How do you solve Maximum Manhattan Distance After K Changes on LeetCode?

Maximum Manhattan Distance After K Changes (LeetCode #3443) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Changing characters strategically can lead to a significant increase in distance.

What is the brute force solution for Maximum Manhattan Distance After K Changes?

The brute force approach for Maximum Manhattan Distance After K Changes is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves trying all possible combinations of changing up to k characters in the string to maximize the Manhattan distance. This method is straightforward but inefficient for larger strings. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Manhattan Distance After K Changes?

Maximum Manhattan Distance After K Changes uses the following concepts: Hash Table, Math, String, Counting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximum Manhattan Distance After K Changes?

Always start with a clear understanding of the problem and constraints. Discuss your thought process and potential approaches aloud during the interview. Be prepared to optimize your initial solution and explain your reasoning.

What are common mistakes when solving Maximum Manhattan Distance After K Changes?

Failing to account for the total number of changes available. Not considering the impact of changing characters on both axes simultaneously.

#3443

Maximum Manhattan Distance After K Changes

Medium

Hash TableMathStringCountingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal approach focuses on calculating the maximum possible Manhattan distance by considering the net effect of changing up to k characters directly, rather than brute-forcing through all combinations.

⚙️

Algorithm

4 steps

1Step 1: Count the occurrences of 'N', 'S', 'E', and 'W' in the string.
2Step 2: Calculate the initial Manhattan distance based on the counts of 'N' and 'S' for y-axis and 'E' and 'W' for x-axis.
3Step 3: Determine how many changes can be made to maximize the distance in both x and y directions.
4Step 4: Calculate the maximum distance achievable by applying the changes.

solution.py8 lines

1def maxManhattanDistance(s, k):
2    n_count = s.count('N')
3    s_count = s.count('S')
4    e_count = s.count('E')
5    w_count = s.count('W')
6    initial_distance = abs(n_count - s_count) + abs(e_count - w_count)
7    total_changes = n_count + s_count + e_count + w_count + k
8    return initial_distance + min(total_changes, k) * 2

ℹ

Complexity note: This complexity is linear because we only traverse the string once to count the characters, and the rest of the calculations are constant time operations.

1Changing characters strategically can lead to a significant increase in distance.
2Understanding the balance between different directions is crucial for maximizing distance.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.