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643. Maximum Average Subarray I

Description

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 <= 105
  • -104 <= nums[i] <= 104

Solutions

Solution 1: Sliding Window

We maintain a sliding window of length $k$, and for each window, we calculate the sum $s$ of the numbers within the window. We take the maximum sum $s$ as the answer.

The time complexity is $O(n)$, where $n$ is the length of the array $nums$. The space complexity is $O(1)$.

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class Solution:
    def findMaxAverage(self, nums: List[int], k: int) -> float:
        ans = s = sum(nums[:k])
        for i in range(k, len(nums)):
            s += nums[i] - nums[i - k]
            ans = max(ans, s)
        return ans / k

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class Solution {
    public double findMaxAverage(int[] nums, int k) {
        int s = 0;
        for (int i = 0; i < k; ++i) {
            s += nums[i];
        }
        int ans = s;
        for (int i = k; i < nums.length; ++i) {
            s += (nums[i] - nums[i - k]);
            ans = Math.max(ans, s);
        }
        return ans * 1.0 / k;
    }
}

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class Solution {
public:
    double findMaxAverage(vector<int>& nums, int k) {
        int s = accumulate(nums.begin(), nums.begin() + k, 0);
        int ans = s;
        for (int i = k; i < nums.size(); ++i) {
            s += nums[i] - nums[i - k];
            ans = max(ans, s);
        }
        return static_cast<double>(ans) / k;
    }
};

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func findMaxAverage(nums []int, k int) float64 {
    s := 0
    for _, x := range nums[:k] {
        s += x
    }
    ans := s
    for i := k; i < len(nums); i++ {
        s += nums[i] - nums[i-k]
        ans = max(ans, s)
    }
    return float64(ans) / float64(k)
}

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function findMaxAverage(nums: number[], k: number): number {
    let s = 0;
    for (let i = 0; i < k; ++i) {
        s += nums[i];
    }
    let ans = s;
    for (let i = k; i < nums.length; ++i) {
        s += nums[i] - nums[i - k];
        ans = Math.max(ans, s);
    }
    return ans / k;
}

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

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class Solution {
    /**
     * @param Integer[] $nums
     * @param Integer $k
     * @return Float
     */
    function findMaxAverage($nums, $k) {
        $s = 0;
        for ($i = 0; $i < $k; $i++) {
            $s += $nums[$i];
        }
        $ans = $s;
        for ($j = $k; $j < count($nums); $j++) {
            $s = $s - $nums[$j - $k] + $nums[$j];
            $ans = max($ans, $s);
        }
        return $ans / $k;
    }
}

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