平衡二叉树(也称为高度平衡二叉树)定义为二叉树,其中任何节点的左和右子树的高度相差不超过1。
要了解有关树/节点的高度的更多信息,请访问树数据结构。以下是高度平衡的二叉树的条件:
- 任何节点的左右子树之间的差异不超过一个
- 左子树是平衡的
- 正确的子树是平衡的
Python,Java和C / C++示例
以下代码用于检查树是否高度平衡。
Python
爪哇
C
C++
# Checking if a binary tree is CalculateHeight balanced in Python
# CreateNode creation
class CreateNode:
def __init__(self, item):
self.item = item
self.left = self.right = None
# Calculate height
class CalculateHeight:
def __init__(self):
self.CalculateHeight = 0
# Check height balance
def is_height_balanced(root, CalculateHeight):
left_height = CalculateHeight()
right_height = CalculateHeight()
if root is None:
return True
l = is_height_balanced(root.left, left_height)
r = is_height_balanced(root.right, right_height)
CalculateHeight.CalculateHeight = max(
left_height.CalculateHeight, right_height.CalculateHeight) + 1
if abs(left_height.CalculateHeight - right_height.CalculateHeight) <= 1:
return l and r
return False
CalculateHeight = CalculateHeight()
root = CreateNode(1)
root.left = CreateNode(2)
root.right = CreateNode(3)
root.left.left = CreateNode(4)
root.left.right = CreateNode(5)
if is_height_balanced(root, CalculateHeight):
print('The tree is balanced')
else:
print('The tree is not balanced')
// Checking if a binary tree is height balanced in Java
// Node creation
class Node {
int data;
Node left, right;
Node(int d) {
data = d;
left = right = null;
}
}
// Calculate height
class Height {
int height = 0;
}
class BinaryTree {
Node root;
// Check height balance
boolean checkHeightBalance(Node root, Height height) {
// Check for emptiness
if (root == null) {
height.height = 0;
return true;
}
Height leftHeighteight = new Height(), rightHeighteight = new Height();
boolean l = checkHeightBalance(root.left, leftHeighteight);
boolean r = checkHeightBalance(root.right, rightHeighteight);
int leftHeight = leftHeighteight.height, rightHeight = rightHeighteight.height;
height.height = (leftHeight > rightHeight ? leftHeight : rightHeight) + 1;
if ((leftHeight - rightHeight >= 2) || (rightHeight - leftHeight >= 2))
return false;
else
return l && r;
}
public static void main(String args[]) {
Height height = new Height();
BinaryTree tree = new BinaryTree();
tree.root = new Node(1);
tree.root.left = new Node(2);
tree.root.right = new Node(3);
tree.root.left.left = new Node(4);
tree.root.left.right = new Node(5);
if (tree.checkHeightBalance(tree.root, height))
System.out.println("The tree is balanced");
else
System.out.println("The tree is not balanced");
}
}
// Checking if a binary tree is height balanced in C
#include
#include
#define bool int
// Node creation
struct node {
int item;
struct node *left;
struct node *right;
};
// Create a new node
struct node *newNode(int item) {
struct node *node = (struct node *)malloc(sizeof(struct node));
node->item = item;
node->left = NULL;
node->right = NULL;
return (node);
}
// Check for height balance
bool checkHeightBalance(struct node *root, int *height) {
// Check for emptiness
int leftHeight = 0, rightHeight = 0;
int l = 0, r = 0;
if (root == NULL) {
*height = 0;
return 1;
}
l = checkHeightBalance(root->left, &leftHeight);
r = checkHeightBalance(root->right, &rightHeight);
*height = (leftHeight > rightHeight ? leftHeight : rightHeight) + 1;
if ((leftHeight - rightHeight >= 2) || (rightHeight - leftHeight >= 2))
return 0;
else
return l && r;
}
int main() {
int height = 0;
struct node *root = newNode(1);
root->left = newNode(2);
root->right = newNode(3);
root->left->left = newNode(4);
root->left->right = newNode(5);
if (checkHeightBalance(root, &height))
printf("The tree is balanced");
else
printf("The tree is not balanced");
}
// Checking if a binary tree is height balanced in C++
#include
using namespace std;
#define bool int
class node {
public:
int item;
node *left;
node *right;
};
// Create anew node
node *newNode(int item) {
node *Node = new node();
Node->item = item;
Node->left = NULL;
Node->right = NULL;
return (Node);
}
// Check height balance
bool checkHeightBalance(node *root, int *height) {
// Check for emptiness
int leftHeight = 0, rightHeight = 0;
int l = 0, r = 0;
if (root == NULL) {
*height = 0;
return 1;
}
l = checkHeightBalance(root->left, &leftHeight);
r = checkHeightBalance(root->right, &rightHeight);
*height = (leftHeight > rightHeight ? leftHeight : rightHeight) + 1;
if ((leftHeight - rightHeight >= 2) || (rightHeight - leftHeight >= 2))
return 0;
else
return l && r;
}
int main() {
int height = 0;
node *root = newNode(1);
root->left = newNode(2);
root->right = newNode(3);
root->left->left = newNode(4);
root->left->right = newNode(5);
if (checkHeightBalance(root, &height))
cout << "The tree is balanced";
else
cout << "The tree is not balanced";
}
平衡二叉树应用
- AVL树
- 平衡二叉搜索树