What is the optimal time complexity of solving Replace each element by rank?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Replace each element by rank?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Replace each element by rank?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Replace each element by rank?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Replace each element by rank

Learn how to solve the 'Replace each element by rank' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function replace_by_rank(arr) that replaces each element in the array with its rank when the array is sorted in ascending order. The smallest element gets rank 1, the second smallest gets rank 2, and so on. If two elements are equal, they get the same rank. Return the array of ranks.

Constraints

•1 <= len(arr) <= 10^5
•-10^9 <= arr[i] <= 10^9

Examples

Example 1

Input

arr = [20, 15, 26, 2, 98, 6]

Output

[4, 3, 5, 1, 6, 2]

Explanation

Sorted: [2,6,15,20,26,98]. Ranks: 2->1, 6->2, 15->3, 20->4, 26->5, 98->6.

Example 2

Input

arr = [10, 10, 10]

Output

[1, 1, 1]

Explanation

All elements are equal, so all get rank 1.

Example 3

Input

arr = [5, 3, 1]

Output

[3, 2, 1]

Explanation

Sorted: [1,3,5]. Ranks: 1->1, 3->2, 5->3.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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