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2256. Minimum Average Difference

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 firsti + 1 elements of nums and the average of the lastn - 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.

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

Solutions (Rust)

1. Solution

implSolution{pubfnminimum_average_difference(nums:Vec<i32>) -> i32{let n = nums.len()asi64;letmut prefix_sum = 0;letmut suffix_sum = nums.iter().map(|&x| x asi64).sum::<i64>();letmut min_avg_diff = i64::MAX;letmut ret = 0;for i in0..nums.len(){ prefix_sum += nums[i]asi64; suffix_sum -= nums[i]asi64;let prefix_avg = prefix_sum / (i asi64 + 1);let suffix_avg = suffix_sum.checked_div(n - i asi64 - 1).unwrap_or(0);let avg_diff = (prefix_avg - suffix_avg).abs();if avg_diff < min_avg_diff { min_avg_diff = avg_diff; ret = i;}} ret asi32}}
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