2834. Find the Minimum Possible Sum of a Beautiful Array

Problem

You are given positive integers n and target.

An array nums is beautiful if it meets the following conditions:

• nums.length == n.
• nums consists of pairwise distinct positive integers.
• There doesn't exist two distinct indices, i and j, in the range [0, n - 1], such that nums[i] + nums[j] == target.

Return **the *minimum* possible sum that a beautiful array could have**.

Example 1:

Input: n = 2, target = 3
Output: 4
Explanation: We can see that nums = [1,3] is beautiful.
- The array nums has length n = 2.
- The array nums consists of pairwise distinct positive integers.
- There doesn't exist two distinct indices, i and j, with nums[i] + nums[j] == 3.
It can be proven that 4 is the minimum possible sum that a beautiful array could have.

Example 2:

Input: n = 3, target = 3
Output: 8
Explanation: We can see that nums = [1,3,4] is beautiful.
- The array nums has length n = 3.
- The array nums consists of pairwise distinct positive integers.
- There doesn't exist two distinct indices, i and j, with nums[i] + nums[j] == 3.
It can be proven that 8 is the minimum possible sum that a beautiful array could have.

Example 3:

Input: n = 1, target = 1
Output: 1
Explanation: We can see, that nums = [1] is beautiful.

Constraints:

• 1 <= n <= 105
• 1 <= target <= 105

Solution (Java)

class Solution {
    public long minimumPossibleSum(int n, int target) {
        Set<Long> st = new HashSet<>();
        long ans = 0;
        for (long i = 1; st.size() < n; ++i) {
            if (!st.contains(target - i)) {
                st.add(i);
                ans += i;
            }
        }
        return ans;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).