Problem Description
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. We define the distance between two integers a and b to be their absolute difference |a - b|. Return the maximum distance.
Key Insights
- The maximum distance can be calculated using the minimum and maximum values from different arrays.
- Since each array is sorted, the smallest value in the first array and the largest value in the last array (or vice versa) will yield the maximum distance.
- We only need to keep track of the overall minimum and maximum values across the arrays to compute the result efficiently.
Space and Time Complexity
Time Complexity: O(m) - where m is the number of arrays, as we iterate through each array once. Space Complexity: O(1) - only a few variables are used to store the minimum and maximum values.
Solution
To solve this problem, we will use a greedy approach. We will iterate through each array to find the minimum and maximum values across all arrays. The maximum distance can then be calculated as the absolute difference between the minimum value of one array and the maximum value of another array.