浙大pta: Build A Binary Search Tree

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.

Given the structure of a binary tree and a sequence of distinct integer keys, there is only one way to fill these keys into the tree so that the resulting tree satisfies the definition of a BST. You are supposed to output the level order traversal sequence of that tree. The sample is illustrated by Figure 1 and 2.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N ($\le$100) which is the total number of nodes in the tree. The next N lines each contains the left and the right children of a node in the format left_index right_index, provided that the nodes are numbered from 0 to N-1, and 0 is always the root. If one child is missing, then -1 will represent the NULL child pointer. Finally N distinct integer keys are given in the last line.

Output Specification:

For each test case, print in one line the level order traversal sequence of that tree. All the numbers must be separated by a space, with no extra space at the end of the line.

Sample Input:

9
1 6
2 3
-1 -1
-1 4
5 -1
-1 -1
7 -1
-1 8
-1 -1
73 45 11 58 82 25 67 38 42

Sample Output:

58 25 82 11 38 67 45 73 42

设计思路：

1. 构建binary search tree（BST）

2. 将节点的value存储在一个数组中，并将其从小到大排序

3. 将数组中的value插入BST中去

4. levelorder遍历输出

突破点：

1. 在构建BST时，要知道第i次（从0开始记）输入的两个值正是BST中标号为i的node的左右

2. 在将value插入BST中去的时候，只需要将中序遍历时的visit操作改为将数值插入node即可，简单点来讲，就是将数

组从小到大排好以后，与中序遍历BST时的节点一一对应起来

代码如下：

/**********************************************************
 * Author        : XiaoXiong
 * Email         : hs_james@163.com
 * Create time   : 2016-10-28 18:14
 * Last modified : 2016-10-28 18:14
 * Filename      : 5.2.c
 * Description   : 
 * *******************************************************/

#include<stdio.h>
#include<stdlib.h>
#include<string.h>

typedef struct node *tree;
struct node{
	int value;
	tree left;
	tree right;
};

int *val;
int k=0;

void sort(int *val, int n);
void levelOrder(tree T,int n);
void insertValue(tree T);

int main()
{
	int n;
	int i;
	int l, r;
	tree T;

	scanf("%d", &n);
	getchar();

	T = (tree)malloc(sizeof(struct node)*n);
	val = (int *)malloc(sizeof(int)*n);

	if(n==0)
		return 1;

	/***根据输入的index值构建树****/
	for(i = 0; i < n; i++){
		scanf("%d %d", &l, &r);
		getchar();
		if(l != -1){
			T[i].left = T+l;
		}
		else{
			T[i].left = NULL;
		}
 		if(r != -1){
			T[i].right = T+r;
		}
		else{
			T[i].right = NULL;
		}
	}
	
	for(i = 0; i < n; i++){
		scanf("%d", &val[i]);
		getchar();	
	}

	sort(val,n);
	insertValue(T);
	levelOrder(T,n);
		
	return 0;
}

/**********将数值插入到树中************/
void insertValue(tree T)
{
	if(T){
		insertValue(T->left);
		T->value=val[k];
		k++;
		insertValue(T->right);
	}	
	return ;
}

/*************层次遍历**************/
void levelOrder(tree T, int n)
{
	int i=0,t=1;
	tree* queue;

	queue = (tree *)malloc(sizeof(tree)*n);

	if(T){
		queue[0]=T;
	}

	for(i=0;i<n;i++){
		if(i==0){
			printf("%d", queue[i]->value);
		}
		else{
			printf(" %d", queue[i]->value);
		}
		if(queue[i] -> left){
			queue[t++] = queue[i]->left;
		}
		if(queue[i] -> right){
			queue[t++] = queue[i]->right;
		}
	}	
}

/***将整型数组从小到打排列***/
void sort(int *val, int n)
{
	int i=0,j=0;
	int tmp;
	int min;
	for(i=0;i<n-1;i++){
		min = val[i];
		for(j=i+1;j<n;j++){
			if(val[j]<val[i]){
				tmp=val[j];
				val[j]=val[i];
				val[i]=tmp;
			}
		}
	}
}