平衡查詢二叉樹

阿新 • • 發佈：2019-01-16

#include <stdio.h>
#include <unistd.h>
#include <malloc.h>
#include <stdlib.h>

struct node {
int key; //資料域，key值
int bf; // 平衡因子。
struct node *lchild,*rchild; //樹的左右孩子
};

typedef struct node avltree;

#define ARRAY_SIZE(x) (sizeof(x) / sizeof((x)[0]))

#define handler_error(msg) \
{perror(msg);exit(EXIT_FAILURE);}

#define LL 1
#define RR 2
#define LR 3
#define RL 4

int insert_avltree(avltree **root,int key)
{
struct node *A,*B,*C,*p,*fp,*father_A;
int choice = 0;
//-----------------------------------------------------------------
// 建立要插入的節點。
struct node *s = (struct node *)malloc(sizeof(struct node));
if (s == NULL) {
printf("file %s,line %d:malloc error\n",__FILE__,__LINE__);
return 1;
}
s->key = key;
s->lchild = s->rchild = NULL;
s->bf = 0;
//----------------------------------------------------------------
if (*root == NULL) {//如果樹的空樹則該節點作為根節點。
*root = s;
goto out1;
}
A = *root;
p = *root;
fp = NULL;
father_A = NULL;
while (p != NULL) { //從根節點開始，走到要插入的節點的位置，也就是要遍歷“祖先節點”那條線。
if (p->bf != 0 ) {
A = p;//用A來記錄插入節點祖先節點中從下到上第一個可能出現失去平衡點的節點。
father_A = fp;//father_A用來記錄A節點的父節點。
}
fp = p;
if (key < p->key)
p = p->lchild;
else
p = p->rchild;
}
//-------------------------------------------------------------
// 插入s節點到指定的位置。
if (key < fp->key)
fp->lchild = s;
else
fp->rchild = s;
//--------------------------------------------------------------
//確定B節點，並修改A的平衡因子。
if (key < A->key) {
B = A->lchild;
A->bf = A->bf + 1;
} else {
B = A->rchild;
A->bf = A->bf - 1;
}
//--------------------------------------------------------------
// 修改B至S路徑上個節點的平衡因子，原來的肯定都是0，思考下，為什麼？結合A是怎麼選擇出來的。
p = B;
while (p != s) {
if(key < p->key) {
p->bf = 1; p = p->lchild;
}else {
p->bf = -1; p = p->rchild;
}
}
//--------------------------------------------------------------
if (A->bf == 2 && B->bf == 1) // 3
choice = LL;
else if (A->bf == -2 && B->bf == -1) //-3
choice = RR;
else if (A->bf == 2 && B->bf == -1) //1
choice = LR;
else if (A->bf == -2 && B->bf == 1) // -1
choice = RL;
else {
choice = 0;
}

//----------------------------------------------------------------
printf("choice = %d\n",choice);
switch (choice) {
case LL:
B = A->lchild;
A->lchild = B->rchild;
B->rchild = A;
A->bf = B->bf = 0;
if (father_A == NULL) *root = B;
else if (A == father_A->lchild) father_A->lchild = B;
elsefather_A->rchild = B;
break;
case LR:
B = A->lchild;
C = B->rchild;
B->rchild = C->lchild;
A->lchild = C->rchild;
C->lchild = B;
C->rchild = A;
if (s->key < C->key) {
A->bf = -1;B->bf = 0;C->bf = 0;
} else if (s->key > C->key) {
A->bf =0;B->bf = 1;C->bf = 0;
} else {
A->bf = 0;B->bf = 0;
}
if (father_A == NULL) *root = C;
else if (A == father_A->lchild) father_A->lchild = C;
else father_A->rchild = C;
break;
case RL:
B = A->rchild;
C = B->lchild;
B->lchild = C->rchild;
A->rchild = C->lchild;
C->lchild = A;
C->rchild = B;
if (s->key < C->key) {
A->bf = 0;B->bf = -1;C->bf = 0;
} else if (s->key > C->key) {
A->bf = 1;B->bf = 0;C->bf = 0;
} else {
A->bf = 0;B->bf = 0;
}
if (father_A == NULL) *root = C;
else if (A == father_A->lchild) father_A->lchild = C;
else father_A->rchild = C;
break;
case RR:
B = A->rchild;
A->rchild = B->lchild;
B->lchild = A;
A->bf = B->bf = 0;
if (father_A == NULL) *root = B;
else if (A == father_A->lchild) father_A->lchild = B;
else father_A->rchild = B;
break;
default:
printf("the avl tree is OK when insert a node!\n");
break;
}

out1:
return 0;
}

int create_avl(avltree **avl)
{
int a[] = {24,12,53,28,45,90};
int length = ARRAY_SIZE(a);
int i = 0;

*avl = NULL;

for (i=0;i<length;i++) {
insert_avltree(avl,a[i]);
printf("insert node %d\n",a[i]);
}

return 0;
}

struct node* search_avl(avltree *root,int key)
{
while (root) {
if (root->key == key)
return root;
else if (key < root->key)
root = root->lchild;
else
root = root->rchild;
}

return NULL;
}

int main(int argc,char *argv[])
{
avltree *root = NULL;
avltree *node = NULL;
int a[] = {10,20,29,24,12,53,45,90,100,290,28};
int length = ARRAY_SIZE(a);
int i = 0;

if (create_avl(&root)) {
printf("create bstree error!\n");
exit(1);
}

for (i=0;i<length;i++) {
node = search_avl(root,a[i]);
if (node == NULL) {
printf("%d you search is not exist in the tree!\n",a[i]);
}else {
printf("search successfully!,and the key is %d\n",node->key);
}
}

return 0;
}

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