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You can't achieve O(n) through bucket sort if you don't know if the input is random. In this problem it is not directly stated. If it was, bucket would seem to be a nice option indeed.

Radix works better for strings, sure longer than 10 digits. Constant factor for such sorting would be unnecessary big, make it slower than qsort.

And you have to be careful with count sort - its speed depends on range of numbers so,
instead of O(n log n) (for qsort n = 10^5) you get O(n) (where n = ai = 10^9).

And, cause

10^5 * log(10^5) < 10^9

log(10^5) < 10^4

then count works longer for big input.

Also, for input like
{0, 10^9}
count sort still needs O(10^9) time.

## Minimum Absolute Difference in an Array

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But that'd be like worse than O(n log n). Guess we could sort by count or radix or bucket to achieve O(n) in sorting

You can't achieve O(n) through bucket sort if you don't know if the input is random. In this problem it is not directly stated. If it was, bucket would seem to be a nice option indeed.

Radix works better for strings, sure longer than 10 digits. Constant factor for such sorting would be unnecessary big, make it slower than qsort.

And you have to be careful with count sort - its speed depends on range of numbers so, instead of O(n log n) (for qsort n = 10^5) you get O(n) (where n = ai = 10^9).

And, cause

then count works longer for big input.

Also, for input like {0, 10^9} count sort still needs O(10^9) time.