2834. Find the Minimum Possible Sum of a Beautiful Array

Problem Statement

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

Intuition

Similar to 2829

Video Links

Approach 1:

Map

C++

class Solution {
public:
    long long minimumPossibleSum(int n, int target) {
        long long sum = 0, start = 1;
        unordered_map<int,int> mp;

        while(n){
            if( mp.find(start) == mp.end() ){
                sum += start;
                mp[target - start] ++;
                n--;
            }
            
            start++;
        }

        return sum;
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++