PAT 1099. Build A Binary Search Tree (30)

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

此题只需要知道BST的前序遍历为递增的序列就可以轻松的设置各个节点的值了

#include <iostream>
#include <vector>
#include <algorithm>
#include <queue>

using namespace std;

struct Node
{
    int value;
    int left = -1;
    int right = -1;
};

Node tree[100];
int num[100];
int cnt = 0;

void PreTraversal(int root)    //use preorder traversal to set the value
{
    if (root == -1)
        return;
    PreTraversal(tree[root].left);
    tree[root].value = num[cnt++];
    PreTraversal(tree[root].right);
}

void levelTraversal(int root)
{
    queue<int> que;
    que.push(root);
    while (!que.empty())
    {
        int index = que.front();
        que.pop();
        if (index != root)
            cout << " ";
        cout << tree[index].value;
        if (tree[index].left != -1)
            que.push(tree[index].left);
        if (tree[index].right != -1)
            que.push(tree[index].right);
    }
}

int main()
{
    int n;
    cin >> n;
    for (int i = 0; i < n; i++)
        cin >> tree[i].left >> tree[i].right;
    for (int i = 0; i < n; i++)
        cin >> num[i];
    sort(num, num + n);

    PreTraversal(0);
    levelTraversal(0);
}