LeetCode 1755: Closest Subsequence Sum
LeetCode 1755 Solution 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:
- Split the input array into two halves.
- Generate all possible sums for each half.
- Sort the sums of one half.
- For each sum in the other half, find the closest sum to the goal using binary search.
- Update the minimum absolute difference found so far.
- Return the minimum absolute difference.
Time Complexity: O(2^(n/2) * n log n)
Space Complexity: O(2^(n/2))
LeetCode 1755 Solutions in Java, C++, Python
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;
}
}Interactive Code Editor for LeetCode 1755
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