Given an array of integers arr and two integers k and threshold, return *the number of sub-arrays of size k and average greater than or equal to *threshold.

Example 1:

Input: arr = [2,2,2,2,5,5,5,8], k = 3, threshold = 4
Output: 3
Explanation: Sub-arrays [2,5,5],[5,5,5] and [5,5,8] have averages 4, 5 and 6 respectively. All other sub-arrays of size 3 have averages less than 4 (the threshold).

Example 2:

Input: arr = [11,13,17,23,29,31,7,5,2,3], k = 3, threshold = 5
Output: 6
Explanation: The first 6 sub-arrays of size 3 have averages greater than 5. Note that averages are not integers.

Constraints:

• 1 <= arr.length <= 10^5
• 1 <= arr[i] <= 10^4
• 1 <= k <= arr.length
• 0 <= threshold <= 10^4

這道題給了一個正整數數組 arr，和兩個參數k，threshold。說是讓找出所有長度為k的子數組的個數，使得該子數組的平均值大于等于 threshold。子數組的平均值的計算方法即為子數組之和除以其長度，這里就是除以k。而求子數組之和的問題，博主下意識的就會想到建立累加和數組，這樣可以快速求出任意長度的子數組之和。這里也可以用這種方法，建立累加和數組 sums，然后就是遍歷所有的長度為k的子數組，然后通過 sums[i]-sums[i-k] 快速得到其數組之和。接下來就要進行比較了，這里博主沒有使用除法，因為除法沒有乘法高效，用k乘以 threshold 的結果進行比較也是一樣的，若滿足條件，則結果自增1即可，參見代碼如下：

解法一：

class Solution {
public:
    int numOfSubarrays(vector<int>& arr, int k, int threshold) {
        int res = 0, n = arr.size(), target = k * threshold;
        vector<int> sums(n + 1);
        for (int i = 1; i <= n; ++i) {
            sums[i] = sums[i - 1] + arr[i - 1];
        }
        for (int i = k; i <= n; ++i) {
            int sum = sums[i] - sums[i - k];
            if (sum >= target) ++res;
        }
        return res;
    }
};

由于這道題只關心長度為k的子數組，那么建立整個累加和數組就略顯多余了，只要維護一個大小為k的窗口就能遍歷所有長度為k的子數組了。這就是滑動窗口 Sliding Window 的思路，遍歷數組，將當前數字加到 sum 中，若i大于等于k，說明此時窗口大小超過了k，需要把左邊界 arr[i-k] 減去，然后把 sum 跟 target 進行比較，注意這里的i必須要大于等于 k-1，因為要保證窗口的大小正好是k，參見代碼如下：

解法二：

class Solution {
public:
    int numOfSubarrays(vector<int>& arr, int k, int threshold) {
        int res = 0, n = arr.size(), sum = 0, target = k * threshold;
        for (int i = 0; i < n; ++i) {
            sum += arr[i];
            if (i >= k) sum -= arr[i - k];
            if (i >= k - 1 && sum >= target) ++res;
        }
        return res;
    }
};

Github 同步地址:

https://github.com/grandyang/leetcode/issues/1343

類似題目：

K Radius Subarray Averages

Count Subarrays With Median K

參考資料：

https://leetcode.com/problems/number-of-sub-arrays-of-size-k-and-average-greater-than-or-equal-to-threshold

https://leetcode.com/problems/number-of-sub-arrays-of-size-k-and-average-greater-than-or-equal-to-threshold/solutions/503786/c-short-solution/

https://leetcode.com/problems/number-of-sub-arrays-of-size-k-and-average-greater-than-or-equal-to-threshold/solutions/502740/java-python-3-2-codes-prefix-sum-and-sliding-window-w-analysis/

LeetCode All in One 題目講解匯總(持續更新中...)