Backtracking-1

[praxpk]

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[super30admin]

No specific feedback provided. Refer to GitHub Comment.

[super30admin]

Your solution is on the right track and demonstrates a good understanding of backtracking. However, there are a few areas for improvement:

1. Base Case Handling: You should return immediately after finding a valid combination (when curr_sum == target) to avoid unnecessary recursive calls. Currently, after appending the result, the function continues to the loop and tries to add more elements, which is inefficient because the sum is already exactly the target. Adding more elements will only exceed the target. So you should add a return statement after appending.

2. Pruning: To improve efficiency, you should check if val (the new sum after adding a candidate) exceeds the target before making the recursive call. This way, you avoid entering the recursion unnecessarily. For example, instead of:
   curr_list.append(candidates[i])
   val = curr_sum + candidates[i]
   self.helper(curr_list, val, i)
   curr_list.pop()

You can do:
if curr_sum + candidates[i] <= target:
curr_list.append(candidates[i])
self.helper(curr_list, curr_sum + candidates[i], i)
curr_list.pop()

This prevents recursive calls when the sum would exceed the target.

3. Deep Copy: Using copy.deepcopy is correct, but note that it can be expensive. An alternative is to create a copy only when we add to the result, which you are already doing. However, in the recursive calls, you are passing the same list reference and then popping, which is standard backtracking. So this is acceptable.

4. Complexity Analysis: Your time complexity analysis should consider the worst-case scenario where the target is large and candidates are small. The number of combinations can be exponential in the target value. The space complexity should account for the recursion stack (which is O(T/min_candidate)) and the space to store the results (which is O(k * n) for k combinations). So please update your analysis accordingly.

5. Code Structure: Consider making the helper function inner or using a different design to avoid storing state in instance variables (self.result, self.target, etc.). This can make the code more self-contained and avoid potential issues if the class is used multiple times. However, it is acceptable as is.

Here is a revised version of your code with the suggested improvements:

class Solution:
    def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
        result = []
        
        def backtrack(curr_list, curr_sum, index):
            if curr_sum > target:
                return
            if curr_sum == target:
                result.append(curr_list[:])  # make a copy
                return
            for i in range(index, len(candidates)):
                if curr_sum + candidates[i] <= target:
                    curr_list.append(candidates[i])
                    backtrack(curr_list, curr_sum + candidates[i], i)
                    curr_list.pop()
        
        backtrack([], 0, 0)
        return result

Note: I used an inner function to avoid instance variables, and I added the check for curr_sum + candidates[i] <= target to prune unnecessary branches. Also, after finding a solution, we return immediately.