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2256.Minimum Average Difference

tags: Medium,Array,Prefix Sum

2256. Minimum Average Difference

題目描述

You are given a 0-indexed integer array nums of length n.

The average difference of the index i is the absolute difference between the average of the first i + 1 elements of nums and the average of the last n - i - 1 elements. Both averages should be rounded down to the nearest integer.

Return the index with the minimum average difference. If there are multiple such indices, return the smallest one.

Note:

  • The absolute difference of two numbers is the absolute value of their difference.
  • The average of n elements is the sum of the n elements divided (integer division) by n.
  • The average of 0 elements is considered to be 0.

範例

Example 1:

Input: nums = [2,5,3,9,5,3]
Output: 3
Explanation:
- The average difference of index 0 is: |2 / 1 - (5 + 3 + 9 + 5 + 3) / 5| = |2 / 1 - 25 / 5| = |2 - 5| = 3.
- The average difference of index 1 is: |(2 + 5) / 2 - (3 + 9 + 5 + 3) / 4| = |7 / 2 - 20 / 4| = |3 - 5| = 2.
- The average difference of index 2 is: |(2 + 5 + 3) / 3 - (9 + 5 + 3) / 3| = |10 / 3 - 17 / 3| = |3 - 5| = 2.
- The average difference of index 3 is: |(2 + 5 + 3 + 9) / 4 - (5 + 3) / 2| = |19 / 4 - 8 / 2| = |4 - 4| = 0.
- The average difference of index 4 is: |(2 + 5 + 3 + 9 + 5) / 5 - 3 / 1| = |24 / 5 - 3 / 1| = |4 - 3| = 1.
- The average difference of index 5 is: |(2 + 5 + 3 + 9 + 5 + 3) / 6 - 0| = |27 / 6 - 0| = |4 - 0| = 4.
The average difference of index 3 is the minimum average difference so return 3.

Example 2:

Input: nums = [0]
Output: 0
Explanation:
The only index is 0 so return 0.
The average difference of index 0 is: |0 / 1 - 0| = |0 - 0| = 0.

Constraints:

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

解答

Python

class Solution: def minimumAverageDifference(self, nums: List[int]) -> int: if len(nums) <= 1: return 0 current_ans = [-1,1000000000] whole_array_sum = sum(nums) firstksum = 0 #print(nums) for idx, v in enumerate(nums): firstksum += v if idx == len(nums)-1: cur = abs( whole_array_sum/len(nums) ) else: cur = abs( floor(firstksum/(idx+1)) - floor( (whole_array_sum - firstksum)/(len(nums)-idx-1)) ) #print(cur, firstksum, idx+1, whole_array_sum - firstksum, len(nums)-idx-1) if cur < current_ans[1]: current_ans = [idx, cur] return current_ans[0]

玉山 Dec 5, 2022

Javascript

function minimumAverageDifference(nums) { let leftSum = 0; let rightSum = 0; for (let i = 0; i < nums.length; i++) { rightSum += nums[i]; } let minimum = Infinity; let index = 0; for (let i = 0; i < nums.length; i++) { leftSum += nums[i]; rightSum -= nums[i]; const miniAvgDiff = Math.abs(~~(leftSum / (i + 1)) - ~~(rightSum / Math.max(1, nums.length - 1 - i))); if (miniAvgDiff < minimum) { minimum = miniAvgDiff; index = i; } } return index; }

Marsgoat Dec 5, 2022

Reference

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