3194. Minimum Average of Smallest and Largest Elements 

Description

You have an array of floating point numbers averages which is initially empty. You are given an array nums of n integers where n is even.

You repeat the following procedure n / 2 times:

Remove the smallest element, minElement, and the largest element maxElement, from nums.
Add (minElement + maxElement) / 2 to averages.

Return the minimum element in averages.

Example 1:

Input: nums = [7,8,3,4,15,13,4,1]

Output: 5.5

Explanation:

step	nums	averages
0	[7,8,3,4,15,13,4,1]	[]
1	[7,8,3,4,13,4]	[8]
2	[7,8,4,4]	[8,8]
3	[7,4]	[8,8,6]
4	[]	[8,8,6,5.5]

The smallest element of averages, 5.5, is returned.

Example 2:

Input: nums = [1,9,8,3,10,5]

Output: 5.5

Explanation:

step	nums	averages
0	[1,9,8,3,10,5]	[]
1	[9,8,3,5]	[5.5]
2	[8,5]	[5.5,6]
3	[]	[5.5,6,6.5]

Example 3:

Input: nums = [1,2,3,7,8,9]

Output: 5.0

Explanation:

step	nums	averages
0	[1,2,3,7,8,9]	[]
1	[2,3,7,8]	[5]
2	[3,7]	[5,5]
3	[]	[5,5,5]

Constraints:

2 <= n == nums.length <= 50
n is even.
1 <= nums[i] <= 50

Solutions

Solution 1: Sorting

First, we sort the array $\textit{nums}$. Then, we start taking elements from both ends of the array, calculating the sum of the two elements, and taking the minimum value. Finally, we return the minimum value divided by 2 as the answer.

The time complexity is $O(n \log n)$, and the space complexity is $O(\log n)$, where $n$ is the length of the array $\textit{nums}$.

Python3

class Solution:
    def minimumAverage(self, nums: List[int]) -> float:
        nums.sort()
        n = len(nums)
        return min(nums[i] + nums[-i - 1] for i in range(n // 2)) / 2

Java

class Solution {
    public double minimumAverage(int[] nums) {
        Arrays.sort(nums);
        int n = nums.length;
        int ans = 1 << 30;
        for (int i = 0; i < n / 2; ++i) {
            ans = Math.min(ans, nums[i] + nums[n - i - 1]);
        }
        return ans / 2.0;
    }
}

C++

class Solution {
public:
    double minimumAverage(vector<int>& nums) {
        sort(nums.begin(), nums.end());
        int ans = 1 << 30, n = nums.size();
        for (int i = 0; i < n; ++i) {
            ans = min(ans, nums[i] + nums[n - i - 1]);
        }
        return ans / 2.0;
    }
};

Go

func minimumAverage(nums []int) float64 {
	sort.Ints(nums)
	n := len(nums)
	ans := 1 << 30
	for i, x := range nums[:n/2] {
		ans = min(ans, x+nums[n-i-1])
	}
	return float64(ans) / 2
}

TypeScript

function minimumAverage(nums: number[]): number {
    nums.sort((a, b) => a - b);
    const n = nums.length;
    let ans = Infinity;
    for (let i = 0; i * 2 < n; ++i) {
        ans = Math.min(ans, nums[i] + nums[n - 1 - i]);
    }
    return ans / 2;
}

Rust

impl Solution {
    pub fn minimum_average(mut nums: Vec<i32>) -> f64 {
        nums.sort();
        let n = nums.len();
        let ans = (0..n / 2).map(|i| nums[i] + nums[n - i - 1]).min().unwrap();
        ans as f64 / 2.0
    }
}