees(BiTree T) {
+    q.push(T);
+    while (!q.empty()) {
+        Node* t = q.front();
+        q.pop();
+        if (t) {
+            q.push(t->lchild);
+            q.push(t->rchild);
+        }
+        else {
+            while (!q.empty()) {
+                Node* x = q.front();
+                q.pop();
+                if (x)
+                    return false;
+            }
+        }
+    }
+    return true;
+}
+
+int main()
+{
+    BiTree T;
+    cout << "请输入先序遍历顺序下各个结点的值,'#'表示没有结点:" << endl;
+//  input(完全二叉树): A B D H # # I # # E G # # K # # C F L # # M # # G N # # #
+//  input(普通二叉树): A B D H # # I # # E # J # # C F # K # # G # #
+    CreateBiTree(T);
+    cout << "中序遍历：" << endl;
+    InOrder(T);
+    cout << endl;
+    if (Judge_Comtrees(T))
+        cout << "是完全二叉树" << endl;
+    else
+        cout << "不是完全二叉树" << endl;
+    return 0;
+}
+
+/*
+
+完全二叉树：
+
+                                            A
+                            B                               C
+                     D             E                 F             G
+               H           I G           K     L           M N           Ø
+            
+
+普通二叉树：
+
+                                            
+                                            A
+                            B                               C
+                     D             E                 F             G
+               H           I Ø           J    Ø           K Ø           Ø
+              Ø Ø        Ø Ø           Ø Ø              Ø Ø
+
+
+ 普通二叉树的图片链接：https://s3.ax1x.com/2021/02/03/yKIbiq.png
+
+*/