Lexicographically smallest array
Detailed guide and Python implementation for the 'Lexicographically smallest array' problem.
1. Concept Overview
The 'Lexicographically smallest array' problem is a key challenge in the Greedy section.
This implementation focuses on medium-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 Lexicographically smallest array.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Lexicographically smallest array 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 lexicographically_smallest(arr, k) that returns the lexicographically smallest array that can be obtained by swapping adjacent elements at most k times. Elements in arr are unique.
- •1 <= len(arr) <= 1000
- •0 <= k <= 10^5
- •-10^9 <= arr[i] <= 10^9
Examples
lexicographically_smallest([7, 6, 9, 2, 1], 3)
[2, 7, 6, 9, 1]
To get the smallest possible element 2 to the front, we swap 9 and 2, then 6 and 2, then 7 and 2. This takes exactly 3 swaps, resulting in [2, 7, 6, 9, 1].
lexicographically_smallest([2, 1, 3], 1)
[1, 2, 3]
Swap 2 and 1 (1 swap) to get [1, 2, 3].
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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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 smallest_array_opt(arr, k):
n = len(arr)
for i in range(n - 1):
pos = i
for j in range(i + 1, n):
if (j - i) > k: break
if arr[j] < arr[pos]: pos = j
for j in range(pos, i, -1): arr[j], arr[j-1] = arr[j-1], arr[j]
k -= (pos - i)
return arrBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def smallest_array_brute(arr, k):
# Bubble sort like swaps (not practical)
return smallest_array_opt(arr, k)Algorithm Pattern Checklist
When dealing with Greedy data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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