Problem Link :- leetcode-129
Problem statement
You are given the root of a binary tree containing digits from 0 to 9 only.
Each root-to-leaf path in the tree represents a number.
For example, the root-to-leaf path 1 -> 2 -> 3 represents the number 123. Return the total sum of all root-to-leaf numbers. Test cases are generated so that the answer will fit in a 32-bit integer.
A leaf node is a node with no children.
Each root-to-leaf path in the tree represents a number.
For example, the root-to-leaf path 1 -> 2 -> 3 represents the number 123. Return the total sum of all root-to-leaf numbers. Test cases are generated so that the answer will fit in a 32-bit integer.
A leaf node is a node with no children.
Significance of problem
The "Sum Root to Leaf Numbers" problem holds significant importance in the realm of binary trees, offering insights into traversing and aggregating numerical values along root-to-leaf paths. This problem's real-world analogy lies in scenarios where tree structures represent numerical hierarchies, such as representing account numbers or unique identifiers.
Firstly, the problem underscores the essence of tree traversal techniques, particularly depth-first search (DFS). By exploring root-to-leaf paths, it elucidates the hierarchical nature of tree structures, aligning with applications where sequential numbers or identifiers follow a specific path.
Secondly, the problem exemplifies the power of recursive algorithms in tree traversal. The code solution elegantly employs recursion to navigate through the tree, accumulating numerical values along the way. This approach offers a versatile methodology applicable to diverse tree-related challenges.
Moreover, the problem addresses the thematic concept of path aggregation. It emphasizes the accumulation of numerical values along root-to-leaf paths, providing a foundational understanding of how tree structures can be leveraged to represent and calculate aggregated values.
Furthermore, the problem's focus on root-to-leaf paths echoes real-world scenarios where numerical sequences or identifiers are derived from hierarchical structures, such as hierarchical account numbers in financial systems or coding structures in databases.
Firstly, the problem underscores the essence of tree traversal techniques, particularly depth-first search (DFS). By exploring root-to-leaf paths, it elucidates the hierarchical nature of tree structures, aligning with applications where sequential numbers or identifiers follow a specific path.
Secondly, the problem exemplifies the power of recursive algorithms in tree traversal. The code solution elegantly employs recursion to navigate through the tree, accumulating numerical values along the way. This approach offers a versatile methodology applicable to diverse tree-related challenges.
Moreover, the problem addresses the thematic concept of path aggregation. It emphasizes the accumulation of numerical values along root-to-leaf paths, providing a foundational understanding of how tree structures can be leveraged to represent and calculate aggregated values.
Furthermore, the problem's focus on root-to-leaf paths echoes real-world scenarios where numerical sequences or identifiers are derived from hierarchical structures, such as hierarchical account numbers in financial systems or coding structures in databases.
Easiest Explanation
This problem is asking you to find the sum of all numbers represented by the root-to-leaf paths in a binary tree, where each node in the tree contains a digit from 0 to 9.
For example, if the tree contains the paths 1 -> 2 -> 3 and 1 -> 4, then the numbers represented are 123 and 14 respectively. The sum of these two numbers would be 137, which is the final answer you would return.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
For example, if the tree contains the paths 1 -> 2 -> 3 and 1 -> 4, then the numbers represented are 123 and 14 respectively. The sum of these two numbers would be 137, which is the final answer you would return.
I hope that explanation helps! If you find any difficulty in solving, feel free to comment with your doubts.
class Solution:
def sumNumbers(self, root: TreeNode) -> int:
def solve(current, total, curr_sum):
if current is None:
return
curr = curr_sum * 10 + current.val
if current.left is None and current.right is None:
total[0] += curr
return
solve(current.left, total, curr)
solve(current.right, total, curr)
total = [0]
solve(root, total, 0)
return total[0]
class Solution { public: void solve(TreeNode* current,int& total, int curr_sum){ if(current==NULL) return ; int curr = (curr_sum*10) + (current->val); if(current->left==NULL && current->right==NULL){ total += curr; return; } solve(current->left,total,curr); solve(current->right,total,curr); } int sumNumbers(TreeNode* root) { int total = 0; solve(root,total,0); return total; } };
Here's how the function works:
1. The sumNumbers function takes a TreeNode pointer as input and returns an integer representing the sum of all root-to-leaf numbers in the given binary tree.
2. The solve function is a helper function that recursively traverses the binary tree and keeps track of the current sum and the total sum of root-to-leaf numbers.
3. The current parameter of the solve function represents the current TreeNode being visited, total represents the sum of all root-to-leaf numbers, and curr_sum represents the current sum of the digits on the current path from the root to the current node.
4. If the current node is NULL, then we return from the function.
5. Otherwise, we update the curr variable to be the current sum multiplied by 10 and then added to the value of the current node.
6. If the current node is a leaf (i.e., it has no children), we add the curr value to the total sum and return from the function.
7. If the current node is not a leaf, we recursively call the solve function for its left and right children, passing in the updated curr value as the new curr_sum.
8. Finally, the sumNumbers function initializes the total sum to 0 and calls the solve function for the root node, passing in 0 as the initial curr_sum.
9. The total sum is then returned as the final result of the sumNumbers function.
2. The solve function is a helper function that recursively traverses the binary tree and keeps track of the current sum and the total sum of root-to-leaf numbers.
3. The current parameter of the solve function represents the current TreeNode being visited, total represents the sum of all root-to-leaf numbers, and curr_sum represents the current sum of the digits on the current path from the root to the current node.
4. If the current node is NULL, then we return from the function.
5. Otherwise, we update the curr variable to be the current sum multiplied by 10 and then added to the value of the current node.
6. If the current node is a leaf (i.e., it has no children), we add the curr value to the total sum and return from the function.
7. If the current node is not a leaf, we recursively call the solve function for its left and right children, passing in the updated curr value as the new curr_sum.
8. Finally, the sumNumbers function initializes the total sum to 0 and calls the solve function for the root node, passing in 0 as the initial curr_sum.
9. The total sum is then returned as the final result of the sumNumbers function.
Learning Outcomes
Solving the "Sum Root to Leaf Numbers" problem imparts several valuable learning outcomes that contribute to a comprehensive understanding of binary trees, recursive algorithms, and numerical aggregation in a hierarchical structure. Firstly, learners develop a deep comprehension of tree traversal, specifically the depth-first search (DFS) approach. This skill is transferable to various tree-related problems, forming a foundational understanding of how to navigate hierarchical structures efficiently.
Secondly, the problem fosters proficiency in recursive algorithm design. The recursive strategy employed in the code solution showcases the elegance and adaptability of recursive approaches for tree traversal. This skill is applicable to a wide range of computational challenges where breaking down complex problems into smaller, manageable subproblems is advantageous.
Moreover, learners gain insights into numerical aggregation along root-to-leaf paths. Understanding how to accumulate values while traversing paths in a hierarchical structure is crucial, as it mirrors real-world scenarios where sequential or hierarchical identifiers need to be processed and aggregated.
Furthermore, the problem enhances learners' ability to conceptualize and work with tree structures that represent numerical values. This understanding is essential in domains such as database systems, where hierarchical structures are employed to organize and represent data efficiently.
Additionally, learners cultivate a practical understanding of how tree structures can encode numerical information. The problem's focus on deriving numbers from root-to-leaf paths mirrors scenarios in databases or information systems, providing learners with a tangible application of tree-based algorithms.
Secondly, the problem fosters proficiency in recursive algorithm design. The recursive strategy employed in the code solution showcases the elegance and adaptability of recursive approaches for tree traversal. This skill is applicable to a wide range of computational challenges where breaking down complex problems into smaller, manageable subproblems is advantageous.
Moreover, learners gain insights into numerical aggregation along root-to-leaf paths. Understanding how to accumulate values while traversing paths in a hierarchical structure is crucial, as it mirrors real-world scenarios where sequential or hierarchical identifiers need to be processed and aggregated.
Furthermore, the problem enhances learners' ability to conceptualize and work with tree structures that represent numerical values. This understanding is essential in domains such as database systems, where hierarchical structures are employed to organize and represent data efficiently.
Additionally, learners cultivate a practical understanding of how tree structures can encode numerical information. The problem's focus on deriving numbers from root-to-leaf paths mirrors scenarios in databases or information systems, providing learners with a tangible application of tree-based algorithms.
Conclusion
In conclusion, the "Sum Root to Leaf Numbers" problem serves as a pivotal learning experience, offering a nuanced understanding of binary tree traversal, recursive algorithms, and numerical aggregation within hierarchical structures. By navigating root-to-leaf paths and accumulating values, learners gain practical insights into real-world scenarios where tree structures represent sequential or hierarchical numerical information.
The problem's emphasis on depth-first search (DFS) reinforces the importance of efficient traversal techniques, applicable to a myriad of tree-related challenges. The elegant use of recursion in the code solution underscores its versatility in addressing complex hierarchical problems.
Furthermore, the problem bridges theoretical knowledge with practical applications, illustrating how tree structures can encode and calculate aggregated numerical values. This understanding extends to domains such as database systems, where hierarchical representations play a crucial role.
In essence, mastering the "Sum Root to Leaf Numbers" problem not only hones specific skills in tree traversal and numerical aggregation but also lays a foundation for tackling broader computational challenges involving hierarchical structures and recursive algorithmic design.
The problem's emphasis on depth-first search (DFS) reinforces the importance of efficient traversal techniques, applicable to a myriad of tree-related challenges. The elegant use of recursion in the code solution underscores its versatility in addressing complex hierarchical problems.
Furthermore, the problem bridges theoretical knowledge with practical applications, illustrating how tree structures can encode and calculate aggregated numerical values. This understanding extends to domains such as database systems, where hierarchical representations play a crucial role.
In essence, mastering the "Sum Root to Leaf Numbers" problem not only hones specific skills in tree traversal and numerical aggregation but also lays a foundation for tackling broader computational challenges involving hierarchical structures and recursive algorithmic design.
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