给定一个数字K ，任务是创建符合以下两个条件的 Tree 的类钻石结构：
- 树的前K层应该是平衡二叉树，节点的值应该从1开始，从左到右增加。
- 接下来的 K-1 层应该通过合并每对节点并将它们的总和存储为它们的子节点来形成一个菱形结构。
例子：
Input: K = 2
Output:
1
2 3
5
Explanation:
Structure will look like
1
/ \
2 3
\ /
5
For the given value k = 2
First, create a balanced
binary tree of level 2
with a value starting from 1.
Then on level 3 merge both
the node with a node
having value 2 + 3 = 5.
Input: K = 3
Output:
1
2 3
4 5 6 7
9 13
22
Explanation:
Structure will look like
1
/ \
2 3
/ \ / \
4 5 6 7
\ / \ /
9 13
\ /
22
Input: K = 4
Output:
1
2 3
4 5 6 7
8 9 10 11 12 13 14 15
17 21 25 29
38 54
92
Explanation:
Structure will look like
1
/ \
2 3
/ \ / \
4 5 6 7
/ \ / \ / \ / \
8 9 10 11 12 13 14 15
\ / \ / \ / \ /
17 21 25 29
\ / \ /
38 54
\ /
92方法：
- 首先使用层序遍历创建 K 层平衡二叉树，并给出从 1 开始并从左到右递增的值。
- 现在开始通过使用级别顺序一次总结两个节点来合并级别
- 最后，打印二叉树的每一层
下面是上述方法的实现：
C++
// C++ programm to create the diamond
// like structure of Binary Tree
// for a given value of K
#include
using namespace std;
// A Tree node
struct Node {
int data;
Node* left;
Node* right;
};
// Utility function to create a new node
Node* createNewNode(int value)
{
Node* temp = NULL;
temp = new Node();
temp->data = value;
temp->left = NULL;
temp->right = NULL;
return temp;
}
// Utility function to create the diamond
// like structure of Binary tree
void createStructureUtil(queue& qu,
int k)
{
int num = 1;
int level = k - 1;
// Run the outer while loop
// and create structure up to
// the k levels
while (level--) {
int qsize = qu.size();
// Run inner while loop to
// create current level
while (qsize--) {
Node* temp = qu.front();
qu.pop();
num += 1;
// Create left child
temp->left = createNewNode(num);
num += 1;
// Create right child
temp->right = createNewNode(num);
// Push the left child into
// the queue
qu.push(temp->left);
// Push the right child into
// the queue
qu.push(temp->right);
}
}
num += 1;
// Run the while loop
while (qu.size() > 1) {
// Pop first element from the queue
Node* first = qu.front();
qu.pop();
// Pop second element from the queue
Node* second = qu.front();
qu.pop();
// Create diamond structure
first->right
= createNewNode(first->data
+ second->data);
second->left = first->right;
// Push the node into the queue
qu.push(first->right);
}
}
// Function to print the Diamond
// Structure of Binary Tree
void printLevelOrder(Node* root, int k)
{
// Base Case
if (root == NULL)
return;
// Create an empty queue
queue qu;
// Enqueue Root and initialize height
qu.push(root);
int level = k - 1;
// while loop to print the element
// up to the (k - 1) levels
while (level--) {
int qsize = qu.size();
while (qsize--) {
Node* temp = qu.front();
qu.pop();
cout << temp->data << " ";
// Enqueue left child
if (temp->left != NULL)
qu.push(temp->left);
// Enqueue right child
if (temp->right != NULL)
qu.push(temp->right);
}
cout << endl;
}
// Loop to print the element
// rest all level except last
// level
while (qu.size() > 1) {
int qsize = qu.size();
while (qsize) {
Node* first = qu.front();
qu.pop();
Node* second = qu.front();
qu.pop();
cout << first->data << " "
<< second->data << " ";
qu.push(first->right);
qsize = qsize - 2;
}
cout << endl;
}
// Print the last element
Node* first = qu.front();
qu.pop();
cout << first->data << endl;
}
// Function to create the
// structure
void createStructure(int k)
{
queue qu;
Node* root = createNewNode(1);
qu.push(root);
// Utility Function call to
// create structure
createStructureUtil(qu, k);
printLevelOrder(root, k);
}
// Driver code
int main()
{
int k = 4;
// Print Structure
createStructure(k);
} Java
// Java programm to create the diamond
// like structure of Binary Tree
// for a given value of K
import java.util.*;
class GFG{
// A Tree node
static class Node {
int data;
Node left;
Node right;
};
// Utility function to create a new node
static Node createNewNode(int value)
{
Node temp = null;
temp = new Node();
temp.data = value;
temp.left = null;
temp.right = null;
return temp;
}
// Utility function to create the diamond
// like structure of Binary tree
static void createStructureUtil(Queue qu,
int k)
{
int num = 1;
int level = k - 1;
// Run the outer while loop
// and create structure up to
// the k levels
while (level-- >0) {
int qsize = qu.size();
// Run inner while loop to
// create current level
while (qsize-- > 0) {
Node temp = qu.peek();
qu.remove();
num += 1;
// Create left child
temp.left = createNewNode(num);
num += 1;
// Create right child
temp.right = createNewNode(num);
// Push the left child into
// the queue
qu.add(temp.left);
// Push the right child into
// the queue
qu.add(temp.right);
}
}
num += 1;
// Run the while loop
while (qu.size() > 1) {
// Pop first element from the queue
Node first = qu.peek();
qu.remove();
// Pop second element from the queue
Node second = qu.peek();
qu.remove();
// Create diamond structure
first.right
= createNewNode(first.data
+ second.data);
second.left = first.right;
// Push the node into the queue
qu.add(first.right);
}
}
// Function to print the Diamond
// Structure of Binary Tree
static void printLevelOrder(Node root, int k)
{
// Base Case
if (root == null)
return;
// Create an empty queue
Queue qu = new LinkedList<>();
// Enqueue Root and initialize height
qu.add(root);
int level = k - 1;
// while loop to print the element
// up to the (k - 1) levels
while (level-- > 0) {
int qsize = qu.size();
while (qsize-- > 0) {
Node temp = qu.peek();
qu.remove();
System.out.print(temp.data+ " ");
// Enqueue left child
if (temp.left != null)
qu.add(temp.left);
// Enqueue right child
if (temp.right != null)
qu.add(temp.right);
}
System.out.println();
}
// Loop to print the element
// rest all level except last
// level
while (qu.size() > 1) {
int qsize = qu.size();
while (qsize > 0) {
Node first = qu.peek();
qu.remove();
Node second = qu.peek();
qu.remove();
System.out.print(first.data+ " "
+ second.data+ " ");
qu.add(first.right);
qsize = qsize - 2;
}
System.out.println();
}
// Print the last element
Node first = qu.peek();
qu.remove();
System.out.print(first.data +"\n");
}
// Function to create the
// structure
static void createStructure(int k)
{
Queue qu = new LinkedList<>();
Node root = createNewNode(1);
qu.add(root);
// Utility Function call to
// create structure
createStructureUtil(qu, k);
printLevelOrder(root, k);
}
// Driver code
public static void main(String[] args)
{
int k = 4;
// Print Structure
createStructure(k);
}
}
// This code is contributed by Rajput-Ji Python3
# Python3 programm to create the diamond
# like structure of Binary Tree
# for a given value of K
# A Tree node
class Node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Utility function to create a new node
def createNewNode(value):
temp = Node(value)
return temp
# Utility function to create the diamond
# like structure of Binary tree
def createStructureUtil(qu, k):
num = 1;
level = k - 1;
# Run the outer while loop
# and create structure up to
# the k levels
while (level != 0):
level -= 1
qsize = len(qu)
# Run inner while loop to
# create current level
while (qsize != 0):
qsize -= 1
temp = qu[0];
qu.pop(0);
num += 1;
# Create left child
temp.left = createNewNode(num);
num += 1;
# Create right child
temp.right = createNewNode(num);
# Push the left child into
# the queue
qu.append(temp.left);
# Push the right child into
# the queue
qu.append(temp.right);
num += 1;
# Run the while loop
while (len(qu) > 1):
# Pop first element from the queue
first = qu[0];
qu.pop(0);
# Pop second element from the queue
second = qu[0];
qu.pop(0);
# Create diamond structure
first.right = createNewNode(first.data + second.data);
second.left = first.right;
# Push the node into the queue
qu.append(first.right);
# Function to print the Diamond
# Structure of Binary Tree
def printLevelOrder(root, k):
# Base Case
if (root == None):
return;
# Create an empty queue
qu = []
# Enqueue Root and initialize height
qu.append(root);
level = k - 1;
# while loop to print the element
# up to the (k - 1) levels
while (level != 0):
level -= 1
qsize = len(qu)
while (qsize != 0):
qsize -= 1
temp = qu[0];
qu.pop(0);
print(temp.data, end = ' ')
# Enqueue left child
if (temp.left != None):
qu.append(temp.left);
# Enqueue right child
if (temp.right != None):
qu.append(temp.right);
print()
# Loop to print the element
# rest all level except last
# level
while (len(qu) > 1):
qsize = len(qu)
while (qsize != 0):
first = qu[0];
qu.pop(0);
second = qu[0];
qu.pop(0);
print(str(first.data)+' '+str(second.data), end = ' ')
qu.append(first.right);
qsize = qsize - 2;
print()
# Print the last element
first = qu[0];
qu.pop(0);
print(first.data)
# Function to create the
# structure
def createStructure(k):
qu = []
root = createNewNode(1);
qu.append(root);
# Utility Function call to
# create structure
createStructureUtil(qu, k);
printLevelOrder(root, k);
# Driver code
if __name__=='__main__':
k = 4;
# Print Structure
createStructure(k);
# This code is contributed by rutvik_56C#
// C# programm to create the diamond
// like structure of Binary Tree
// for a given value of K
using System;
using System.Collections.Generic;
class GFG{
// A Tree node
class Node {
public int data;
public Node left;
public Node right;
};
// Utility function to create a new node
static Node createNewNode(int value)
{
Node temp = null;
temp = new Node();
temp.data = value;
temp.left = null;
temp.right = null;
return temp;
}
// Utility function to create the diamond
// like structure of Binary tree
static void createStructureUtil(Queue qu,
int k)
{
int num = 1;
int level = k - 1;
// Run the outer while loop
// and create structure up to
// the k levels
while (level-- >0) {
int qsize = qu.Count;
// Run inner while loop to
// create current level
while (qsize-- > 0) {
Node temp = qu.Peek();
qu.Dequeue();
num += 1;
// Create left child
temp.left = createNewNode(num);
num += 1;
// Create right child
temp.right = createNewNode(num);
// Push the left child into
// the queue
qu.Enqueue(temp.left);
// Push the right child into
// the queue
qu.Enqueue(temp.right);
}
}
num += 1;
// Run the while loop
while (qu.Count > 1) {
// Pop first element from the queue
Node first = qu.Peek();
qu.Dequeue();
// Pop second element from the queue
Node second = qu.Peek();
qu.Dequeue();
// Create diamond structure
first.right
= createNewNode(first.data
+ second.data);
second.left = first.right;
// Push the node into the queue
qu.Enqueue(first.right);
}
}
// Function to print the Diamond
// Structure of Binary Tree
static void printLevelOrder(Node root, int k)
{
// Base Case
if (root == null)
return;
// Create an empty queue
Queue qu = new Queue();
// Enqueue Root and initialize height
qu.Enqueue(root);
int level = k - 1;
// while loop to print the element
// up to the (k - 1) levels
while (level-- > 0) {
int qsize = qu.Count;
while (qsize-- > 0) {
Node temp = qu.Peek();
qu.Dequeue();
Console.Write(temp.data+ " ");
// Enqueue left child
if (temp.left != null)
qu.Enqueue(temp.left);
// Enqueue right child
if (temp.right != null)
qu.Enqueue(temp.right);
}
Console.WriteLine();
}
// Loop to print the element
// rest all level except last
// level
Node first;
while (qu.Count > 1) {
int qsize = qu.Count;
while (qsize > 0) {
first = qu.Peek();
qu.Dequeue();
Node second = qu.Peek();
qu.Dequeue();
Console.Write(first.data+ " "
+ second.data+ " ");
qu.Enqueue(first.right);
qsize = qsize - 2;
}
Console.WriteLine();
}
// Print the last element
first = qu.Peek();
qu.Dequeue();
Console.Write(first.data +"\n");
}
// Function to create the
// structure
static void createStructure(int k)
{
Queue qu = new Queue();
Node root = createNewNode(1);
qu.Enqueue(root);
// Utility Function call to
// create structure
createStructureUtil(qu, k);
printLevelOrder(root, k);
}
// Driver code
public static void Main(String[] args)
{
int k = 4;
// Print Structure
createStructure(k);
}
}
// This code is contributed by Princi Singh 输出：
1
2 3
4 5 6 7
8 9 10 11 12 13 14 15
17 21 25 29
38 54
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