先将平衡二叉树代码存在这里,具体的原理解释,以后有时间再补充
代码:
#include<iostream>
#define maxn 1000
using namespace std;
struct node
{
int data;
int height;
node *lchild, *rchild;
};
int key[maxn];
int n;
int getheight(node* root)
{
if(root != NULL)
{
return root->height;
}else
{
return 0;
}
}
void updataheight(node* &root)
{
if(root != NULL)
{
root->height = max(getheight(root->lchild), getheight(root->rchild)) + 1;
}
}
int getbalancefactor(node* root)
{
return (getheight(root->lchild) - getheight(root->rchild));
}
void L(node* &root)
{
node* temp = root->rchild;
root->rchild = temp->lchild;
temp->lchild = root;
updataheight(root);
updataheight(temp);
root = temp;
}
void R(node* &root)
{
node* temp = root->lchild;
root->lchild = temp->rchild;
temp->rchild = root;
updataheight(root);
updataheight(temp);
root = temp;
}
node* newnode(int x)
{
node* root = new node;
root->data = x;
root->height = 1;
root->lchild = root->rchild = NULL;
return root;
}
void insert(node* &root , int x)
{
if(root == NULL)
{
root = newnode(x);
return;
}
if(root->data == x)
{
return;
}
if(root->data > x)
{
insert(root->lchild, x);
updataheight(root);
if(getbalancefactor(root) == 2)
{
if(getbalancefactor(root->lchild) == 1)
{
R(root);
}
if(getbalancefactor(root->lchild) == -1)
{
L(root->lchild);
R(root);
}
}
}else if(root->data < x)
{
insert(root->rchild, x);
updataheight(root);
if(getbalancefactor(root) == -2)
{
if(getbalancefactor(root->rchild) == 1)
{
R(root->rchild);
L(root);
}
if(getbalancefactor(root->rchild) == -1)
{
L(root);
}
}
}
}
node* create(int key[], int n)
{
node* root = NULL;
for(int i = 0; i < n; i ++)
{
insert(root, key[i]);
}
return root;
}
void inorder(node* root)
{
if(root == NULL)
{
return;
}
inorder(root->lchild);
printf("%d ", root->data);
inorder(root->rchild);
}
int main()
{
cin >> n;
for(int i = 0; i < n; i++)
{
scanf("%d",&key[i]);
}
node* root = create(key, n);
inorder(root);
return 0;
}
测试用例:
输入 :
8
10 20 30 7 14 25 40 48
输出:(经过处理的平衡二叉树的中序遍历)
7 10 14 20 25 30 40 48