2090.k-radius-subarray-averages.cpp

//  Tag: Array, Sliding Window
//  Time: O(N)
//  Space: O(1)
//  Ref: -
//  Note: -

//  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
//  
//  

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