PAT甲级-1135 Is It A Red-Black Tree

主要是要理解红黑树的定义：

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.

翻译：

（1）红黑树的节点只能为红或者黑。

（2）根节点是黑。

（3）null为黑，表示叶子节点（没有child的节点为叶子节点）可以为红为黑。如果条件改为null节点为红，则叶子节点必须为黑。

（4）如果该节点为红，其child节点都为黑。

（5）每个节点到叶子节点的路径上的black节点数都相等。其实这跟从根节点到叶子节点的每条路径上的总black节点数都相等是一个意思，想一下就能理解。

所以这题，只需判断：

1. 根节点是否为黑。

2. 每个红节点的所有child是否都为黑。

3. 根节点到每个叶子节点的路径上的黑节点数是否都相等。

#include <bits/stdc++.h>
using namespace std;
typedef struct node {
int key;
struct node *left;
struct node *right;
} Node, *Tree;
int T, N;
Node* tree_create(int key) {
// Node *p = (Node *)malloc(sizeof(Node));
Node *p = new Node();
p->key = key;
p->left = NULL;
p->right = NULL;
return p;
}
Node* tree_insert(Node *tree, int key) {
if(tree == NULL) {
tree = tree_create(key);
}
else if(abs(key) < abs(tree->key)) {
tree->left = tree_insert(tree->left, key);
}
else if(abs(key) > abs(tree->key)) {
tree->right = tree_insert(tree->right, key);
}
return tree;
}
int flag, reals;
bool red_jg(Node *tree, int cnt) {
if(tree == NULL) {
if(reals == -1) {
reals = cnt;
}
else if(reals != cnt){
flag = 0;
}
return true;
}
if(tree->key < 0) {
if(tree->left && tree->left->key < 0) {
return false;
}
if(tree->right && tree->right->key < 0) {
return false;
}
}
int tmp = tree->key > 0 ? 1 : 0;
if(!red_jg(tree->left, cnt+tmp)) {
return false;
}
if(!red_jg(tree->right, cnt+tmp)) {
return false;
}
return true;
}
int judge(Node *tree) {
if(tree->key < 0) {
return 0;
}
if(!red_jg(tree, 0)) {
return 0;
}
return flag;
}
void Free(Node *tree) {
if(tree->left) {
Free(tree->left);
}
if(tr
4000
ee->right) {
Free(tree->right);
}
delete tree;
// free(tree);
tree = NULL;
}
int main() {
scanf("%d", &T);
for(int _ = 1; _ <= T; ++_) {
scanf("%d", &N);
flag = 1, reals = -1;
Tree root = NULL;
for(int i = 1; i <= N; ++i) {
int key;
scanf("%d", &key);
root = tree_insert(root, key);
}
if(judge(root)) {
printf("Yes\n");
}
else {
printf("No\n");
}
Free(root);
}
return 0;
}

另外补充c的free和c++的delete的区别：

delete 用于释放new分配的内存，和new成对调用

free 用于释放malloc分配的内存，和malloc成对调用

使用free释放时需要判断指针是否为NULL，delete不用

free 释放内存，但不调用对象的析构函数

delete 不仅释放内存，还调用对象的析构函数

delete 和new是对对象的操作，是运算符

free 和malloc是对内存空间的操作

继续加油~