Maximizing Distance in Arrays | LeetCode Problem 624 | Leetcode Daily Question

LeetCode Problem 624, titled "Maximum Distance in Arrays," challenges us to find the maximum distance between any two elements from different arrays within a given list of arrays. In this blog post, we will break down the problem, explain the code solution step-by-step, and discuss the time and space complexity of the solution.

Problem Explanation

The problem presents us with a 2D array where each sub-array is sorted in ascending order. Our task is to determine the maximum distance between any two elements such that the elements come from different sub-arrays.

Code Explanation

Here's a clean and efficient solution to the problem using C++:

    class Solution {

    public:

        int maxDistance(vector<vector<int>>& arrays)

        {

            int min_value = arrays[0][0];

            int max_value = arrays[0][arrays[0].size()-1];

            int maximum_distance = 0;

            for(int i = 1; i< arrays.size(); i++)

            {

                vector<int> temp = arrays[i];

                maximum_distance = max(maximum_distance, abs(temp[0] - max_value));

                maximum_distance = max(maximum_distance, abs(temp[temp.size()-1] - min_value));

                min_value = min(min_value, temp[0]);

                max_value = max(max_value, temp[temp.size()-1]);

            }

            return maximum_distance;

        }

    };

   

Code Walkthrough

1. Initialization:
• We start by initializing min_value to the first element of the first sub-array and max_value to the last element of the first sub-array. These will keep track of the smallest and largest elements encountered so far.
2. Iterate Through Arrays:
• For each subsequent sub-array, calculate the potential maximum distance by considering:
• The difference between the current sub-array’s last element and the smallest element encountered so far (min_value).
• The difference between the current sub-array’s first element and the largest element encountered so far (max_value).
• Update maximum_distance with the maximum of these differences.
3. Update Extremes:
• Update min_value and max_value based on the current sub-array's first and last elements, respectively.
4. Return the Result:
• After processing all sub-arrays, return the maximum distance found.

Time Complexity

The time complexity of this solution is O(n), where n is the number of sub-arrays. The reason is that each sub-array is processed exactly once, and each operation within the loop is O(1). Thus, the dominant factor is the iteration over n sub-arrays.

Space Complexity

The space complexity is O(1), excluding the input storage. The solution uses only a constant amount of extra space for variables such as min_value, max_value, and maximum_distance. The temporary vector<int> temp used to hold each sub-array does not affect the overall space complexity significantly.

 

The solution to LeetCode Problem 624 effectively finds the maximum distance between elements from different arrays with a time complexity of O(n) and a space complexity of O(1). By leveraging the sorted nature of the sub-arrays and maintaining a running record of minimum and maximum values, this approach ensures both efficiency and clarity.