给定一个二叉树和一个正整数K 。任务是检查给定的二叉树中是否存在大小为K的平衡 BST。如果存在，则打印“是”，否则打印“否” 。
例子：
Input: K = 4,
Below is the given Tree:
15
/ \
10 26
/ \ / \
5 12 25 40
/ / \
20 35 50
\
60
Output: Yes
Explanation:
Subtree of the given tree with
size k is given below:
40
/ \
35 50
\
60
Input: K = 4,
Below is the given Tree:
18
/
9
/ \
7 10
Output: No
Explanation:
There is no subtree of size K
which forms a balanced BT.
方法：想法是使用后序遍历。以下是解决问题的步骤：
- 对给定的树执行后序遍历并检查每个节点的BST 条件，其中左子树中的最大值应小于当前值，右子树中的较小值应大于当前值。
- 然后检查 BST 是否平衡，即左右子树之间的绝对差异应该是0 或 1 。
- 然后将值从子树返回到父树。
- 对所有节点执行上述步骤，并获取最初标记为 false 的布尔变量ans ，用于检查是否存在平衡的 BST。
- 如果找到大小为K的平衡 BST，则打印“是”，否则打印“否” 。
下面是上述方法的实现：
C++
// C++ program for the above approach
#include
using namespace std;
// A tree node
struct node {
int data;
node* left;
node* right;
};
// Structure of temporary variable
struct minMax {
bool isBST;
bool balanced;
int size;
int hight;
int min;
int max;
};
// Function to create the node
node* createNode(int value)
{
node* temp = new node();
temp->left = NULL;
temp->right = NULL;
temp->data = value;
}
// Utility function to find Balanced
// BST of size k
minMax findBalancedBstUtil(node* root,
int k, bool& ans)
{
// Base condition
if (root == NULL)
return { true, true, 0, 0,
INT_MAX, INT_MIN };
// Temporary variable
minMax temp;
// Recursive call for left sub-tree
minMax lsTree
= findBalancedBstUtil(root->left,
k, ans);
if (ans == true)
return temp;
// Recursive call for right sub-tree
minMax rsTree
= findBalancedBstUtil(root->right,
k, ans);
if (ans == true)
return temp;
// Check those conditions which
// violated the rules of BST
if (!lsTree.isBST || !rsTree.isBST
|| lsTree.max > root->data
|| rsTree.min < root->data) {
temp.isBST = false;
return temp;
}
// Check whether the Bst is
// height balanced or not
if (abs(lsTree.hight
- rsTree.hight)
== 1
|| abs(lsTree.hight
- rsTree.hight)
== 0)
temp.balanced = true;
else
temp.balanced = false;
// Make the variable true
// as sub-tree is BST
temp.isBST = true;
// Store the size
temp.size = 1 + lsTree.size
+ rsTree.size;
// Store the height
temp.hight = max(lsTree.hight,
rsTree.hight)
+ 1;
// Store the minimum of BST
temp.min = root->left != NULL
? lsTree.min
: root->data;
// Store the maximum of BST
temp.max = root->right != NULL
? rsTree.max
: root->data;
// Condition to check whether the
// size of Balnced BST is K or not
if (temp.balanced == true
&& temp.size == k) {
ans = true;
}
// Return the temporary variable
// with updated data
return temp;
}
// Function to find the Balanced
// BST of size k
string findBalancedBst(node* root,
int k)
{
bool ans = false;
// Utility function call
findBalancedBstUtil(root, k, ans);
return ans == true ? "Yes" : "No";
}
// Driver Code
int main()
{
// Given Binary Tree
node* root = createNode(15);
root->left = createNode(10);
root->right = createNode(26);
root->left->left = createNode(5);
root->left->right = createNode(12);
root->right->left = createNode(25);
root->right->left->left = createNode(20);
root->right->right = createNode(40);
root->right->right->left = createNode(35);
root->right->right->right = createNode(50);
root->right->right->right->right = createNode(60);
int k = 4;
// Function Call
cout << findBalancedBst(root, k);
return 0;
} Java
// Java program for the above approach
import java.util.*;
class GFG{
static boolean ans;
// A tree node
static class node
{
int data;
node left;
node right;
};
// Structure of temporary variable
static class minMax
{
boolean isBST;
boolean balanced;
int size;
int hight;
int min;
int max;
public minMax(boolean isBST, boolean balanced,
int size, int hight, int min,
int max)
{
super();
this.isBST = isBST;
this.balanced = balanced;
this.size = size;
this.hight = hight;
this.min = min;
this.max = max;
}
public minMax()
{
// TODO Auto-generated constructor stub
}
};
// Function to create the node
static node createNode(int value)
{
node temp = new node();
temp.left = null;
temp.right = null;
temp.data = value;
return temp;
}
// Utility function to find Balanced
// BST of size k
static minMax findBalancedBstUtil(node root,
int k)
{
// Base condition
if (root == null)
return new minMax(true, true, 0, 0,
Integer.MAX_VALUE,
Integer.MIN_VALUE );
// Temporary variable
minMax temp = new minMax();
// Recursive call for left sub-tree
minMax lsTree = findBalancedBstUtil(root.left,
k);
if (ans == true)
return temp;
// Recursive call for right sub-tree
minMax rsTree = findBalancedBstUtil(root.right,
k);
if (ans == true)
return temp;
// Check those conditions which
// violated the rules of BST
if (!lsTree.isBST || !rsTree.isBST ||
lsTree.max > root.data ||
rsTree.min < root.data)
{
temp.isBST = false;
return temp;
}
// Check whether the Bst is
// height balanced or not
if (Math.abs(lsTree.hight -
rsTree.hight) == 1 ||
Math.abs(lsTree.hight -
rsTree.hight) == 0)
temp.balanced = true;
else
temp.balanced = false;
// Make the variable true
// as sub-tree is BST
temp.isBST = true;
// Store the size
temp.size = 1 + lsTree.size +
rsTree.size;
// Store the height
temp.hight = Math.max(lsTree.hight,
rsTree.hight) + 1;
// Store the minimum of BST
temp.min = root.left != null ?
lsTree.min : root.data;
// Store the maximum of BST
temp.max = root.right != null ?
rsTree.max : root.data;
// Condition to check whether the
// size of Balnced BST is K or not
if (temp.balanced == true &&
temp.size == k)
{
ans = true;
}
// Return the temporary variable
// with updated data
return temp;
}
// Function to find the Balanced
// BST of size k
static String findBalancedBst(node root,
int k)
{
ans = false;
// Utility function call
findBalancedBstUtil(root, k);
return ans == true ? "Yes" : "No";
}
// Driver Code
public static void main(String[] args)
{
// Given Binary Tree
node root = createNode(15);
root.left = createNode(10);
root.right = createNode(26);
root.left.left = createNode(5);
root.left.right = createNode(12);
root.right.left = createNode(25);
root.right.left.left = createNode(20);
root.right.right = createNode(40);
root.right.right.left = createNode(35);
root.right.right.right = createNode(50);
root.right.right.right.right = createNode(60);
int k = 4;
// Function call
System.out.print(findBalancedBst(root, k));
}
}
// This code is contributed by Amit KatiyarPython3
# Python3 program for the above approach
import sys
ans = False
# A tree node
class createNode:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Structure of temporary variable
class newMinMax:
def __init__(self, isBST, balanced, size,
height, mn, mx):
self.isBST = isBST
self.balanced = balanced
self.size = size
self.height = height
self.mn = mn
self.mx = mx
# Utility function to find Balanced
# BST of size k
def findBalancedBstUtil(root, k):
global ans
# Base condition
if (root == None):
return newMinMax(True, True, 0, 0,
sys.maxsize,
-sys.maxsize - 1)
# Temporary variable
temp = newMinMax(True, True, 0, 0,
sys.maxsize,
-sys.maxsize - 1)
# Recursive call for left sub-tree
lsTree = findBalancedBstUtil(root.left, k)
if (ans == True):
return temp
# Recursive call for right sub-tree
rsTree = findBalancedBstUtil(root.right, k)
if (ans == True):
return temp
# Check those conditions which
# violated the rules of BST
if (lsTree.isBST == False or
rsTree.isBST == False or
lsTree.mx > root.data or
rsTree.mn < root.data):
temp.isBST = False
return temp
# Check whether the Bst is
# height balanced or not
if (abs(lsTree.height - rsTree.height) == 1 or
abs(lsTree.height - rsTree.height) == 0):
temp.balanced = True
else:
temp.balanced = False
# Make the variable true
# as sub-tree is BST
temp.isBST = True
# Store the size
temp.size = 1 + lsTree.size + rsTree.size
# Store the height
temp.height = max(lsTree.height ,
rsTree.height) + 1
# Store the minimum of BST
if root.left != None:
temp.mn = lsTree.mn
else:
temp.mn = root.data
# Store the maximum of BST
if root.right != None:
temp.mx = rsTree.mx
else:
temp.mx = root.data
# Condition to check whether the
# size of Balnced BST is K or not
if (temp.balanced == True and
temp.size == k):
ans = True
# Return the temporary variable
# with updated data
return temp
# Function to find the Balanced
# BST of size k
def findBalancedBst(root, k):
global ans
# Utility function call
findBalancedBstUtil(root, k)
if ans == True:
return "Yes"
else:
return "No"
# Driver Code
if __name__ == '__main__':
# Given Binary Tree
root = createNode(15)
root.left = createNode(10)
root.right = createNode(26)
root.left.left = createNode(5)
root.left.right = createNode(12)
root.right.left = createNode(25)
root.right.left.left = createNode(20)
root.right.right = createNode(40)
root.right.right.left = createNode(35)
root.right.right.right = createNode(50)
root.right.right.right.right = createNode(60)
k = 4
# Function Call
print(findBalancedBst(root, k))
# This code is contributed by ipg2016107C#
// C# program for the
// above approach
using System;
class GFG{
static bool ans;
// A tree node
public class node
{
public int data;
public node left;
public node right;
};
// Structure of temporary
// variable
public class minMax
{
public bool isBST;
public bool balanced;
public int size;
public int hight;
public int min;
public int max;
public minMax(bool isBST, bool balanced,
int size, int hight, int min,
int max)
{
this.isBST = isBST;
this.balanced = balanced;
this.size = size;
this.hight = hight;
this.min = min;
this.max = max;
}
public minMax()
{
// TODO Auto-generated constructor stub
}
};
// Function to create the node
static node createNode(int value)
{
node temp = new node();
temp.left = null;
temp.right = null;
temp.data = value;
return temp;
}
// Utility function to find Balanced
// BST of size k
static minMax findBalancedBstUtil(node root,
int k)
{
// Base condition
if (root == null)
return new minMax(true, true, 0, 0,
int.MaxValue,
int.MinValue);
// Temporary variable
minMax temp = new minMax();
// Recursive call for left sub-tree
minMax lsTree =
findBalancedBstUtil(root.left, k);
if (ans == true)
return temp;
// Recursive call for right sub-tree
minMax rsTree =
findBalancedBstUtil(root.right, k);
if (ans == true)
return temp;
// Check those conditions which
// violated the rules of BST
if (!lsTree.isBST || !rsTree.isBST ||
lsTree.max > root.data ||
rsTree.min < root.data)
{
temp.isBST = false;
return temp;
}
// Check whether the Bst is
// height balanced or not
if (Math.Abs(lsTree.hight -
rsTree.hight) == 1 ||
Math.Abs(lsTree.hight -
rsTree.hight) == 0)
temp.balanced = true;
else
temp.balanced = false;
// Make the variable true
// as sub-tree is BST
temp.isBST = true;
// Store the size
temp.size = 1 + lsTree.size +
rsTree.size;
// Store the height
temp.hight = Math.Max(lsTree.hight,
rsTree.hight) + 1;
// Store the minimum of BST
temp.min = root.left != null ?
lsTree.min : root.data;
// Store the maximum of BST
temp.max = root.right != null ?
rsTree.max : root.data;
// Condition to check whether the
// size of Balnced BST is K or not
if (temp.balanced == true &&
temp.size == k)
{
ans = true;
}
// Return the temporary
// variable with updated data
return temp;
}
// Function to find the Balanced
// BST of size k
static String findBalancedBst(node root,
int k)
{
ans = false;
// Utility function call
findBalancedBstUtil(root, k);
return ans == true ? "Yes" : "No";
}
// Driver Code
public static void Main(String[] args)
{
// Given Binary Tree
node root = createNode(15);
root.left = createNode(10);
root.right = createNode(26);
root.left.left = createNode(5);
root.left.right = createNode(12);
root.right.left = createNode(25);
root.right.left.left = createNode(20);
root.right.right = createNode(40);
root.right.right.left = createNode(35);
root.right.right.right = createNode(50);
root.right.right.right.right = createNode(60);
int k = 4;
// Function call
Console.Write(findBalancedBst(root, k));
}
}
// This code is contributed by Princi Singh输出：
Yes
时间复杂度： O(N)
辅助空间： O(1)
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