Rank the values of an array of distinct integers

You get an array of distinct integers. Replace each value with its rank: the smallest value gets 1, the next smallest 2, and so on. It is the one-row case of ranking a matrix, where only cells that share a row or a column constrain each other.

Interface

Unless you agree on a different interface with the interviewer, assume:

• array_ranks(nums: list[int]) -> list[int] — the rank of each element, in the original order.

Example

array_ranks([40, 10, 30, 20])  ->  [4, 1, 3, 2]
array_ranks([-5, 100, 7])      ->  [1, 3, 2]
array_ranks([8])               ->  [1]

Constraints

• 1 <= len(nums) <= 10^5.
• -10^9 <= nums[i] <= 10^9, all distinct.

Clarifying questions

• Are the values guaranteed distinct? If not, do equal values share a rank?
• Rank from smallest or from largest?
• Return a new array, or overwrite the input?

What a strong answer covers

• Sort a copy, build a hash map from value to its position plus one, then map the original array: O(n log n) time, O(n) space.
• Why hashing matters: the lookup back into original order is O(1) per element because the values are distinct.
• When the value range is small, counting sort gives O(n + range).
• Tests: one element, negatives, already sorted and reversed input.

Follow-ups

• Equal values must share a rank, with no gaps (dense ranking).
• The 2D version: a matrix of distinct values where a larger value in the same row or column must get a strictly larger rank, with ranks as small as possible.
• Values stream in: report the rank of each new value among those seen so far.