从其前序遍历构造完整的 k-ary 树
给定一个包含完整 k-ary 树的前序遍历的数组，构造完整的 k-ary 树并打印其后序遍历。完整的 k-ary 树是每个节点有 0 个或 k 个子节点的树。
例子：
Input : preorder[] = {1, 2, 5, 6, 7,
3, 8, 9, 10, 4}
k = 3
Output : Postorder traversal of constructed
full k-ary tree is: 5 6 7 2 8 9 10
3 4 1
Tree formed is: 1
/ | \
2 3 4
/|\ /|\
5 6 7 8 9 10
Input : preorder[] = {1, 2, 5, 6, 7, 3, 4}
k = 3
Output : Postorder traversal of constructed
full k-ary tree is: 5 6 7 2 4 3 1
Tree formed is: 1
/ | \
2 3 4
/|\
5 6 7 我们在下面的帖子中讨论了二叉树的这个问题。
从给定的前序遍历构造一棵特殊的树
在这篇文章中，讨论了 k-ary 树的解决方案。
在前序遍历中，首先处理根节点，然后处理左子树和右子树。正因为如此，要构造一棵完整的 k-ary 树，我们只需要继续创建节点，而不用关心之前构造的节点。我们可以使用它来递归地构建树。
以下是解决问题的步骤：
1. 找到树的高度。
2.遍历前序数组，递归添加每个节点
C++
// C++ program to build full k-ary tree from
// its preorder traversal and to print the
// postorder traversal of the tree.
#include
using namespace std;
// Structure of a node of an n-ary tree
struct Node {
int key;
vector child;
};
// Utility function to create a new tree
// node with k children
Node* newNode(int value)
{
Node* nNode = new Node;
nNode->key = value;
return nNode;
}
// Function to build full k-ary tree
Node* BuildKaryTree(int A[], int n, int k, int h, int& ind)
{
// For null tree
if (n <= 0)
return NULL;
Node* nNode = newNode(A[ind]);
if (nNode == NULL) {
cout << "Memory error" << endl;
return NULL;
}
// For adding k children to a node
for (int i = 0; i < k; i++) {
// Check if ind is in range of array
// Check if height of the tree is greater than 1
if (ind < n - 1 && h > 1) {
ind++;
// Recursively add each child
nNode->child.push_back(BuildKaryTree(A, n, k, h - 1, ind));
} else {
nNode->child.push_back(NULL);
}
}
return nNode;
}
// Function to find the height of the tree
Node* BuildKaryTree(int* A, int n, int k, int ind)
{
int height = (int)ceil(log((double)n * (k - 1) + 1)
/ log((double)k));
return BuildKaryTree(A, n, k, height, ind);
}
// Function to print postorder traversal of the tree
void postord(Node* root, int k)
{
if (root == NULL)
return;
for (int i = 0; i < k; i++)
postord(root->child[i], k);
cout << root->key << " ";
}
// Driver program to implement full k-ary tree
int main()
{
int ind = 0;
int k = 3, n = 10;
int preorder[] = { 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 };
Node* root = BuildKaryTree(preorder, n, k, ind);
cout << "Postorder traversal of constructed"
" full k-ary tree is: ";
postord(root, k);
cout << endl;
return 0;
} Java
// Java program to build full k-ary tree from
// its preorder traversal and to print the
// postorder traversal of the tree.
import java.util.*;
class GFG
{
// Structure of a node of an n-ary tree
static class Node
{
int key;
Vector child;
};
// Utility function to create a new tree
// node with k children
static Node newNode(int value)
{
Node nNode = new Node();
nNode.key = value;
nNode.child= new Vector();
return nNode;
}
static int ind;
// Function to build full k-ary tree
static Node BuildKaryTree(int A[], int n,
int k, int h)
{
// For null tree
if (n <= 0)
return null;
Node nNode = newNode(A[ind]);
if (nNode == null)
{
System.out.println("Memory error" );
return null;
}
// For adding k children to a node
for (int i = 0; i < k; i++)
{
// Check if ind is in range of array
// Check if height of the tree is greater than 1
if (ind < n - 1 && h > 1)
{
ind++;
// Recursively add each child
nNode.child.add(BuildKaryTree(A, n, k, h - 1));
}
else
{
nNode.child.add(null);
}
}
return nNode;
}
// Function to find the height of the tree
static Node BuildKaryTree_1(int[] A, int n, int k, int in)
{
int height = (int)Math.ceil(Math.log((double)n * (k - 1) + 1) /
Math.log((double)k));
ind = in;
return BuildKaryTree(A, n, k, height);
}
// Function to print postorder traversal of the tree
static void postord(Node root, int k)
{
if (root == null)
return;
for (int i = 0; i < k; i++)
postord(root.child.get(i), k);
System.out.print(root.key + " ");
}
// Driver Code
public static void main(String args[])
{
int ind = 0;
int k = 3, n = 10;
int preorder[] = { 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 };
Node root = BuildKaryTree_1(preorder, n, k, ind);
System.out.println("Postorder traversal of " +
"constructed full k-ary tree is: ");
postord(root, k);
System.out.println();
}
}
// This code is contributed by Arnab Kundu Python3
# Python3 program to build full k-ary tree
# from its preorder traversal and to print the
# postorder traversal of the tree.
from math import ceil, log
# Utility function to create a new
# tree node with k children
class newNode:
def __init__(self, value):
self.key = value
self.child = []
# Function to build full k-ary tree
def BuildkaryTree(A, n, k, h, ind):
# For None tree
if (n <= 0):
return None
nNode = newNode(A[ind[0]])
if (nNode == None):
print("Memory error")
return None
# For adding k children to a node
for i in range(k):
# Check if ind is in range of array
# Check if height of the tree is
# greater than 1
if (ind[0] < n - 1 and h > 1):
ind[0] += 1
# Recursively add each child
nNode.child.append(BuildkaryTree(A, n, k,
h - 1, ind))
else:
nNode.child.append(None)
return nNode
# Function to find the height of the tree
def BuildKaryTree(A, n, k, ind):
height = int(ceil(log(float(n) * (k - 1) + 1) /
log(float(k))))
return BuildkaryTree(A, n, k, height, ind)
# Function to print postorder traversal
# of the tree
def postord(root, k):
if (root == None):
return
for i in range(k):
postord(root.child[i], k)
print(root.key, end = " ")
# Driver Code
if __name__ == '__main__':
ind = [0]
k = 3
n = 10
preorder = [ 1, 2, 5, 6, 7, 3, 8, 9, 10, 4]
root = BuildKaryTree(preorder, n, k, ind)
print("Postorder traversal of constructed",
"full k-ary tree is: ")
postord(root, k)
# This code is contributed by pranchalKC#
// C# program to build full k-ary tree from
// its preorder traversal and to print the
// postorder traversal of the tree.
using System;
using System.Collections.Generic;
class GFG
{
// Structure of a node of an n-ary tree
class Node
{
public int key;
public List child;
};
// Utility function to create a new tree
// node with k children
static Node newNode(int value)
{
Node nNode = new Node();
nNode.key = value;
nNode.child= new List();
return nNode;
}
static int ind;
// Function to build full k-ary tree
static Node BuildKaryTree(int []A, int n,
int k, int h)
{
// For null tree
if (n <= 0)
return null;
Node nNode = newNode(A[ind]);
if (nNode == null)
{
Console.WriteLine("Memory error" );
return null;
}
// For adding k children to a node
for (int i = 0; i < k; i++)
{
// Check if ind is in range of array
// Check if height of the tree is greater than 1
if (ind < n - 1 && h > 1)
{
ind++;
// Recursively add each child
nNode.child.Add(BuildKaryTree(A, n, k, h - 1));
}
else
{
nNode.child.Add(null);
}
}
return nNode;
}
// Function to find the height of the tree
static Node BuildKaryTree_1(int[] A, int n, int k, int iN)
{
int height = (int)Math.Ceiling(Math.Log((double)n * (k - 1) + 1) /
Math.Log((double)k));
ind = iN;
return BuildKaryTree(A, n, k, height);
}
// Function to print postorder traversal of the tree
static void postord(Node root, int k)
{
if (root == null)
return;
for (int i = 0; i < k; i++)
postord(root.child[i], k);
Console.Write(root.key + " ");
}
// Driver Code
public static void Main(String []args)
{
int ind = 0;
int k = 3, n = 10;
int []preorder = { 1, 2, 5, 6, 7, 3, 8, 9, 10, 4 };
Node root = BuildKaryTree_1(preorder, n, k, ind);
Console.WriteLine("Postorder traversal of " +
"constructed full k-ary tree is: ");
postord(root, k);
Console.WriteLine();
}
}
// This code is contributed by PrinciRaj1992 Javascript
输出：
Postorder traversal of constructed full k-ary
tree is: 5 6 7 2 8 9 10 3 4 1