[LeetCode] 1093. Statistics from a Large Sample 大样本统计

You are given a large sample of integers in the range [0, 255]. Since the sample is so large, it is represented by an array count where count[k] is the number of times that k appears in the sample.

Calculate the following statistics:

• minimum: The minimum element in the sample.
• maximum: The maximum element in the sample.
• mean: The average of the sample, calculated as the total sum of all elements divided by the total number of elements.
• median:
  • If the sample has an odd number of elements, then the median is the middle element once the sample is sorted.
  • If the sample has an even number of elements, then the median is the average of the two middle elements once the sample is sorted.
• mode: The number that appears the most in the sample. It is guaranteed to be unique.

Return the statistics of the sample as an array of floating-point numbers [minimum, maximum, mean, median, mode]. Answers within 10-5 of the actual answer will be accepted.

Example 1:

Input: count = [0,1,3,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
Output: [1.00000,3.00000,2.37500,2.50000,3.00000]
Explanation: The sample represented by count is [1,2,2,2,3,3,3,3].
The minimum and maximum are 1 and 3 respectively.
The mean is (1+2+2+2+3+3+3+3) / 8 = 19 / 8 = 2.375.
Since the size of the sample is even, the median is the average of the two middle elements 2 and 3, which is 2.5.
The mode is 3 as it appears the most in the sample.

Example 2:

Input: count = [0,4,3,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]
Output: [1.00000,4.00000,2.18182,2.00000,1.00000]
Explanation: The sample represented by count is [1,1,1,1,2,2,2,3,3,4,4].
The minimum and maximum are 1 and 4 respectively.
The mean is (1+1+1+1+2+2+2+3+3+4+4) / 11 = 24 / 11 = 2.18181818... (for display purposes, the output shows the rounded number 2.18182).
Since the size of the sample is odd, the median is the middle element 2.
The mode is 1 as it appears the most in the sample.

Constraints:

• count.length == 256
• 0 <= count[i] <= 109
• 1 <= sum(count) <= 109
• The mode of the sample that count represents is unique.

这道题说是有很多在0到 255 中的整数，由于重复的数字太多了，所以这里采用的是统计每个数字出现的个数的方式，用数组 count 来表示，其中 count[i] 表示数字i出现的次数。现在让统计原始数组中的最大值，最小值，平均值，中位数，和众数。这里面的最大最小值很好求，最小值就是 count 数组中第一个不为0的位置，最大值就是 count 数组中最后一个不为0的位置。最小值 mn 初始化为 256，在遍历 count 数组的过程中，遇到不为0的数字时，若此时 mn 为 256，则更新为坐标i。最大值 mx 直接每次更新为值不为0的坐标i即可。平均值也好求，只要求出所有的数字之和，跟数字的个数相除就行了，注意由于数字之和可能很大，需要用 double 来表示。众数也不难求，只要找出 count 数组中的最大值，则其坐标就是众数。比较难就是中位数了，由于数组的个数可奇可偶，中位数的求法不同，这里为了统一，采用一个小 trick，比如数组 1，2，3 和 1，2，3，4，可以用坐标为 (n-1)/2 和 n/2 的两个数字求平均值得到，对于长度为奇数的数组，这两个坐标表示的是相同的数字。这里由于是统计数组，所以要找的两个位置是 (cnt+1)/2 和 (cnt+2)/2，其中 cnt 是所有数字的个数。再次遍历 count 数组，使用 cur 来累计当前经过的数字个数，若 cur 小于 first，且 cur 加上 count[i] 大于等于 first，说明当前数字i即为所求，加上其的一半到 median。同理，若 cur 小于 second，cur 加上 count[i] 大于等于 second，说明当前数字i即为所求，加上其的一半到 median 即可，参见代码如下：

class Solution {
public:
    vector<double> sampleStats(vector<int>& count) {
        double mn = 256, mx = 0, mean = 0, median = 0, sum = 0;
        int cnt = 0, mode = 0;
        for (int i = 0; i < count.size(); ++i) {
            if (count[i] == 0) continue;
            if (mn == 256) mn = i;
            mx = i;
            sum += (double)i * count[i];
            cnt += count[i];
            if (count[i] > count[mode]) mode = i;
        }
        mean = sum / cnt;
        int first = (cnt + 1) / 2, second = (cnt + 2) / 2, cur = 0;
        for (int i = 0; i < count.size(); ++i) {
            if (cur < first && cur + count[i] >= first) median += i / 2.0;
            if (cur < second && cur + count[i] >= second) median += i / 2.0;
            cur += count[i];
        }
        return {mn, mx, sum / cnt, median, (double)mode};
    }
};

Github 同步地址:

https://github.com/grandyang/leetcode/issues/1093

参考资料：

https://leetcode.com/problems/statistics-from-a-large-sample/

https://leetcode.com/problems/statistics-from-a-large-sample/discuss/317626/Python-Solution

https://leetcode.com/problems/statistics-from-a-large-sample/discuss/317857/Java-Simple-2-pass-code-w-comments-and-explanation.

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