数据结构课程期末总结二
第一：
二叉树三种遍历方式（由前两种得到第三种 HDU1710）
#include<iostream> #include<cstring> #include<cstdio> using namespace std; int num=0; struct donser { int data; donser*lson; donser*rson; }; donser *root; donser *creat(int *a,int *b,int n)//da下标从i开始依次找 db下标从j开始向后扫 n向后扫几个 { donser *ss; for(int k=0;k<n;k++) { if(b[k]==a[0]) { ss=new donser; ss->data=b[k]; ss->lson=creat(a+1,b,k); ss->rson=creat(a+k+1,b+1+k,n-k-1); return ss; } } return NULL; } void solve(donser *r) { if(r!=NULL) { solve(r->lson); solve(r->rson); if(r!=root) cout<<r->data<<" "; else cout<<r->data<<endl; } } int main() { int da[1010],db[1010];//前中 while(~scanf("%d",&num)) { for(int i=0;i<num;i++) {scanf("%d",&da[i]);} for(int i=0;i<num;i++) {scanf("%d",&db[i]);} root=creat(da,db,num); solve(root); } return 0; }
第二：
构建一颗普通二叉树
/* 一颗普通的二叉树 */ #include<iostream.h> struct tree { int data; tree *left,*right; }; class Btree { static int n; static int m; public: tree *root; Btree() { root=NULL; } void create_Btree(int); void Preorder(tree *); //先序遍历 void inorder(tree *); //中序遍历 void Postorder(tree *); //后序遍历 void display1() { Preorder(root); cout<<endl; } void display2() { inorder(root); cout<<endl; } void display3() { Postorder(root); cout<<endl; } int count(tree *); //计算二叉树的个数 int findleaf(tree *); //求二叉树叶子的个数 int findnode(tree *); //求二叉树中度数为1的结点数量,这是当初考数据结构时候的最后一道题目 }; int Btree::n=0; int Btree::m=0; void Btree::create_Btree(int x) { tree *newnode=new tree; newnode->data=x; newnode->right=newnode->left=NULL; if(root==NULL) root=newnode; else { tree *back; tree *current=root; while(current!=NULL) { back=current; if(current->data>x) current=current->left; else current=current->right; } if(back->data>x) back->left=newnode; else back->right=newnode; } } int Btree::count(tree *p) { if(p==NULL) return 0; else return count(p->left)+count(p->right)+1; //这是运用了函数嵌套即递归的方法。 } void Btree::Preorder(tree *temp) //这是先序遍历二叉树，采用了递归的方法。 { if(temp!=NULL) { cout<<temp->data<<" "; Preorder(temp->left); Preorder(temp->right); } } void Btree::inorder(tree *temp) //这是中序遍历二叉树，采用了递归的方法。 { if(temp!=NULL) { inorder(temp->left); cout<<temp->data<<" "; inorder(temp->right); } } void Btree::Postorder(tree *temp) //这是后序遍历二叉树，采用了递归的方法。 { if(temp!=NULL) { Postorder(temp->left); Postorder(temp->right); cout<<temp->data<<" "; } } int Btree::findleaf(tree *temp) { if(temp==NULL)return 0; else { if(temp->left==NULL&&temp->right==NULL)return n+=1; else { findleaf(temp->left); findleaf(temp->right); } return n; } } int Btree::findnode(tree *temp) { if(temp==NULL)return 0; else { if(temp->left!=NULL&&temp->right!=NULL) { findnode(temp->left); findnode(temp->right); } if(temp->left!=NULL&&temp->right==NULL) { m+=1; findnode(temp->left); } if(temp->left==NULL&&temp->right!=NULL) { m+=1; findnode(temp->right); } } return m; } void main() { Btree A; int array[]= {7,4,2,3,15,35,6,45,55,20,1,14,56,57,58}; int k; k=sizeof(array)/sizeof(array[0]); cout<<"建立排序二叉树顺序: "<<endl; for(int i=0; i<k; i++) { cout<<array[i]<<" "; A.create_Btree(array[i]); } cout<<endl; cout<<"二叉树节点个数： "<<A.count(A.root)<<endl; cout<<"二叉树叶子个数："<<A.findleaf(A.root)<<endl; cout<<"二叉树中度数为1的结点的数量为："<<A.findnode(A.root)<<endl; cout<<endl<<"先序遍历序列: "<<endl; A.display1(); cout<<endl<<"中序遍历序列: "<<endl; A.display2(); cout<<endl<<"后序遍历序列: "<<endl; A.display3(); }
第三：
构建一棵二叉排序树并遍历输出（HDU3999）
#include<iostream> #include<cstdio> #include<cstring> using namespace std; int ld[100010],rd[100010],a,num,root,i; void build(int root,int al) { if(al>root) { if(rd[root]==-1) { rd[root]=al; //cout<<"al:"<<al<<" r root:"<<root<<endl; } else build(rd[root],al); } else { if(ld[root]==-1) { ld[root]=al; //cout<<"al:"<<al<<" l root:"<<root<<endl; } else build(ld[root],al); } } void solve(int root) { if(ld[root]!=-1) { cout<<" "<<ld[root]; solve(ld[root]); } if(rd[root]!=-1) { cout<<" "<<rd[root]; solve(rd[root]); } else return; } int main() { while(~scanf("%d",&num)) { memset(ld,-1,sizeof(ld)); memset(rd,-1,sizeof(rd)); for(i=1;i<=num;i++) { scanf("%d",&a); if(i==1){root=a;} else build(root,a); } cout<<root; solve(root); cout<<endl; } return 0; }
第四：
构建一棵哈夫曼树
/* 哈夫曼树构建（最优二叉树） */ #include <iostream> #include <stdlib.h> using namespace std; const int MaxValue = 10000;//初始设定的权值最大值 const int MaxBit = 4;//初始设定的最大编码位数 const int MaxN = 10;//初始设定的最大结点个数 struct HaffNode//哈夫曼树的结点结构 { int weight;//权值 int flag;//标记 int parent;//双亲结点下标 int leftChild;//左孩子下标 int rightChild;//右孩子下标 }; struct Code//存放哈夫曼编码的数据元素结构 { int bit[MaxBit];//数组 int start;//编码的起始下标 int weight;//字符的权值 }; void Haffman(int weight[], int n, HaffNode haffTree[]) //建立叶结点个数为n权值为weight的哈夫曼树haffTree { int j, m1, m2, x1, x2; //哈夫曼树haffTree初始化。n个叶结点的哈夫曼树共有2n-1个结点 for (int i = 0; i<2 * n - 1; i++) { if (i<n) haffTree[i].weight = weight[i]; else haffTree[i].weight = 0; //注意这里没打else那{}，故无论是n个叶子节点还是n-1个非叶子节点都会进行下面4步的初始化 haffTree[i].parent = 0; haffTree[i].flag = 0; haffTree[i].leftChild = -1; haffTree[i].rightChild = -1; } //构造哈夫曼树haffTree的n-1个非叶结点 for (int i = 0; i<n - 1; i++) { m1 = m2 = MaxValue;//Maxvalue=10000;(就是一个相当大的数) x1 = x2 = 0;//x1、x2是用来保存最小的两个值在数组对应的下标 for (j = i; j<n + i; j++)//循环找出所有权重中，最小的二个值--morgan { if (haffTree[j].weight<m1&&haffTree[j].flag == 0) { m2 = m1; x2 = x1; m1 = haffTree[j].weight; x1 = j; } else if(haffTree[j].weight<m2&&haffTree[j].flag == 0) { m2 = haffTree[j].weight; x2 = j; } } //将找出的两棵权值最小的子树合并为一棵子树 haffTree[x1].parent = n + i; haffTree[x2].parent = n + i; haffTree[x1].flag = 1; haffTree[x2].flag = 1; haffTree[n + i].weight = haffTree[x1].weight + haffTree[x2].weight; haffTree[n + i].leftChild = x1; haffTree[n + i].rightChild = x2; } } void HaffmanCode(HaffNode haffTree[], int n, Code haffCode[]) //由n个结点的哈夫曼树haffTree构造哈夫曼编码haffCode { Code *cd = new Code; int child, parent; //求n个叶结点的哈夫曼编码 for (int i = 0; i<n; i++) { //cd->start=n-1;//不等长编码的最后一位为n-1, cd->start = 0;//,----修改从0开始计数--morgan cd->weight = haffTree[i].weight;//取得编码对应权值的字符 child = i; parent = haffTree[child].parent; //由叶结点向上直到根结点 while (parent != 0) { if (haffTree[parent].leftChild == child) cd->bit[cd->start] = 0;//左孩子结点编码0 else cd->bit[cd->start] = 1;//右孩子结点编码1 //cd->start--; cd->start++;//改成编码自增--morgan child = parent; parent = haffTree[child].parent; } //保存叶结点的编码和不等长编码的起始位 //for(intj=cd->start+1;j<n;j++) for (int j = cd->start - 1; j >= 0; j--)//重新修改编码，从根节点开始计数--morgan haffCode[i].bit[cd->start - j - 1] = cd->bit[j]; haffCode[i].start = cd->start; haffCode[i].weight = cd->weight;//保存编码对应的权值 } } int main() { int i, j, n = 4, m = 0; int weight[] = { 2,4,5,7 }; HaffNode*myHaffTree = new HaffNode[2 * n - 1]; Code*myHaffCode = new Code[n]; if (n>MaxN) { cout << "定义的n越界，修改MaxN!" << endl; exit(0); } Haffman(weight, n, myHaffTree); HaffmanCode(myHaffTree, n, myHaffCode); //输出每个叶结点的哈夫曼编码 for (i = 0; i<n; i++) { cout << "Weight=" << myHaffCode[i].weight << " Code="; //for(j=myHaffCode[i].start+1;j<n;j++) for (j = 0; j<myHaffCode[i].start; j++) cout << myHaffCode[i].bit[j]; m = m + myHaffCode[i].weight*myHaffCode[i].start; cout << endl; } cout << "huffman's WPLis:"; cout << m; cout << endl; return 0; }
