数据结构练习题目（二叉树部分）

一、判断二叉树A中是否有与B相同的子树

#include<iostream>#include<stdlib.h>#include<malloc.h>#include <stack>using namespace std;struct BinaryTreeNode {    char value;    BinaryTreeNode *left;    BinaryTreeNode *right;};class BinaryTree {public:    BinaryTreeNode* root;    BinaryTree() {}//构造函数    BinaryTreeNode * CreateBinaryTree();  //建立二叉树};BinaryTreeNode * BinaryTree::CreateBinaryTree() //建树函数{    BinaryTreeNode *T;    char data;    cin >> data;    if (data == '#')        T = NULL;    else    {        T = new BinaryTreeNode;        T->value = data;        T->left = CreateBinaryTree();        T->right = CreateBinaryTree();    }    return T;}bool isSameTree(BinaryTreeNode *rootT,  BinaryTreeNode * rootB)//判断树是否相同{    if (rootT == NULL && rootB == NULL) //子父都为空，为真        return true;    else if ((rootT == NULL && rootB != NULL) || (rootT != NULL && rootB == NULL))        return false;    else if (rootT->value == rootB->value) //如果相同，进入下一层比较    {        return isSameTree(rootT->left, rootB->left) && isSameTree(rootT->right, rootB->right);    }    return false;}bool isSubTree(BinaryTreeNode *rootA, BinaryTreeNode * rootB)//判断是否是子树{    if (isSameTree(rootA, rootB)) //如果两树相同，返回true        return true;    if (rootB == NULL) //B为空，返回true        return true;    if (rootA == NULL) //A为空，则返回false        return false;    if (rootA->value == rootB->value) //如果相同，进入下一层比较        return isSubTree(rootA->left, rootB->left) || isSubTree(rootA->right, rootB->right);    return isSubTree(rootA->left, rootB) || isSubTree(rootA->right, rootB);//相似只需要某个部分相同，所以可以比较左子树部分和右子树部分，取两者其一}int main(){    BinaryTree A, B;    A.root=A.CreateBinaryTree();    B.root = B.CreateBinaryTree();    if (isSameTree(A.root, B.root))        cout << "两树相同\n";    if (isSubTree(A.root, B.root))        cout << "B是A的子树\n";    return 0;}

二、编写一个将二叉树的所有叶子结点从左向右链接成单链表的算法

#include<iostream>#include<stdlib.h>#include<malloc.h>#include <stack>#include <queue>using namespace std;struct BinaryTreeNode {  //结点结构体定义    char value;    BinaryTreeNode *left;    BinaryTreeNode *right;};struct listNode {         //链表结点定义    char data;    listNode *next;};listNode *L = new listNode;BinaryTreeNode* CreateTree()//建树{    BinaryTreeNode * T;    char ch;    cin >> ch;    if (ch == '#')        T = NULL;    else    {        T = new BinaryTreeNode;        T->value = ch;        T->left = CreateTree();        T->right = CreateTree();    }    return T;}void Creatlist(BinaryTreeNode*T,listNode*&L)//利用先序遍历递归，用链表L把结点串起来{    if (T != NULL) {        if (T->left == NULL&&T->right == NULL) //如果左右子树为空，则为叶子结点        {            listNode *temp = new listNode;  //串起来            temp->data = T->value;            L->next = temp;            L = L->next;            }        Creatlist(T->left,L);     //递归左子树        Creatlist(T->right,L);    //递归右子树    }    L->next = NULL;}int main(){    //ABD##E##CF##G##    //           A    //      B         C    //    D    E    F    G      BinaryTreeNode * A;    A = CreateTree();    listNode *first = L;//first作为L的首地址    Creatlist(A,L);    first = first->next;    for (; first!=NULL&&first->next!=NULL;)    {        if (first == NULL)            break;        cout << first->data;        first = first->next;    }    return 0;}

三、设一棵二叉树用二叉链表表示，编写一个算法，判断二叉树是否为完全二叉树

#include<iostream>#include<stdlib.h>#include<malloc.h>#include <stack>#include <queue>using namespace std;enum Tag { L, R };struct BinaryTreeNode {    char value;    BinaryTreeNode *left;    BinaryTreeNode *right;};BinaryTreeNode * CreateBinaryTree()//建树{    BinaryTreeNode *T;    char data;    cin >> data;    if (data == '#')        T = NULL;    else    {        T = new BinaryTreeNode;        T->value = data;        T->left = CreateBinaryTree();        T->right = CreateBinaryTree();    }    return T;}int CompBTNode(BinaryTreeNode  *b){    queue<BinaryTreeNode*> q;//定义一个队列，用于分层判断    BinaryTreeNode * p=new BinaryTreeNode;    int cm = 1;                       //cm=1表示二叉树为完全二叉树    int bj = 1;                       //bj=1表示到目前为止所有结点均有左右孩子    if (b != NULL)    {        q.push(b);        while (!q.empty())                {            p = q.front();            q.pop();            if (p->left == NULL)   //*p结点没有左孩子            {                bj = 0;                if (p->right != NULL)//没有左孩子但有右孩子，不满足完全二叉树性质                    cm = 0;            }            else                    //*p结点有左孩子            {                if (bj == 1)         //结点均有左孩子                {                    //左孩子进队                    q.push(p->left);                    if (p->right == NULL)//*p有左孩子但没有右孩子,则 bj=0                        bj = 0;                    else            //*p有右孩子,则继续判断                    {                        q.push(p->right); //右孩子进队                    }                }                else                //bj=0: 迄今为止,已有结点缺左或右孩子                    cm = 0;         //此时*p结点有左孩子            }        }          return cm;    }    return  1;}int main(){    BinaryTreeNode *T = NULL;    //A B C # # # D # #    T = CreateBinaryTree();    if (CompBTNode(T))        cout << "Yes";    else        cout << "NO";    return 0;}

四、统计二叉树的宽度

int maxx = 0;//存储最大结点个数int wid[100] = { 0 };//存储每一层结点个数int getwidth(BinaryTreeNode*T)//递归计算二叉树宽度{    int static floor = 1;    if (T != NULL)    {        if (floor == 1) //当是根结点的时候        {            wid[floor]++;            floor++;            if (T->left)wid[floor]++; //存在左子树，数组的值加1            if (T->right)wid[floor]++; //存在右子树，数组的值加1        }        else        {            floor++;            if (T->left)wid[floor]++; //存在左子树，数组的值加1            if (T->right)wid[floor]++; //存在右子树，数组的值加1        }        if (wid[floor] > maxx) //如果大于maxx，替换maxx的值            maxx = wid[floor];        maxx=getwidth(T->left);         floor--;     //访问过要减一        maxx=getwidth(T->right);    }        return maxx;}

五、以前序次序输出一棵二叉树所有结点的数据值及结点所在层次

//ABD##E##CF##G##    //            A    //       B        C    //   D    E     F   G   int nfloor = 1;void getnode(BinaryTreeNode*T){    if (T != NULL)    {           cout << T->value<<" ";        cout << nfloor << endl;        nfloor++;        getnode(T->left);  //递归搜索左子树        getnode(T->right);//递归搜索右子树        nfloor--;    }}