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LeetCode 1755: Closest Subsequence Sum Solution

Master LeetCode problem 1755 (Closest Subsequence Sum), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

Problem Explanation

Explanation

To solve this problem, we can use a divide and conquer approach combined with a binary search. We can split the given array into two halves and calculate the sums of all possible subsequences for each half. By sorting the sums of one half, we can iterate through the other half and find the closest sum to the goal using binary search. The final solution will be the minimum absolute difference between the goal and the closest sum found.

Algorithm:

  1. Split the input array into two halves.
  2. Generate all possible sums for each half.
  3. Sort the sums of one half.
  4. For each sum in the other half, find the closest sum to the goal using binary search.
  5. Update the minimum absolute difference found so far.
  6. Return the minimum absolute difference.

Time Complexity: O(2^(n/2) * n log n)
Space Complexity: O(2^(n/2))

Solution Code

class Solution {
    public int minAbsDifference(int[] nums, int goal) {
        List<Integer> sums1 = new ArrayList<>();
        List<Integer> sums2 = new ArrayList<>();
        
        generateSums(nums, 0, nums.length / 2, 0, sums1);
        generateSums(nums, nums.length / 2, nums.length, 0, sums2);
        
        Collections.sort(sums2);
        
        int minDiff = Integer.MAX_VALUE;
        for (int sum : sums1) {
            int target = goal - sum;
            int index = binarySearchClosest(sums2, target);
            if (index < sums2.size()) {
                minDiff = Math.min(minDiff, Math.abs(goal - (sum + sums2.get(index))));
            }
            if (index > 0) {
                minDiff = Math.min(minDiff, Math.abs(goal - (sum + sums2.get(index - 1))));
            }
        }
        
        return minDiff;
    }
    
    private void generateSums(int[] nums, int start, int end, int sum, List<Integer> sums) {
        if (start == end) {
            sums.add(sum);
            return;
        }
        generateSums(nums, start + 1, end, sum + nums[start], sums);
        generateSums(nums, start + 1, end, sum, sums);
    }
    
    private int binarySearchClosest(List<Integer> sums, int target) {
        int left = 0, right = sums.size() - 1;
        while (left <= right) {
            int mid = left + (right - left) / 2;
            if (sums.get(mid) == target) {
                return mid;
            } else if (sums.get(mid) < target) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        return left;
    }
}

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