PAT 1135.Is It A Red-Black Tree（30 分）

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.

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 (≤30) which is the total number of cases. For each case, the first line gives a positive integer N (≤30), 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

红黑树 是一种二叉查找树 左<根<右 

根为红 孩子结点必是黑

点到叶子结点的黑色树相同

根必为黑  

#include <stdio.h>
#include <stdlib.h>
#include <cmath>
#include <vector>
using namespace std;
vector<int> preOrder;
struct BitNode{
    int data;
    struct BitNode *rchild, *lchild;
};
BitNode* create(BitNode *root,int x)
{
    if(root == NULL)
    {
        root = new BitNode();
        root->data=x;
        root->lchild = root->rchild=NULL;
    }else if(abs(x)< abs(root->data)){
        root->lchild = create(root->lchild,x);
    }else{
        root->rchild = create(root->rchild,x);
    }
    return root;
}
bool fRedcBlack(BitNode *root)
{
    if(root == NULL)
    {
        return true;
    }else{
        if(root->data <0)
        {
            if(root->lchild != NULL && root->lchild->data<0){
                return false;
            }if(root->rchild != NULL && root->rchild->data<0)
            {
                return false;
            }
        }
    }
    return fRedcBlack(root->lchild) && fRedcBlack(root->rchild);
}
int blackNumber(BitNode * root)
{
    if(root == NULL)
        return 0;
    int l = blackNumber(root->lchild);
    int r = blackNumber(root->rchild);
    
    return root->data > 0 ? max(l, r)+1:max(l, r);
    
}
bool sameBNumber(BitNode *root)
{
    if(root == NULL)
    {
        return true;
    }
    int l = blackNumber(root->lchild);
    int r = blackNumber(root->rchild);
    if(l!=r)
        return false;
    return sameBNumber(root->lchild) && sameBNumber(root->rchild);
}
int main()
{
    int k,m;
    scanf("%d",&k);
    while(k--)
    {
        scanf("%d",&m);
        preOrder.resize(m);
        BitNode *root = NULL;
        for(int i=0;i<m;i++)
        {
            scanf("%d",&preOrder[i]);
            root = create(root, preOrder[i]);
        }
        if(preOrder[0]<0 || !fRedcBlack(root) || !sameBNumber(root))
        {
            printf("No\n");
        }else{
            printf("Yes\n");
        }
    }
    return 0;
}