Problem Link :- leetcode-106
Problem statement
Given two integer arrays inorder and postorder where inorder is the inorder traversal of a binary tree and postorder is the postorder traversal of the same tree, construct and return the binary tree.
Significance of problem
The "Construct Binary Tree from Inorder and Postorder Traversals" problem holds substantial significance in the realm of binary tree construction and traversal. This problem encapsulates crucial concepts in tree reconstruction, providing learners with a profound understanding of the interplay between inorder and postorder traversals.
Primarily, this problem emphasizes the importance of deciphering the relationship between different traversal orders. It delves into the intricacies of using postorder traversal to reconstruct a binary tree, fostering a deep comprehension of how each traversal order uniquely contributes to the tree's structure. This skill is foundational in various domains, from compiler design to database indexing, where efficient tree reconstruction is paramount.
Furthermore, the problem highlights the efficiency of recursive algorithms in solving tree-related challenges. By breaking down the reconstruction process into smaller, manageable subproblems, learners gain insight into the elegance of recursive solutions. This proficiency in recursion extends beyond this specific problem, serving as a valuable tool in solving a myriad of algorithmic challenges.
Moreover, constructing a binary tree from inorder and postorder traversals exemplifies real-world scenarios where tree structures represent hierarchical relationships, such as organizational charts or file system representations. The problem bridges theoretical knowledg
Primarily, this problem emphasizes the importance of deciphering the relationship between different traversal orders. It delves into the intricacies of using postorder traversal to reconstruct a binary tree, fostering a deep comprehension of how each traversal order uniquely contributes to the tree's structure. This skill is foundational in various domains, from compiler design to database indexing, where efficient tree reconstruction is paramount.
Furthermore, the problem highlights the efficiency of recursive algorithms in solving tree-related challenges. By breaking down the reconstruction process into smaller, manageable subproblems, learners gain insight into the elegance of recursive solutions. This proficiency in recursion extends beyond this specific problem, serving as a valuable tool in solving a myriad of algorithmic challenges.
Moreover, constructing a binary tree from inorder and postorder traversals exemplifies real-world scenarios where tree structures represent hierarchical relationships, such as organizational charts or file system representations. The problem bridges theoretical knowledg
Easiest Explanation
Imagine you have a big puzzle of a tree, but it's broken into many pieces. You have two lists: one tells you the order that the tree's branches and leaves appear from left to right (we'll call this the "inorder" list), and the other tells you the order that you should put the pieces of the puzzle together to make the tree (we'll call this the "postorder" list).
To put the puzzle back together, we need to start with the last piece in the postorder list. That will be the very top of the tree, where the trunk starts. Then, we can use the inorder list to figure out which pieces go on the left and which go on the right of the trunk. We keep doing this recursively until we've put all the pieces back together to make the entire tree.
In the end, we'll have a beautiful tree, just like the original one, and we'll have used the two lists to put it back together!
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
To put the puzzle back together, we need to start with the last piece in the postorder list. That will be the very top of the tree, where the trunk starts. Then, we can use the inorder list to figure out which pieces go on the left and which go on the right of the trunk. We keep doing this recursively until we've put all the pieces back together to make the entire tree.
In the end, we'll have a beautiful tree, just like the original one, and we'll have used the two lists to put it back together!
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
class Solution:
def buildTree(self, ino: List[int], post: List[int]) -> TreeNode:
i = [len(post) - 1]
return self.solve(i, ino, post, 0, len(ino) - 1)
def solve(self, i: List[int], ino: List[int], post: List[int], l: int, r: int) -> TreeNode:
if l > r:
return None
x = r
while post[i[0]] != ino[x]:
x -= 1
i[0] -= 1
root = TreeNode(ino[x])
root.right = self.solve(i, ino, post, x + 1, r)
root.left = self.solve(i, ino, post, l, x - 1)
return root
class Solution { public: TreeNode* buildTree(vector<int>& ino, vector<int>& post) { int i1 = post.size()-1; return solve(i1,ino,post,0,ino.size()-1); } TreeNode* solve(int &i,vector<int> &in,vector<int> &post,int l,int r){ if(l>r)return NULL; int x = r; while(post[i] != in[x]){ x--; } i--; TreeNode* root = new TreeNode(in[x]); root->right = solve(i,in,post,x+1,r); root->left = solve(i,in,post,l,x-1); return root; } };
Here's how the function works:
1. The function buildTree takes in two vectors ino and post representing the inorder and postorder traversals of a binary tree, respectively.
2. It initializes i1 to be the index of the last element in the post vector.
3. It then calls the function solve with arguments i1, ino, post, 0, and ino.size()-1.
4. The function solve takes in a reference to i (which is passed by reference so that its value can be updated in recursive calls), references to in and post, and the indices l and r which represent the left and right boundaries of the current subtree being constructed.
5. The base case for the recursion is when l > r, which means that there are no more nodes to add to the subtree.
6. In each recursive call, the function first finds the index x of the root node in the inorder traversal by searching for the value of the last element in the postorder traversal (post[i]) in the inorder traversal.
7. It then creates a new TreeNode object with the value of in[x], which is the value of the root node for the current subtree.
8. The function then recursively calls itself twice to construct the left and right subtrees, passing the updated value of i, the in and post vectors, and the new boundaries l and r for each subtree.
9. Finally, the function returns the root node of the current subtree.
10. The buildTree function returns the root node of the entire binary tree constructed from the ino and post vectors.
2. It initializes i1 to be the index of the last element in the post vector.
3. It then calls the function solve with arguments i1, ino, post, 0, and ino.size()-1.
4. The function solve takes in a reference to i (which is passed by reference so that its value can be updated in recursive calls), references to in and post, and the indices l and r which represent the left and right boundaries of the current subtree being constructed.
5. The base case for the recursion is when l > r, which means that there are no more nodes to add to the subtree.
6. In each recursive call, the function first finds the index x of the root node in the inorder traversal by searching for the value of the last element in the postorder traversal (post[i]) in the inorder traversal.
7. It then creates a new TreeNode object with the value of in[x], which is the value of the root node for the current subtree.
8. The function then recursively calls itself twice to construct the left and right subtrees, passing the updated value of i, the in and post vectors, and the new boundaries l and r for each subtree.
9. Finally, the function returns the root node of the current subtree.
10. The buildTree function returns the root node of the entire binary tree constructed from the ino and post vectors.
Learning Outcomes
Solving the "Construct Binary Tree from Inorder and Postorder Traversals" problem yields a comprehensive set of learning outcomes, spanning crucial aspects of tree traversal, recursive algorithms, and the practical application of binary tree structures.
Firstly, learners gain a profound understanding of tree traversal orders. By working with both inorder and postorder traversals, they cultivate the ability to interpret the relationships between different traversal sequences. This knowledge is foundational for grasping the intricacies of tree structures, applicable across various computational domains where hierarchical relationships are prevalent.
Secondly, the problem fosters proficiency in recursive algorithms. Learners navigate the intricacies of breaking down the tree reconstruction process into smaller subproblems, unveiling the elegance and efficiency of recursive solutions. This skill is transferable, empowering learners to approach a myriad of algorithmic challenges with a structured and recursive mindset.
Moreover, learners develop a practical insight into the application of binary tree structures. The problem mirrors real-world scenarios where hierarchical relationships need to be represented and manipulated efficiently, such as in organizing data within databases or visualizing organizational hierarchies. This practical application enhances the learners' ability to translate theoretical knowledge into solutions for real-world computational challenges.
Furthermore, learners hone their analytical and problem-solving skills through the process of reconstructing a binary tree from traversals. They develop a strategic approach to dissecting complex problems, identifying patterns within traversal sequences, and formulating recursive strategies for efficient tree construction.
Firstly, learners gain a profound understanding of tree traversal orders. By working with both inorder and postorder traversals, they cultivate the ability to interpret the relationships between different traversal sequences. This knowledge is foundational for grasping the intricacies of tree structures, applicable across various computational domains where hierarchical relationships are prevalent.
Secondly, the problem fosters proficiency in recursive algorithms. Learners navigate the intricacies of breaking down the tree reconstruction process into smaller subproblems, unveiling the elegance and efficiency of recursive solutions. This skill is transferable, empowering learners to approach a myriad of algorithmic challenges with a structured and recursive mindset.
Moreover, learners develop a practical insight into the application of binary tree structures. The problem mirrors real-world scenarios where hierarchical relationships need to be represented and manipulated efficiently, such as in organizing data within databases or visualizing organizational hierarchies. This practical application enhances the learners' ability to translate theoretical knowledge into solutions for real-world computational challenges.
Furthermore, learners hone their analytical and problem-solving skills through the process of reconstructing a binary tree from traversals. They develop a strategic approach to dissecting complex problems, identifying patterns within traversal sequences, and formulating recursive strategies for efficient tree construction.
Conclusion
In conclusion, the "Construct Binary Tree from Inorder and Postorder Traversals" problem offers learners a valuable journey into the intricacies of binary tree reconstruction. By working with both inorder and postorder traversals, learners gain a solid grasp of tree traversal relationships, laying a foundation for understanding hierarchical structures in diverse computational contexts.
The problem's emphasis on recursive algorithms enhances learners' problem-solving skills, enabling them to approach complex challenges with a structured and efficient mindset. Additionally, the practical application of binary tree structures mirrors real-world scenarios, providing learners with insights into representing and manipulating hierarchical relationships within databases or organizational hierarchies.
Mastering this problem empowers learners to interpret traversal orders, design recursive solutions, and apply these skills in practical computational scenarios. Overall, the "Construct Binary Tree from Inorder and Postorder Traversals" problem is a key milestone in algorithmic proficiency, equipping learners with essential tools for navigating tree-related challenges in various domains.
The problem's emphasis on recursive algorithms enhances learners' problem-solving skills, enabling them to approach complex challenges with a structured and efficient mindset. Additionally, the practical application of binary tree structures mirrors real-world scenarios, providing learners with insights into representing and manipulating hierarchical relationships within databases or organizational hierarchies.
Mastering this problem empowers learners to interpret traversal orders, design recursive solutions, and apply these skills in practical computational scenarios. Overall, the "Construct Binary Tree from Inorder and Postorder Traversals" problem is a key milestone in algorithmic proficiency, equipping learners with essential tools for navigating tree-related challenges in various domains.
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