Encoded Tree Sums in JavaScript

Given a tree encoded as a string, for every node, compute the sum of its subtree values and return the sums tree encoded as a string.

For example, the following tree is given as an encoded string "1{2{3,4},5{6}}" :

After computing the sums, the tree will look like the following:

    21
   /  \
  9    11
 / \     \
3   4     6

Therefore the output will be "21{9{3,4},11{6}}"

Example 1:

Input:  "1{2{3,4},5{6}}"

Output: "21{9{3,4},11{6}}"

Example 2:

Input:  "1{1,1{1,1,1},1}"

Output: "7{1,4{1,1,1},1}"

Understanding the Problem

The core challenge of this problem is to parse the encoded tree string, compute the sum of each node's subtree, and then re-encode the tree with these sums. This problem is significant in scenarios where hierarchical data needs to be processed and summarized, such as in organizational structures or file systems.

Potential pitfalls include correctly parsing the tree structure and ensuring that the sums are computed accurately for each subtree.

Approach

To solve this problem, we need to:

Parse the encoded tree string into a tree data structure.
Compute the sum of each node's subtree values.
Re-encode the tree with the computed sums.

Naive Solution

A naive solution might involve manually parsing the string and computing sums, but this would be error-prone and inefficient. Instead, we can use a more structured approach with recursion.

Optimized Solution

We can use a recursive approach to parse the tree and compute the sums. This approach is more efficient and easier to implement correctly.

Algorithm

Here is a step-by-step breakdown of the algorithm:

Parse the encoded string to build the tree structure.
Use a recursive function to compute the sum of each node's subtree.
Rebuild the encoded string with the computed sums.

Code Implementation

/**
 * Function to parse the encoded tree string and compute subtree sums.
 * @param {string} str - The encoded tree string.
 * @returns {string} - The encoded tree string with subtree sums.
 */
function encodedTreeSums(str) {
    // Helper function to parse the tree string
    function parseTree(s, index) {
        let num = 0;
        while (index < s.length && !isNaN(s[index])) {
            num = num * 10 + parseInt(s[index]);
            index++;
        }
        let node = { value: num, children: [] };
        if (index < s.length && s[index] === '{') {
            index++;
            while (index < s.length && s[index] !== '}') {
                let child;
                [child, index] = parseTree(s, index);
                node.children.push(child);
                if (s[index] === ',') index++;
            }
            index++;
        }
        return [node, index];
    }

    // Helper function to compute subtree sums
    function computeSums(node) {
        if (!node) return 0;
        let sum = node.value;
        for (let child of node.children) {
            sum += computeSums(child);
        }
        node.value = sum;
        return sum;
    }

    // Helper function to encode the tree back to string
    function encodeTree(node) {
        if (!node) return '';
        let result = node.value.toString();
        if (node.children.length > 0) {
            result += '{' + node.children.map(encodeTree).join(',') + '}';
        }
        return result;
    }

    // Parse the tree, compute sums, and encode back to string
    let [root, _] = parseTree(str, 0);
    computeSums(root);
    return encodeTree(root);
}

// Example usage:
console.log(encodedTreeSums("1{2{3,4},5{6}}")); // Output: "21{9{3,4},11{6}}"
console.log(encodedTreeSums("1{1,1{1,1,1},1}")); // Output: "7{1,4{1,1,1},1}"

Complexity Analysis

The time complexity of this solution is O(n), where n is the number of nodes in the tree. This is because we visit each node exactly once to compute the sums. The space complexity is also O(n) due to the recursion stack and the tree structure.

Edge Cases

Potential edge cases include:

Empty tree string: The function should handle this gracefully.
Single node tree: The function should return the same node value.

Examples of edge cases and their expected outputs:

Input: ""
Output: ""

Input: "1"
Output: "1"

Testing

To test the solution comprehensively, we should include a variety of test cases:

Simple trees with few nodes.
Complex trees with multiple levels.
Edge cases as mentioned above.

We can use JavaScript testing frameworks like Jest or Mocha to automate the testing process.

Thinking and Problem-Solving Tips

When approaching such problems, it's important to:

Break down the problem into smaller, manageable parts.
Use helper functions to handle specific tasks.
Think recursively for problems involving hierarchical data.

Practicing similar problems and studying algorithms can help improve problem-solving skills.

Conclusion

In this blog post, we discussed how to solve the problem of computing subtree sums for an encoded tree string. We covered the problem definition, approach, algorithm, code implementation, complexity analysis, edge cases, and testing. Understanding and solving such problems is crucial for developing strong problem-solving skills in programming.

Additional Resources

For further reading and practice, consider the following resources:

LeetCode - Practice problems on trees and recursion.
GeeksforGeeks - Tutorials and problems on tree data structures.
MDN Web Docs - JavaScript documentation and tutorials.

Encoded Tree Sums in JavaScript with Time Complexity Analysis