PAT-1099(Build A Binary Search Tree)

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  题目见这里

      (分析) 分四步进行:

      1)根据给定的结点情况建二叉树  2)对输入的键值排序(asending) 3)对二叉树中序遍历,同时对应赋key值 4)层次遍历(队列应用)

      题目并不困难,但是我误入了trick,错误假定了结点按先序遍历是按顺序编号的(当然是受样例的影响),所以有了下面22分(满分30) 的submit(贴出来是因为这不失为好的巩固二叉树知识的程序)

#include <stdio.h> 
#include <stdlib.h> //qsort,malloc
#define N 105

typedef struct node{
	int data;
	struct node *lChild,*rChild;
}BiNode,*BiTree;

void CreatBiTree(BiTree *bt){
	(*bt) = (BiTree)malloc(sizeof(BiNode));
	(*bt)->lChild = (*bt)->rChild = NULL;
	int left,right;
	scanf("%d%d",&left,&right);
	if(left!=-1) CreatBiTree(&((*bt)->lChild));
	if(right!=-1) CreatBiTree(&((*bt)->rChild)); 
}


int cmp(const void *a, const void *b){ //asending 
	return *(int *)a - *(int *)b;
}

void Sort(int *key, int n){
	int i;
	for(i=0;i<n;i++)
		scanf("%d",&key[i]);
	qsort((void*)key,n,sizeof(key[0]),cmp);
}

void LDR(BiTree bt, int key[]){
	static int i = 0;
	if(bt){
		LDR(bt->lChild,key);
		bt->data = key[i++];
		LDR(bt->rChild,key);
	}
}

void LOT(BiTree bt){
	BiTree q[N],bNode;
	int front,rear,flag;
	rear = front = flag = 0;
	q[rear] = bt;
	while(front<=rear){
		bNode = q[front++];
		if(!flag){
			printf("%d",bNode->data);
			flag = 1;
		}
		else printf(" %d",bNode->data);
		if(bNode->lChild) q[++rear] = bNode->lChild;
		if(bNode->rChild) q[++rear] = bNode->rChild;
	}
	printf("\n");
}

void DestryBiTree(BiTree *bt){
	if(*bt){
		DestryBiTree(&((*bt)->lChild));
		DestryBiTree(&((*bt)->rChild));
		free(*bt);
	}
}

int main(){
	int key[N];
	BiTree bt;
	int n;	
//	freopen("Data.txt","r",stdin);
	scanf("%d",&n);
	CreatBiTree(&bt,n);
	Sort(key,n);
	LDR(bt,key); //中序遍历 
	LOT(bt); //层次遍历 
	DestryBiTree(&bt);	
	return 0;
}

  当然,既然认识到这个错误,当然是因为找到了反例:

       8
  7 1
  2 3
  -1 -1
  -1 4
  5 6
  -1 -1
  -1 -1
  -1 -1
  33 37 34 30 50 43 37 33

      从上面的反例中,我们注意到创建链表形式的二叉树是不太可能的,而应采用数组形式,所以有了AC的提交:

#include <stdio.h> 
#define N 105

typedef struct{
	int lChild,rChild;
	int data;
}Node;

void CreatBiTree(Node node[], int n){
	int i = 0;
	for(;i<n;i++) scanf("%d%d",&node[i].lChild,&node[i].rChild);
}

int cmp(const void *a, const void *b){ //asending 
	return *(int *)a - *(int *)b;
}

void Sort(int *key, int n){
	int i;
	for(i=0;i<n;i++)
		scanf("%d",&key[i]);
	qsort((void*)key,n,sizeof(key[0]),cmp);
}

void LDR(Node *node, int key[], int i){
	static int j = 0;
	if(node[i].lChild!=-1) LDR(node,key,node[i].lChild);
	node[i].data = key[j++];
	if(node[i].rChild!=-1) LDR(node,key,node[i].rChild);//注意不要写误 
}

void LOT(Node node[]){
	Node q[N],qNode;
	int front,rear;
	rear = front = 0;
	q[rear] = node[0];
	while(front<=rear){
		qNode = q[front++];
		if(rear) printf(" ");
		printf("%d",qNode.data);
		if(qNode.lChild!=-1) q[++rear] = node[qNode.lChild];
		if(qNode.rChild!=-1) q[++rear] = node[qNode.rChild];
	}
	printf("\n");
}

int main(){
	int key[N];
	Node node[N];
	int n;	
//	freopen("Data.txt","r",stdin);
	scanf("%d",&n);
	CreatBiTree(node,n);
	Sort(key,n);
	LDR(node,key,0); //中序遍历
	LOT(node); //层次遍历 
	return 0;
}

 

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