PAT1099:Build A Binary Search Tree

1099. Build A Binary Search Tree (30)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

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;
}