Question

2090. K Radius Subarray Averages

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Description

You are given a 0-indexed array nums of n integers, and an integer k.

The k-radius average for a subarray of nums centered at some index i with the radius k is the average of all elements in nums between the indices i - k and i + k (inclusive). If there are less than k elements before or after the index i, then the k-radius average is -1.

Build and return _an array _avgs_ of length _n_ where _avgs[i]_ is the k-radius average for the subarray centered at index _i.

The average of x elements is the sum of the x elements divided by x, using integer division. The integer division truncates toward zero, which means losing its fractional part.

• For example, the average of four elements 2, 3, 1, and 5 is (2 + 3 + 1 + 5) / 4 = 11 / 4 = 2.75, which truncates to 2.

 

Example 1:

Input: nums = [7,4,3,9,1,8,5,2,6], k = 3
Output: [-1,-1,-1,5,4,4,-1,-1,-1]
Explanation:
- avg[0], avg[1], and avg[2] are -1 because there are less than k elements before each index.
- The sum of the subarray centered at index 3 with radius 3 is: 7 + 4 + 3 + 9 + 1 + 8 + 5 = 37.
  Using integer division, avg[3] = 37 / 7 = 5.
- For the subarray centered at index 4, avg[4] = (4 + 3 + 9 + 1 + 8 + 5 + 2) / 7 = 4.
- For the subarray centered at index 5, avg[5] = (3 + 9 + 1 + 8 + 5 + 2 + 6) / 7 = 4.
- avg[6], avg[7], and avg[8] are -1 because there are less than k elements after each index.

Example 2:

Input: nums = [100000], k = 0
Output: [100000]
Explanation:
- The sum of the subarray centered at index 0 with radius 0 is: 100000.
  avg[0] = 100000 / 1 = 100000.

Example 3:

Input: nums = [8], k = 100000
Output: [-1]
Explanation: 
- avg[0] is -1 because there are less than k elements before and after index 0.

 

Constraints:

• n == nums.length
• 1 <= n <= 105
• 0 <= nums[i], k <= 105

Solutions

Solution 1

class Solution:
  def getAverages(self, nums: List[int], k: int) -> List[int]:
    n = len(nums)
    ans = [-1] * n
    s = list(accumulate(nums, initial=0))
    for i in range(n):
      if i - k >= 0 and i + k < n:
        ans[i] = (s[i + k + 1] - s[i - k]) // (k << 1 | 1)
    return ans

class Solution {
  public int[] getAverages(int[] nums, int k) {
    int n = nums.length;
    long[] s = new long[n + 1];
    for (int i = 0; i < n; ++i) {
      s[i + 1] = s[i] + nums[i];
    }
    int[] ans = new int[n];
    Arrays.fill(ans, -1);
    for (int i = 0; i < n; ++i) {
      if (i - k >= 0 && i + k < n) {
        ans[i] = (int) ((s[i + k + 1] - s[i - k]) / (k << 1 | 1));
      }
    }
    return ans;
  }
}

class Solution {
public:
  vector<int> getAverages(vector<int>& nums, int k) {
    int n = nums.size();
    long s[n + 1];
    s[0] = 0;
    for (int i = 0; i < n; ++i) {
      s[i + 1] = s[i] + nums[i];
    }
    vector<int> ans(n, -1);
    for (int i = 0; i < n; ++i) {
      if (i - k >= 0 && i + k < n) {
        ans[i] = (s[i + k + 1] - s[i - k]) / (k << 1 | 1);
      }
    }
    return ans;
  }
};

func getAverages(nums []int, k int) []int {
  n := len(nums)
  s := make([]int, n+1)
  for i, v := range nums {
    s[i+1] = s[i] + v
  }
  ans := make([]int, n)
  for i := 0; i < n; i++ {
    ans[i] = -1
    if i-k >= 0 && i+k < n {
      ans[i] = (s[i+k+1] - s[i-k]) / (k<<1 | 1)
    }
  }
  return ans
}

function getAverages(nums: number[], k: number): number[] {
  const n = nums.length;
  const s = new Array(n + 1).fill(0);
  for (let i = 0; i < n; ++i) {
    s[i + 1] = s[i] + nums[i];
  }
  const ans: number[] = new Array(n).fill(-1);
  for (let i = 0; i < n; ++i) {
    if (i - k >= 0 && i + k < n) {
      ans[i] = Math.floor((s[i + k + 1] - s[i - k]) / ((k << 1) | 1));
    }
  }
  return ans;
}

Solution 2

class Solution:
  def getAverages(self, nums: List[int], k: int) -> List[int]:
    s = 0
    ans = [-1] * len(nums)
    for i, v in enumerate(nums):
      s += v
      if i >= k * 2:
        ans[i - k] = s // (k * 2 + 1)
        s -= nums[i - k * 2]
    return ans

class Solution {
  public int[] getAverages(int[] nums, int k) {
    int n = nums.length;
    int[] ans = new int[n];
    Arrays.fill(ans, -1);
    long s = 0;
    for (int i = 0; i < n; ++i) {
      s += nums[i];
      if (i >= k * 2) {
        ans[i - k] = (int) (s / (k * 2 + 1));
        s -= nums[i - k * 2];
      }
    }
    return ans;
  }
}

class Solution {
public:
  vector<int> getAverages(vector<int>& nums, int k) {
    int n = nums.size();
    vector<int> ans(n, -1);
    long s = 0;
    for (int i = 0; i < n; ++i) {
      s += nums[i];
      if (i >= k * 2) {
        ans[i - k] = s / (k * 2 + 1);
        s -= nums[i - k * 2];
      }
    }
    return ans;
  }
};

func getAverages(nums []int, k int) []int {
  ans := make([]int, len(nums))
  s := 0
  for i, v := range nums {
    ans[i] = -1
    s += v
    if i >= k*2 {
      ans[i-k] = s / (k*2 + 1)
      s -= nums[i-k*2]
    }
  }
  return ans
}

function getAverages(nums: number[], k: number): number[] {
  const n = nums.length;
  const ans: number[] = new Array(n).fill(-1);
  let s = 0;
  for (let i = 0; i < n; ++i) {
    s += nums[i];
    if (i >= k * 2) {
      ans[i - k] = Math.floor(s / (k * 2 + 1));
      s -= nums[i - k * 2];
    }
  }
  return ans;
}