1135 Is It A Red-Black Tree (30 分)

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

红黑树也不过是如此嘛，反正都是跟着规则来。
我的output函数基本上解决了所有的判断。

#include <bits/stdc++.h>
using namespace std;
int n, m, x;
struct Node
{
    int val;
    Node *left, *right;
};
set<int> st;
Node *insert(Node *root, int val){
    if(root == NULL){
        root = new Node();
        root->val = val;
        root->left = root->right = NULL;
    }else{
        if(abs(root->val) > abs(val)){
            root->left = insert(root->left, val);
        }else{
            root->right = insert(root->right, val);
        }
    }
    return root;
}
bool output(Node *root, int x){
    if(root != NULL){
        int y = root->val<0?0:1;
        if(root->left != NULL && root->val<0&&root->left->val<0)
            return false;
        if(root->right != NULL && root->val<0&&root->right->val<0)
            return false;
        if(!output(root->left, x+y)) return false;
        if(!output(root->right, x+y)) return false;
    }else{
        st.insert(x);
    }
    return true;
}
int main(){
    cin >> n;
    while(n--){
        Node *tree = NULL;
        st.clear();
        cin >> m;
        for(int i = 0; i < m; i++){
            cin >> x;
            tree = insert(tree, x);
        }
        if(tree->val < 0){
            cout << "No" << endl;
        }else{
            bool flag = output(tree, 0);
            if(flag && st.size() == 1){
                cout <<"Yes"<<endl;
            }else{
                cout << "No"<<endl;
            }
        }
    }
    return 0;
}