A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:
- The left subtree of a node contains only nodes with keys less than the node’s key.
- The right subtree of a node contains only nodes with keys greater than or equal to the node’s key.
- Both the left and right subtrees must also be binary search trees.
A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.
Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (<=1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.
Output Specification:
For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.
Sample Input:
|
1 2 |
10 1 2 3 4 5 6 7 8 9 0 |
Sample Output:
|
1 |
6 3 8 1 5 7 9 0 2 4 |
注意 Complete Binary Search Tree 的特性即可
代码如下：
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#include<stdio.h> #include<stdlib.h> typedef struct tree_ { int number; struct tree_ *left; struct tree_ *right; } tree; typedef struct queue_ { int size; int capacity; int front; int rear; void **data; } queue; #define is_queue_empty(X) (!((X)->size)) queue *init_queue(int n) { queue *temp; temp=(queue *)malloc(sizeof(queue)); temp->size=0; temp->capacity=n; temp->front=0; temp->rear=-1; temp->data=(void **)malloc(n*sizeof(void *)); return temp; } int enqueue(queue *q,void *data) { if(q->size==q->capacity) { return 1; } q->size++; q->rear=(q->rear+1)%q->capacity; q->data[q->rear]=data; return 0; } int dequeue(queue *q,void **data) { if(q->size==0) { *data=NULL; return 1; } q->size--; *data=q->data[q->front]; q->front=(q->front+1)%q->capacity; return 0; } int delete_queue(queue *q) { free(q->data); free(q); return 0; } void level_order(tree *t,int n) { queue *q; tree *temp; int flag=0; q=init_queue(n); enqueue(q,t); while(!is_queue_empty(q)) { dequeue(q,(void **)&temp); if(flag==0) { printf("%d",temp->number); flag=1; } else { printf(" %d",temp->number); } if(temp->left!=NULL) { enqueue(q,temp->left); } if(temp->right!=NULL) { enqueue(q,temp->right); } } printf("\n"); } int compare(const void *a,const void *b) { return *(int *)a-*(int *)b; } tree *build_cbst(int *sequence,int n) { tree *root; int edge,bottom,count,temp; if(n<=0) { return NULL; } root=(tree *)malloc(sizeof(tree)); if(n==1) { root->left=NULL; root->right=NULL; root->number=sequence[0]; return root; } temp=2; count=1; while(temp-1<n) { count++; temp=temp<<1; } temp=temp>>1; bottom=temp; if(n-temp+1>bottom/2) { edge=(temp-1-1)/2+bottom/2; } else { edge=(temp-1-1)/2+n-temp+1; } root->number=sequence[edge]; root->left=build_cbst(sequence,edge); root->right=build_cbst(sequence+edge+1,n-1-edge); return root; } int main() { int n,i,buf[1000]; tree *root; scanf("%d",&n); for(i=0;i<n;i++) { scanf("%d",buf+i); } qsort(buf,n,sizeof(int),compare); root=build_cbst(buf,n); level_order(root,n); } |