Given an array which contains the preorder traversal of full k-ary tree, construct the full k-ary tree and print its postorder traversal. A full k-ary tree is a tree where each node has either 0 or k children.
Examples:
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 3 4 1
Tree formed is: 1
/ |
2 3 4
/|
5 6 7
We have discussed this problem for Binary tree in below post.
Construct a special tree from given preorder traversal
In this post, solution for a k-ary tree is discussed.
In Preorder traversal, first root node is processed then followed by the left subtree and right subtree. Because of this, to construct a full k-ary tree, we just need to keep on creating the nodes without bothering about the previous constructed nodes. We can use this to build the tree recursively.
Following are the steps to solve the problem:
1. Find the height of the tree.
2. Traverse the preorder array and recursively add each node
C++
// C++ program to build full k-ary tree from // its preorder traversal and to print the // postorder traversal of the tree. #include <bits/stdc++.h> using namespace std; // Structure of a node of an n-ary tree struct Node { int key; vector<Node*> 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; } |
Python3
# Python3 program to build full k-ary tree
# from its preorder traversal and to prthe
# 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 prpostorder 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 pranchalK
Output:
Postorder traversal of constructed full k-ary tree is: 5 6 7 2 8 9 10 3 4 1
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