主要是要理解紅黑樹的定義：
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.
翻譯：
（1）紅黑樹的節點只能爲紅或者黑。
（2）根節點是黑。
（3）null爲黑，表示葉子節點（沒有child的節點爲葉子節點）可以爲紅爲黑。如果條件改爲null節點爲紅，則葉子節點必須爲黑。
（4）如果該節點爲紅，其child節點都爲黑。
（5）每個節點到葉子節點的路徑上的black節點數都相等。其實這跟從根節點到葉子節點的每條路徑上的總black節點數都相等是一個意思，想一下就能理解。
所以這題，只需判斷：
1. 根節點是否爲黑。
2. 每個紅節點的所有child是否都爲黑。
3. 根節點到每個葉子節點的路徑上的黑節點數是否都相等。
#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(tree->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;
}另外補充c的free和c++的delete的區別：
delete 用於釋放new分配的內存，和new成對調用
free 用於釋放malloc分配的內存，和malloc成對調用
使用free釋放時需要判斷指針是否爲NULL，delete不用
free 釋放內存，但不調用對象的析構函數
delete 不僅釋放內存，還調用對象的析構函數
delete 和new是對對象的操作，是運算符
free 和malloc是對內存空間的操作
繼續加油~