Completed Backtracking -2 problems

[thondaha]

1. PalindromePartitioning
   2.Subsets

[super30admin]

Strengths:

• You implemented two different approaches, showing a good understanding of the problem.
• The code is well-commented and includes test cases.
• The choose/skip method is efficient and uses backtracking correctly.

Areas for Improvement:

• In the for-loop method for subsets, avoid creating a new list at each recursive call. Instead, use backtracking by adding the element before recursing and removing it afterwards. This will improve space efficiency.
• The current for-loop method creates a new list for every recursive call, which leads to O(n * 2^n) memory usage for the recursion (due to copying), whereas backtracking would use O(n) space for the recursion stack and the current path.
• Remove unrelated code (like PalindromePartitioning) when submitting for the Subsets problem to avoid confusion.

Here is an optimized for-loop method using backtracking:

private void forLoopHelper(int[] nums, int start, List<Integer> path) {
    result.add(new ArrayList<>(path));
    for (int i = start; i < nums.length; i++) {
        path.add(nums[i]);
        forLoopHelper(nums, i + 1, path);
        path.remove(path.size() - 1);
    }
}