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1135 Is It A Red-Black Tree

Statement

Metadata

  • 作者: CHEN, Yue
  • 单位: 浙江大学
  • 代码长度限制: 16 KB
  • 时间限制: 400 ms
  • 内存限制: 64 MB

There is a kind of balanced binary search tree named red-black tree in the data structure. It has the following 5 properties:

  • (1) Every node is either red or black.
  • (2) The root is black.
  • (3) Every leaf (NULL) is black.
  • (4) If a node is red, then both its children are black.
  • (5) For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.

For example, the tree in Figure 1 is a red-black tree, while the ones in Figure 2 and 3 are not.

rbf1.jpg rbf2.jpg rbf3.jpg
Figure 1 Figure 2 Figure 3

For each given binary search tree, you are supposed to tell if it is a legal red-black tree.

Input Specification

Each input file contains several test cases. The first line gives a positive integer K (\le30) which is the total number of cases. For each case, the first line gives a positive integer N (\le30), the total number of nodes in the binary tree. The second line gives the preorder traversal sequence of the tree. While all the keys in a tree are positive integers, we use negative signs to represent red nodes. All the numbers in a line are separated by a space. The sample input cases correspond to the trees shown in Figure 1, 2 and 3.

Output Specification

For each test case, print in a line "Yes" if the given tree is a red-black tree, or "No" if not.

Sample Input 

3
9
7 -2 1 5 -4 -11 8 14 -15
9
11 -2 1 -7 5 -4 8 14 -15
8
10 -7 5 -6 8 15 -11 17

Sample Output 

Yes
No
No

Last update: May 4, 2022
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