Statistics from a Large Sample — LeetCode 1093 Python Solution

The problem

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.

Example

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].

Python solution

class Solution:
    def sampleStats(self, count: List[int]) -> List[float]:
        def find(i: int) -> int:
            t = 0
            for k, x in enumerate(count):
                t += x
                if t >= i:
                    return k

        mi, mx = inf, -1
        s = cnt = 0
        mode = 0
        for k, x in enumerate(count):
            if x:
                mi = min(mi, k)
                mx = max(mx, k)
                s += k * x
                cnt += x
                if x > count[mode]:
                    mode = k

        median = (
            find(cnt // 2 + 1) if cnt & 1 else (find(cnt // 2) + find(cnt // 2 + 1)) / 2
        )
        return [mi, mx, s / cnt, median, mode]

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 1093. Statistics from a Large Sample is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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