Encoded Tree Sums in Java

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 string representation of a tree, compute the sum of values for each 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 string representation and ensuring that the sums are computed accurately for each subtree.

Approach

To solve this problem, we need to:

Parse the encoded string to reconstruct the tree structure.
Traverse the tree to compute the sum of values for each subtree.
Re-encode the tree with the computed sums.

Naive Solution

A naive solution might involve manually parsing the string and using nested loops to compute sums, but this would be inefficient and error-prone.

Optimized Solution

An optimized approach involves using a recursive function to parse the string and compute sums simultaneously. This ensures that each node and its subtree are processed in a single pass.

Algorithm

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

Define a recursive function to parse the string and compute subtree sums.
For each node, parse its value and recursively process its children.
Compute the sum of the node's value and the sums of its children's subtrees.
Reconstruct the encoded string with the computed sums.

Code Implementation

import java.util.*;

public class EncodedTreeSums {
    // Helper class to represent a tree node
    static class TreeNode {
        int value;
        List children;

        TreeNode(int value) {
            this.value = value;
            this.children = new ArrayList<>();
        }
    }

    // Function to parse the encoded string and build the tree
    private static TreeNode parseTree(String s, int[] index) {
        int value = 0;
        while (index[0] < s.length() && Character.isDigit(s.charAt(index[0]))) {
            value = value * 10 + (s.charAt(index[0]) - '0');
            index[0]++;
        }
        TreeNode node = new TreeNode(value);
        if (index[0] < s.length() && s.charAt(index[0]) == '{') {
            index[0]++; // skip '{'
            while (s.charAt(index[0]) != '}') {
                node.children.add(parseTree(s, index));
                if (s.charAt(index[0]) == ',') {
                    index[0]++; // skip ','
                }
            }
            index[0]++; // skip '}'
        }
        return node;
    }

    // Function to compute subtree sums and re-encode the tree
    private static int computeSums(TreeNode node, StringBuilder sb) {
        int sum = node.value;
        sb.append(node.value);
        if (!node.children.isEmpty()) {
            sb.append('{');
            for (int i = 0; i < node.children.size(); i++) {
                if (i > 0) {
                    sb.append(',');
                }
                sum += computeSums(node.children.get(i), sb);
            }
            sb.append('}');
        }
        node.value = sum;
        return sum;
    }

    // Main function to process the encoded tree string
    public static String encodedTreeSums(String s) {
        int[] index = {0};
        TreeNode root = parseTree(s, index);
        StringBuilder sb = new StringBuilder();
        computeSums(root, sb);
        return sb.toString();
    }

    public static void main(String[] args) {
        String input1 = "1{2{3,4},5{6}}";
        String input2 = "1{1,1{1,1,1},1}";
        System.out.println(encodedTreeSums(input1)); // Output: "21{9{3,4},11{6}}"
        System.out.println(encodedTreeSums(input2)); // Output: "7{1,4{1,1,1},1}"
    }
}

Complexity Analysis

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

Edge Cases

Potential edge cases include:

Empty input string: Should return an empty string.
Single node tree: Should return the same node value.
Deeply nested trees: Ensure the recursion depth is handled properly.

Testing

To test the solution comprehensively, consider the following test cases:

Simple tree with one level of children.
Tree with multiple levels of nesting.
Tree with varying numbers of children per node.

Thinking and Problem-Solving Tips

When approaching such problems, it is helpful to:

Break down the problem into smaller, manageable parts.
Use recursion to handle hierarchical data structures.
Write helper functions to keep the code organized and readable.

Conclusion

Understanding and solving problems involving tree structures is crucial for many applications in computer science. By practicing such problems, you can improve your problem-solving skills and gain a deeper understanding of data structures and algorithms.

Additional Resources

For further reading and practice, consider the following resources:

LeetCode - Practice problems on tree structures.
GeeksforGeeks - Tutorials on data structures and algorithms.
Coursera - Courses on data structures and algorithms.

Encoded Tree Sums in Java with Time Complexity Analysis