Leetcode #624: Maximum Distance in Arrays
In this guide, we solve Leetcode #624 Maximum Distance in Arrays in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given m arrays, where each array is sorted in ascending order. You can pick up two integers from two different arrays (each array picks one) and calculate the distance.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: arrays = [[1,2,3],[4,5],[1,2,3]]
Output: 4
Explanation: One way to reach the maximum distance 4 is to pick 1 in the first or third array and pick 5 in the second array.
Python Solution
class Solution:
def maxDistance(self, arrays: List[List[int]]) -> int:
ans = 0
mi, mx = arrays[0][0], arrays[0][-1]
for arr in arrays[1:]:
a, b = abs(arr[0] - mx), abs(arr[-1] - mi)
ans = max(ans, a, b)
mi = min(mi, arr[0])
mx = max(mx, arr[-1])
return ans
Complexity
The time complexity is , where is the number of arrays. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.