Completed Backtracking-1

[sarvanibaru]

No description provided.

[super30admin]

Combination Sum (Combination-Sum.java)

Your solution is excellent and demonstrates a good understanding of backtracking. Here are some strengths and areas for improvement:

Strengths:

• You correctly implemented backtracking with a for-loop recursion, which efficiently explores all combinations without duplicates.
• The use of a pivot index ensures that each candidate is considered only once per combination branch, avoiding redundant checks.
• The code is clean, well-commented, and follows good coding practices.

Areas for Improvement:

• While not necessary for the given constraints, you could optimize further by sorting the candidates and adding a condition to break out of the loop if the current candidate is greater than the remaining target. This would prune unnecessary branches and improve performance in some cases.
• The time complexity comment could be more precise. The worst-case time complexity is actually O(n^target) because each candidate can be chosen multiple times, leading to a tree of depth at most target (if the smallest candidate is 1). However, the backtracking and pivot index help reduce this in practice.

Overall, your solution is efficient and correct. Keep up the good work!

VERDICT: PASS

---

Operations and expressions (ExpressionAddOperators.java)

Your approach is on the right track, and you have correctly identified the need to handle numbers without leading zeros. However, there are a few critical issues:

1. Backtracking with Path: You are using string concatenation which creates new strings every time. This is inefficient and does not allow backtracking. Instead, use a StringBuilder like in the reference solution. This way, you can append and then set the length back to the original to backtrack.

2. Method Signature: Your helper method uses String path which is immutable. Change it to StringBuilder path so that you can modify it and backtrack.

3. Recursive Calls: When you make recursive calls, you need to ensure that after each call, the path is reset to its original state. This is done by setting the length of the StringBuilder after each recursive call.

4. Edge Cases: Make sure to test with numbers that have zeros, like "105" with target 5, to ensure that leading zeros are handled correctly.

Here is how you can modify your code:

• Change the helper method to take StringBuilder path instead of String path.
• In the base case, when you add to result, use path.toString().
• For the case when pivot==0, append the current number to the path and then after the recursive call, set the length back.
• For the other cases, append the operator and the number, then call recursively, and then set the length back.

Example modification:

private void helper(String num, int target, StringBuilder path, int pivot, long calc, long tail) {
    if (pivot == num.length()) {
        if (calc == target) {
            result.add(path.toString());
        }
        return;
    }
    for (int i = pivot; i < num.length(); i++) {
        if (num.charAt(pivot) == '0' && i != pivot) break;
        long curr = Long.parseLong(num.substring(pivot, i+1));
        int len = path.length();
        if (pivot == 0) {
            path.append(curr);
            helper(num, target, path, i+1, curr, curr);
            path.setLength(len);
        } else {
            path.append('+').append(curr);
            helper(num, target, path, i+1, calc + curr, curr);
            path.setLength(len);

            path.append('-').append(curr);
            helper(num, target, path, i+1, calc - curr, -curr);
            path.setLength(len);

            path.append('*').append(curr);
            helper(num, target, path, i+1, calc - tail + tail * curr, tail * curr);
            path.setLength(len);
        }
    }
}

Also, remember to call the helper with a StringBuilder initially: helper(num, target, new StringBuilder(), 0, 0, 0);

Your current solution will not produce correct results due to the lack of backtracking. Please revise your code to use StringBuilder and backtrack properly.

VERDICT: NEEDS_IMPROVEMENT