1099. Build A Binary Search Tree (30)

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

思路

1.1064的老办法，将节点值升序排序后就是搜索树的中序遍历序列。

2.从根节点开始按中序遍历构造整棵树。

3.层次遍历打印整棵树(用队列BFS)。

代码

#include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
using namespace std;
class Node
{
public:
int left;
int right;
int val;
};
vector<Node> bstnodes(101);
vector<int>  nodevalue(101);
int index;

void createBST(int root)
{
if(bstnodes[root].left != -1)
createBST(bstnodes[root].left);
bstnodes[root].val = nodevalue[index++];
if(bstnodes[root].right != -1)
createBST(bstnodes[root].right);
}

int main()
{
int N;
while(cin >> N)
{
index = 0;
for(int i = 0;i < N;i++)
{
cin >> bstnodes[i].left >> bstnodes[i].right;
}
for(int i = 0;i < N;i++)
{
cin >> nodevalue[i];
}
sort(nodevalue.begin(),nodevalue.begin()+N);
createBST(0);

//print
queue<int> q;
q.push(0);
while(!q.empty())
{
int temp = q.front();
q.pop();
if(temp != 0)
cout <<" ";
cout << bstnodes[temp].val;
if(bstnodes[temp].left != -1)
q.push(bstnodes[temp].left);
if(bstnodes[temp].right != -1)
q.push(bstnodes[temp].right);
}
cout << endl;
}
return 0;
}