3.1 树与数的表示

3.1.1 顺序查找

int SequentialSearch(List Tbl,ElementType K){
	int i;
	Tbl->Element[0]=K;
	for(i=Tbl->Length;Tbl->Element[i]!=K;i--);
	return i;
} 

typedef struct LNode *List;
struct LNode{
	ElementType Element[MAXSIZE];
	int Length;
};

3.1.2 二分查找例子

3.1.3 二分查找实现

int BinarySearch(List Tbl,ElementType K){
	int left,right,mid,NoFound=-1;
	left=1;
	right=Tbl->Length;
	while(left<=right){
		mid=(left+right)/2;
		if(K<TBl->Element[mid]){
			right=mid-1;
		}else if(K>Tbl->Element[mid]){
			left=mid+1;
		}else{
			return mid;
		}
		return NotFound;
	}
}

3.1.4 树的定义和术语

3.1.5 树的表示

3.2 二叉树及存储结构

3.2.1 二叉树的定义及性质

3.2.2 二叉树的存储结构

3.3 二叉树的遍历

3.3.1 先序中序后序遍历

//先序遍历 
void PreOrderTraversal(BinTree BT){
	if(BT){
		printf("%d",BT->Data);
		PreOrderTraversal(BT->Left);
		PreOrderTraversal(BT->Right);
	}
}

//中序遍历 
void InOrderTraversal(BinTree BT){
	if(BT){
		PreOrderTraversal(BT->Left);
		printf("%d",BT->Data);
		PreOrderTraversal(BT->Right);
	}
}

//后序遍历 
void PostOrderTraversal(BinTree BT){
	if(BT){
		PreOrderTraversal(BT->Left);
		PreOrderTraversal(BT->Right);
		printf("%d",BT->Data);
	}
}

3.3.2 中序非递归遍历

基本思路：使用堆栈

//中序遍历非递归
void InOrderTraversal(BinTree BT){
	BinTree T=BT;
	Stack S=CreateStack(MaxSize){
		while(T||!IsEmpty(S)){
			while(T){
				Push(S,T);
				T=T->Left;
			}
			if(!IsEmpty(S)){
				T=Pop(S);
				printf("%5d",T->Data);
				T=T->Right;
			}
		}
	}
} 

//先序遍历非递归
void PreOrderTraversal(BinTree BT){
	BinTree T=BT;
	Stack S=CreateStack(MaxSize){
		while(T||!IsEmpty(S)){
			while(T){
				Push(S,T);
				printf("%5d",T->Data);
				T=T->Left;
			}
			if(!IsEmpty(S)){
				T=Pop(S);
				T=T->Right;
			}
		}
	}
}

3.3.3 层序遍历

//层序遍历
void LevelOrderTraversal(BinTree BT){
	Queue Q;
	BinTree T;
	if(!BT){
		return;
	}
	Q=CreateQueue(MaxSize);
	AddQ(Q,BT);
	while(!IsEmptyQ(Q)){
		T=DeleteQ(Q);
		printf("%d\n",T->Data);
		if(T->Left){
			AddQ(Q,T->Left);
		}
		if(T->Right){
			AddQ(Q,T->Right);
		} 
	}
} 

3.3.4 遍历应用例子

小白专场

#include <stdio.h>
#define MaxTree 10
#define ElementType char
#define Tree int
#define Null -1

struct TreeNode{
	ElementType Element;
	Tree Left;
	Tree Right;
}T1[MaxTree],T2[MaxTree]; 

Tree BuildTree(struct TreeNode T[]){
	Tree Root;
	int N,i,t;
	scanf("%d",&N);
	int check[MaxTree];
	char cl,cr;
	if(N){
		for(t=0;t<N;t++){
			check[t]=0;
		}
		for(i=0;i<N;i++){
			scanf(" %c %c %c",&T[i].Element,&cl,&cr);
			if(cl!='-'){
				T[i].Left=cl-'0';
				check[T[i].Left]=1;
			}else{
				T[i].Left=Null;
			}
			if(cr!='-'){
				T[i].Right=cr-'0';
				check[T[i].Right]=1;
			}else{
				T[i].Right=Null;
			}
		}
		for(t=0;t<N;t++){
			if(!check[t]){
				break;
			}
		}
		Root=t;
	}
	return Root;
}

int lsomorphic(Tree R1,Tree R2){
	if((R1==Null)&&(R2==Null)){//全空 
		return 1;
	}
	if((R1==Null)&&(R2!=Null)){//一个空一个不空 
		return 0;
	}
	if(T1[R1].Element!=T2[R2].Element){//当前值不同 
		return 0;
	}
	if((T1[R1].Left==Null)&&(T2[R2].Left==Null)){//都没有左子树 
		return lsomorphic(T1[R1].Right,T2[R2].Right);
	}
	if(((T1[R1].Left!=Null)&&(T2[R2].Left!=Null))&&((T1[T1[R1].Left].Element)==(T2[T2[R2].Left].Element))){//都存在左子树且值相同，则递归判断左子树和右子树是否同构 
		return (lsomorphic(T1[R1].Left,T2[R2].Left)&&lsomorphic(T1[R1].Right,T2[R2].Right));
	}else{
		return (lsomorphic(T1[R1].Left,T2[R2].Right)&&lsomorphic(T1[R1].Right,T2[R2].Left));//否则判断相互左右子树是否同构 
	}
}

int main(){
	Tree R1,R2;
	R1=BuildTree(T1);
	R2=BuildTree(T2);
	if(lsomorphic(R1,R2)){
		printf("Yes\n");
	}else{
		printf("No\n");
	}
	return 0;
}