PAT-1099(Build A Binary Search Tree)

　　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)

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#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：

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#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; }