其它pta数据结构编程题请参见：pta
这道题考察平衡二叉查找树的插入。
为了保证二叉查找树的平衡，当一个结点的左右子树的高度差大于1时就要进行调整。
分为以下四种情况：
插入新节点后，以及旋转之后，需要更新结点的高度。
RL旋转可以通过右孩子的LL旋转，然后当前节点的RR旋转实现。
同理，LR旋转可以通过左孩子的RR旋转，然后当前节点的LL旋转实现。
1 #include <iostream> 2 using namespace std; 3 4 typedef struct Node *Tree; 5 struct Node 6 { 7 int data; 8 Tree left; 9 Tree right; 10 int height; 11 }; 12 13 Tree insert(Tree T, int X); 14 Tree ll(Tree A); 15 Tree lr(Tree A); 16 Tree rr(Tree A); 17 Tree rl(Tree A); 18 int getHeight(Tree T); 19 int max(int a, int b); 20 Tree createNode(int X); 21 22 int main() 23 { 24 int N, X, i; 25 cin >> N >> X; 26 Tree root = createNode(X); 27 for (i = 1; i < N; i++) 28 { 29 cin >> X; 30 root = insert(root, X); 31 } 32 cout << root->data; 33 return 0; 34 } 35 36 Tree insert(Tree T, int X) 37 { 38 if (!T) 39 T = createNode(X); 40 else if (X < T->data) 41 { 42 T->left = insert(T->left, X); 43 if (getHeight(T->left) - getHeight(T->right) == 2) 44 { 45 if (X < T->left->data) 46 T = ll(T); 47 else 48 T = lr(T); 49 } 50 } 51 else if (X > T->data) 52 { 53 T->right = insert(T->right, X); 54 if (getHeight(T->right) - getHeight(T->left) == 2) 55 { 56 if (X > T->right->data) 57 T = rr(T); 58 else 59 T = rl(T); 60 } 61 } 62 T->height = max(getHeight(T->left), getHeight(T->right)) + 1; 63 return T; 64 } 65 66 Tree ll(Tree A) 67 { 68 Tree B = A->left; 69 A->left = B->right; 70 B->right = A; 71 A->height = max(getHeight(A->left), getHeight(A->right)) + 1; 72 B->height = max(getHeight(A->left), A->height) + 1; 73 return B; 74 } 75 76 Tree rr(Tree A) 77 { 78 Tree B = A->right; 79 A->right = B->left; 80 B->left = A; 81 A->height = max(getHeight(A->left), getHeight(A->right)) + 1; 82 B->height = max(A->height, getHeight(B->right)) + 1; 83 return B; 84 } 85 86 Tree lr(Tree A) 87 { 88 A->left = rr(A->left); 89 return ll(A); 90 } 91 92 Tree rl(Tree A) 93 { 94 A->right = ll(A->right); 95 return rr(A); 96 } 97 98 int getHeight(Tree T) 99 { 100 if (T == NULL) return 0; 101 else return T->height; 102 } 103 104 int max(int a, int b) 105 { 106 return a > b ? a : b; 107 } 108 109 Tree createNode(int X) 110 { 111 Tree T; 112 T = new Node; 113 T->data = X; 114 T->left = T->right = NULL; 115 T->height = 1; 116 return T; 117 }