做了7道题

树与二叉树/二叉树的遍历和线索二叉树/P150.10.cpp

@@ -0,0 +1,99 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P150.10
+//假设二叉树采用二叉链存储结构存储, 设计一个算法, 求先序遍历序列中第k(1≤k≤
+//二叉树中结点个数)个结点的值
+
+queue<Node*> q;
+stack<Node*> s;
+
+int Count = 1;
+void Visit(BiTree& T,int K) {
+    if (Count == K)
+        cout << T->val;
+    Count++;
+}
+
+void GetNumK(BiTree& T,int K) {
+    if (T) {
+        Visit(T,K);
+        GetNumK(T->lchild,K);
+        GetNumK(T->rchild,K);
+    }
+}
+
+
+
+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;
+    int k = 4;
+    cout << "先序遍历序列中第" << k << "个结点的值为" << endl;
+    GetNumK(T,k);
+    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/P150.11.cpp

@@ -0,0 +1,119 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P150.11
+//已知二叉树以二叉链表存储, 编写算法完成:对于树中每个元素值为x的结点, 删去以
+//它为根的子树, 并释放相应的空间
+
+queue<Node*> q;
+stack<Node*> s;
+
+void DeleteNode(BiTree &T) {
+    if (T) {
+        DeleteNode(T->lchild);
+        DeleteNode(T->rchild);
+        delete T;
+    }
+}
+
+void DeleteX(BiTree& T, ElemType X) {
+    q.push(T);
+    while (!q.empty()) {
+        BiTree p = q.front();
+        q.pop();
+        if (p->lchild) {
+            if (p->lchild->val == X) {
+                DeleteNode(p->lchild);
+                p->lchild = NULL;
+            }
+            else
+                q.push(p->lchild);
+        }
+        if (p->rchild) {
+            if (p->rchild->val == X) {
+                DeleteNode(p->rchild);
+                p->rchild = NULL;
+            }
+            else
+                q.push(p->rchild);
+        }
+
+    }
+}
+
+
+
+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;
+    char X = 'D';
+    cout << "删除" << X << "后中序遍历为" << endl;
+    DeleteX(T, X);
+    InOrder(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/P150.12.cpp

@@ -0,0 +1,104 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P150.12
+//在二又树中查找值为x的结点, 试编写算法(用C语言)打印值为x的结点的所有祖
+//先, 假设值为x的结点不多于一个。
+
+queue<Node*> q;
+stack<Node*> s;
+
+bool FindAncestors(BiTree T,ElemType X) {
+    if (!T)
+        return false;
+    if (T->val == X)
+        return true;
+    if (FindAncestors(T->lchild, X) || FindAncestors(T->rchild, X)) {
+        s.push(T);
+        return true;
+    }
+    return false;
+}
+
+void print() {
+    while (!s.empty()) {
+        cout << s.top()->val << " ";
+        s.pop();
+    }
+}
+
+
+
+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;
+    char X = 'I';
+    FindAncestors(T, X);
+    cout << X << "的祖先结点为：" << endl;
+    print();
+    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/P150.13.cpp

@@ -0,0 +1,119 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+void FindX(BiTree T,ElemType X,Node* &r) {
+    if (T) {
+        FindX(T->lchild,X,r);
+        if (T->val == X)
+            r = T;
+        FindX(T->rchild,X,r);
+    }
+}
+
+#pragma endregion
+
+//P150.13
+//设一棵二叉树的结点结构为(LLINK, INFO, RLINK), ROOT为指向该二叉树根结点的
+//指针, p和q分别为指向该二叉树中任意两个结点的指针, 试编写算法
+//ANCESTOR(ROOT, p, q, r), 找到p和q的最近公共祖先结点r。
+
+queue<Node*> q1, q2;
+stack<Node*> s1, s2;
+
+bool FindAncestors(BiTree T, Node* X, queue<Node*> &q) {
+    if (!T)
+        return false;
+    if (T == X)
+        return true;
+    if (FindAncestors(T->lchild, X, q) || FindAncestors(T->rchild, X, q)) {
+        q.push(T);
+        return true;
+    }
+    return false;
+}
+
+void ANCESTOR(BiTree ROOT, Node* p, Node* q, Node* &r) {
+    FindAncestors(ROOT, p, q1);
+    FindAncestors(ROOT, q, q2);
+    while (!q1.empty() && !q2.empty() && q1.front() != q2.front()) {
+        q1.pop();
+    }
+    r = q1.front();
+    return;
+}
+
+
+
+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;
+    Node* p = NULL, * q = NULL;
+    FindX(T, 'K', p);
+    FindX(T, 'G', q);
+    Node* r = NULL;
+    ANCESTOR(T, p, q, r);
+    cout << p->val << "和" << q->val << "的最近公共祖先结点为：" << r->val << 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/P150.14.cpp

@@ -0,0 +1,131 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+void FindX(BiTree T, ElemType X, Node*& r) {
+    if (T) {
+        FindX(T->lchild, X, r);
+        if (T->val == X)
+            r = T;
+        FindX(T->rchild, X, r);
+    }
+}
+
+#pragma endregion
+
+//P150.14
+//假设二叉树采用二叉链表存储结构, 设计一个算法, 求非空二叉树b的宽度(即具有结
+//点数最多的那一层的结点个数
+
+queue<Node*> q;
+stack<Node*> s;
+
+int GetWidth(BiTree T) {
+    int width = 0;
+    int Nowidth = 1;
+    BiTree front, last;
+    front = last = T;
+    q.push(T);
+    while (!q.empty()) {
+        front = q.front();
+        if (front->lchild) {
+            q.push(front->lchild);
+            Nowidth++;
+        }
+        if (front->rchild) {
+            q.push(front->rchild);
+            Nowidth++;
+        }
+        if (front == last) {
+            if (Nowidth > width)
+                width = Nowidth;
+            Nowidth = 0;
+            last = q.back();
+        }
+        q.pop();
+    }
+    return width;
+}
+
+
+
+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(普通二叉树): A B D H # # I # # E # J # # C F # K # # G # #
+//  input(完全二叉树): A B D H # # I # # E G # # K # # C F L # # M # # G N # # #
+    CreateBiTree(T);
+    cout << "中序遍历：" << endl;
+    InOrder(T);
+    cout << endl;
+    cout << "二叉树的宽度为:" << GetWidth(T) << 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
+
+*/

树与二叉树/二叉树的遍历和线索二叉树/P150.8.cpp

@@ -0,0 +1,90 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P150.8
+//假设二叉树采用二叉链表存储结构存储,试设计一个算法,
+//计算一棵给定二叉树的所有双分支结点个数
+
+queue<Node*> q;
+stack<Node*> s;
+int num = 0;
+int Get_DouNum(BiTree T) {
+    if (T) {
+        Get_DouNum(T->lchild);
+        if (T->lchild && T->rchild)
+            num++;
+        Get_DouNum(T->rchild);
+    }
+    return num;
+}
+
+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 << "双结点的个数为：" << Get_DouNum(T) << 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/P150.9.cpp

@@ -0,0 +1,100 @@
+#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) {
+        InOrder(T->lchild);
+        visit(T);
+        InOrder(T->rchild);
+    }
+}
+
+#pragma endregion
+
+//P150.9
+//设树B是一棵采用链式结构存储的二叉树, 编写一个把树B中所有结点的左、右子树进
+//行交换的函数
+
+queue<Node*> q;
+stack<Node*> s;
+
+
+void Swap(BiTree & a, BiTree& b) {
+    BiTree t = a;
+    a = b;
+    b = t;
+}
+
+void SwapNode(BiTree &T) {
+    if (T) {
+        SwapNode(T->lchild);
+        SwapNode(T->rchild);
+        Swap(T->lchild, T->rchild);
+    }
+}
+
+
+
+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 << "交换完后（中序遍历）：" << endl;
+    SwapNode(T);
+    InOrder(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
+*/