LeetCode(Medium) : Maximum Gap #164

Introduction:

• The problem at hand: finding the maximum difference between two successive elements in a sorted array.
• Key constraints: Linear time complexity and the use of linear extra space.
• Code snippet provided as a solution.

Logic and Approach:

• Sorting the Array: The initial step involves sorting the input array in ascending order using the sort function.
• Calculating Differences: Iterate

through the sorted array, calculating the difference between each pair of successive elements.

• Updating Maximum Gap: Keep track of the maximum difference encountered during the iteration.

Implementation:

• The provided C++ code follows a simple and straightforward implementation.
• Sorting the array using the sort function from the C++ Standard Template Library (STL).
• Iterating through the sorted array to calculate differences and updating the maximum gap.

Intuition:

• The sorting step ensures that elements with larger values are positioned towards the end of the array.
• By iterating through the sorted array, we can efficiently calculate the differences between successive elements.
• The maximum difference encountered represents the maximum gap in the original unsorted array.

Optimization and Insights:

• Time Complexity: The sorting step dominates the time complexity, making it O(N log N), where N is the number of elements in the array.
• Space Complexity: The algorithm uses linear extra space due to the sorting operation.
• Linear Time Requirement: Achieving linear time complexity while solving this problem might be challenging. The sorting operation typically takes O(N log N) time.
• Possible Optimization: The Radix Sort algorithm is an example of a linear time sorting algorithm, but it may not always be more efficient than the standard comparison-based sorting algorithms for small datasets.

Conclusion:

• The provided solution effectively finds the maximum gap between successive elements in linear time and uses linear extra space through the use of sorting.
• Understanding the time and space complexity is crucial for optimizing algorithms and making informed choices.
• Further exploration of linear time sorting algorithms could be considered for potential optimization in specific scenarios.

(Note: The Radix Sort algorithm is just mentioned as an example of a linear time sorting algorithm. The actual implementation may require careful consideration and testing based on specific use cases.)

class Solution {
public:
    int maximumGap(vector<int>& nums) {
        int maxi =0 ;
        sort(nums.begin(),nums.end());
        for(int i = 0;i<nums.size()-1;i++){
        int count =  nums[i+1]-nums[i];
        maxi =max(maxi,count);
    }
    return maxi;
    }
};