1099 Build A Binary Search Tree (30 分)
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
一,注意事项
1,本题同A1064是一样的,都是给定二叉排序树的结构往里面添加数据,处理方法也是一样的,先把整个数组由小到大排序,再按照中序遍历的顺序插入。
二,我的代码
#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;
const int max_n = 110;
int N = 0;
int index = 0, num_of_ans = 0;
int arr[max_n];
struct Node {
int data;
int lchild;
int rchild;
}node[max_n];
void insert_binary_tree(int root) {
if (root == -1)return;
insert_binary_tree(node[root].lchild);
node[root].data = arr[index++];
insert_binary_tree(node[root].rchild);
}
void BFS(int root) {
queue<int> que;
que.push(root);
while (!que.empty()) {
int top = que.front();
que.pop();
printf("%d", node[top].data);
num_of_ans++;
if (num_of_ans != N) {
printf(" ");
}
if (node[top].lchild != -1)que.push(node[top].lchild);
if (node[top].rchild != -1)que.push(node[top].rchild);
}
}
int main() {
int lchild = 0, rchild = 0;
scanf("%d", &N);
for (int i = 0; i < N; i++) {
scanf("%d %d", &lchild, &rchild);
node[i].lchild = lchild;
node[i].rchild = rchild;
}
for (int i = 0; i < N; i++) {
scanf("%d", &arr[i]);
}
sort(arr, arr + N);
insert_binary_tree(0);
BFS(0);
return 0;
}