Replace each element by rank
Detailed guide and Python implementation for the 'Replace each element by rank' problem.
1. Concept Overview
The 'Replace each element by rank' problem is a key challenge in the Arrays section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Replace each element by rank.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Replace each element by rank carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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.
- •1 <= len(arr) <= 10^5
- •-10^9 <= arr[i] <= 10^9
Examples
arr = [20, 15, 26, 2, 98, 6]
[4, 3, 5, 1, 6, 2]
Sorted: [2,6,15,20,26,98]. Ranks: 2->1, 6->2, 15->3, 20->4, 26->5, 98->6.
arr = [10, 10, 10]
[1, 1, 1]
All elements are equal, so all get rank 1.
arr = [5, 3, 1]
[3, 2, 1]
Sorted: [1,3,5]. Ranks: 1->1, 3->2, 5->3.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def replace_with_rank(arr):
# Optimized: Use sorting and a dictionary
if not arr: return []
# Get unique elements sorted
sorted_unique = sorted(list(set(arr)))
# Map each element to its rank
rank_map = {val: i + 1 for i, val in enumerate(sorted_unique)}
# Replace elements with ranks
return [rank_map[x] for x in arr]Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def replace_with_rank(arr):
# Brute force: For each element, count how many smaller unique elements exist
n = len(arr)
ranks = []
for i in range(n):
smaller_unique = set()
for j in range(n):
if arr[j] < arr[i]:
smaller_unique.add(arr[j])
ranks.append(len(smaller_unique) + 1)
return ranksAlgorithm Pattern Checklist
When dealing with Arrays data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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