643. Maximum Average Subarray I

Description of Problem

You are given an integer array nums consisting of n elements, and an integer k.

Find a contiguous subarray whose length is equal to k that has the maximum average value and return this value. Any answer with a calculation error less than 10^-5 will be accepted.

Example 1:

Input: nums = [1,12,-5,-6,50,3], k = 4
Output: 12.75000
Explanation: Maximum average is (12 - 5 - 6 + 50) / 4 = 51 / 4 = 12.75

Example 2:

Input: nums = [5], k = 1
Output: 5.00000

Constraints:

n == nums.length
1 <= k <= n <= 10^5
-10^4 <= nums[i] <= 10^4

Solution

Tags: Sliding Window

Code (Rust)

impl Solution {
    pub fn find_max_average(nums: Vec<i32>, k: i32) -> f64 {
        use std::iter::zip;
        let (n, k) = (nums.len() as usize, k as usize);
        
        let mut sum = 0;
        for i in 0..k {
            sum += nums[i];
        }
        let mut max = sum;

        // window range (i..=j)
        for (i,j) in zip(1..,k..n) {
            sum = sum - nums[i - 1] + nums[j];
            max = max.max(sum);
        }
        
        return max as f64 / k as f64;
    }
}

Complexity

n is length of nums

Time Complexity

\(T(n) = \Theta(n)\)

Auxuiliary

\(S(n) = O(1)\)

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