平衡二叉树
LL RR LR RL 注意画图理解法
An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.
Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (≤20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.
Output Specification:
For each test case, print the root of the resulting AVL tree in one line.
Sample Input 1:
5
88 70 61 96 120
Sample Output 1:
70
Sample Input 2:
7
88 70 61 96 120 90 65
Sample Output 2:
88
1 //平衡二叉树 AVL 2 #include <stdio.h> 3 #include <stdlib.h> 4 5 typedef int ElementType; 6 7 typedef struct AVLNode *Position; 8 typedef Position AVLTree; /* AVL树类型 */ 9 typedef struct AVLNode{ 10 ElementType data; /* 结点数据 */ 11 AVLTree left; /* 指向左子树 */ 12 AVLTree right; /* 指向右子树 */ 13 int height; /* 树高 */ 14 }; 15 16 int Max ( int a, int b ) 17 { 18 return a > b ? a : b; 19 } 20 21 int GetHeight( Position p ) 22 { 23 if(!p) 24 return -1; 25 return p->height; 26 } 27 28 /* 将A与B做左单旋，更新A与B的高度，返回新的根结点B */ 29 /* 注意：A必须有一个左子结点B */ 30 AVLTree SingleLeftRotation ( AVLTree A ) 31 { 32 AVLTree B = A->left; 33 A->left = B->right; 34 B->right = A; 35 A->height = Max( GetHeight(A->left), GetHeight(A->right) ) + 1; 36 B->height = Max( GetHeight(B->left), A->height ) + 1; 37 38 return B; 39 } 40 /* 将A与B做右单旋，更新A与B的高度，返回新的根结点B */ 41 /* 注意：A必须有一个右子结点B */ 42 AVLTree SingleRightRotation ( AVLTree A ) 43 { 44 AVLTree B = A->right; 45 A->right = B->left; 46 B->left = A; 47 A->height = Max( GetHeight(A->left), GetHeight(A->right) ) + 1; 48 B->height = Max( A->height, GetHeight(B->right) ) + 1; 49 50 return B; 51 } 52 53 /* 注意：A必须有一个左子结点B，且B必须有一个右子结点C */ 54 /* 将A、B与C做两次单旋，返回新的根结点C */ 55 AVLTree DoubleLeftRightRotation ( AVLTree A ) 56 { 57 /* 将B与C做右单旋，C被返回 */ 58 A->left = SingleRightRotation(A->left); 59 /* 将A与C做左单旋，C被返回 */ 60 return SingleLeftRotation(A); 61 } 62 63 /* 将A、B与C做两次单旋，返回新的根结点C */ 64 /* 注意：A必须有一个右子结点B，且B必须有一个左子结点C */ 65 AVLTree DoubleRightLeftRotation ( AVLTree A ) 66 { 67 /* 将B与C做右单旋，C被返回 */ 68 A->right = SingleLeftRotation(A->right); 69 /* 将A与C做左单旋，C被返回 */ 70 return SingleRightRotation(A); 71 } 72 73 /* 将X插入AVL树T中，并且返回调整后的AVL树 */ 74 AVLTree Insert( AVLTree T, ElementType X ) 75 { 76 if ( !T ) { /* 若插入空树，则新建包含一个结点的树 */ 77 T = (AVLTree)malloc(sizeof(struct AVLNode)); 78 T->data = X; 79 T->height = 0; 80 T->left = T->right = NULL; 81 } /* if (插入空树) 结束 */ 82 83 else if ( X < T->data ) { 84 T->left = Insert( T->left, X);/* 插入T的左子树 */ 85 if ( GetHeight(T->left)-GetHeight(T->right) == 2 ) /* 如果需要左旋 */ 86 if ( X < T->left->data ) 87 T = SingleLeftRotation(T); //左单旋 LL 88 else 89 T = DoubleLeftRightRotation(T); //左-右双旋LR 90 } /* else if (插入左子树) 结束 */ 91 92 else if ( X > T->data ) { 93 T->right = Insert( T->right, X );/* 插入T的右子树 */ 94 if ( GetHeight(T->left)-GetHeight(T->right) == -2 )/* 如果需要右旋 */ 95 if ( X > T->right->data ) 96 T = SingleRightRotation(T); //右单旋 RR 97 else 98 T = DoubleRightLeftRotation(T); //右-左双旋 RL 99 } /* else if (插入右子树) 结束 */ 100 101 /*else X == T->Data，无须插入 */ 102 T->height = Max( GetHeight(T->left), GetHeight(T->right) ) + 1; //更新树高 103 104 return T; 105 } 106 107 int main() 108 { 109 int N, data; 110 AVLTree T; 111 scanf("%d",&N); 112 for(int i = 0; i < N; i++) { 113 scanf("%d",&data); 114 T = Insert(T,data); 115 } 116 printf("%d ",T->data); 117 return 0; 118 }