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:
10
1 2 3 4 5 6 7 8 9 0
Sample Output:
6 3 8 1 5 7 9 0 2 4
Show me the code:
#include <stdio.h>
#include <stdlib.h>
#include<math.h>
#ifndef NULL
#define NULL 0
#endif // NULL
#define MAXSIZE 10
#define Null -1
typedef int ElementType;
typedef struct TNode *BinTree;
struct TNode
{
ElementType Data;
BinTree Left;
BinTree Right;
};
typedef BinTree TPosition;
struct QNode
{
TPosition Data;
struct QNode *Next;
};
typedef struct QNode *Position;
typedef Position Queque;
Queque CreateQueue();
int add(Queque q, TPosition e);
TPosition Delete(Queque q);
int IsEmpty(Queque q);
BinTree CreateTNode();
void BubbleSort(int*,int);
BinTree BuildCompleteTree(int Data[],int N);
int TreeHeight(int n);
void LevelOrderTraversal(BinTree root);
int main()
{
int N;
scanf("%d",&N);
if(N)
{
int i, Data[N];
BinTree T;
for(i=0;i<N;i++)
scanf("%d",Data+i);
BubbleSort(Data,N);
T = BuildCompleteTree(Data,N);
LevelOrderTraversal(T);
}
return 0;
}
/*队列抽象数据结构*/
Queque CreateQueue()
{
Queque q;
q = (Queque)malloc(sizeof(struct QNode));
q->Data = NULL;
q->Next = NULL;
return q;
}
int add(Queque q, TPosition e)
{
Position p,tmp;
if(!q)
q = CreateQueue();
tmp = q;
while(tmp->Next)
tmp = tmp->Next;
p = (Position)malloc(sizeof(struct QNode));
p->Data = e;
p->Next = NULL;
tmp->Next = p;
return 0;
}
TPosition Delete(Queque q)
{
TPosition First;
Position tmp;
if(!q || q->Next == NULL)
return NULL;
else
{
tmp = q->Next;
q->Next = tmp->Next;
First = tmp->Data;
free(tmp);
return First;
}
}
int IsEmpty(Queque q)
{
return(q->Next == NULL);
}
/*二叉搜索树数据结构*/
BinTree CreateTNode()
{
BinTree T;
T = (BinTree)malloc(sizeof(struct TNode));
T->Data = 0;
T->Left = T->Right = NULL;
return T;
}
BinTree BuildCompleteTree(int Data[],int N)
{
BinTree T;
int H,R,i;
int LeftCnt;
H = TreeHeight(N);
if(H>-1)
{
if(H == 0)
{
T = CreateTNode();
T->Data = Data[0];
}
else
{
R = N- pow(2,H) + 1;
if(R > (int)pow(2,(H-1)))
{
LeftCnt = pow(2,H) - 1;
}
else
LeftCnt = pow(2,H-1) - 1 + R;
int RightCnt = N - LeftCnt - 1;
int LeftData[LeftCnt];
for(i=0;i<LeftCnt;i++)
{
LeftData[i] = Data[i];
}
T = CreateTNode();
T->Data = Data[LeftCnt];
T->Left = BuildCompleteTree(LeftData,LeftCnt);
if(RightCnt)
{
int RightData[RightCnt];
for(i=0;i<RightCnt;i++)
{
RightData[i] = Data[LeftCnt+1+i];
}
T->Right = BuildCompleteTree(RightData,RightCnt);
}
}
return T;
}
else
{
printf("Tree Height Error");
return NULL;
}
}
int TreeHeight(int n)
{
if(n)
return (int)(log(n)/log(2));
else
return -1;
}
void BubbleSort(int a[], int n)
{
int i, j, temp;
for (j = 0; j < n - 1; j++)
for (i = 0; i < n - 1 - j; i++)
{
if(a[i] > a[i + 1])
{
temp = a[i];
a[i] = a[i + 1];
a[i + 1] = temp;
}
}
}
void LevelOrderTraversal(BinTree root)
{
Queque q;
q = CreateQueue();
if(!root)
return;
int flag = 1;
TPosition tmp;
add(q,root);
while(!IsEmpty(q))
{
tmp = Delete(q);
if(flag)
{
printf("%d",tmp->Data);
flag = 0;
}
else
printf(" %d",tmp->Data);
if(tmp->Left == NULL && tmp->Right == NULL)
;
else if(tmp->Left == NULL)
add(q,tmp->Right);
else if(tmp->Right == NULL)
add(q,tmp->Left);
else
{
add(q,tmp->Left);
add(q,tmp->Right);
}
}
}