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 (≤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 : [email protected]
* Create time : 2016-10-28 18:14
* Last modified : 2016-10-28 18:14
* Filename : 5.2.c
* Description :
* *******************************************************/
#include
#include
#include
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;ivalue);
}
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