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The simplest approach to solve this problem is to first sort the array. Once sorted, the maximum gap will be found between consecutive elements. By iterating over the sorted array and computing the difference between each pair of consecutive elements, we can find the maximum difference.
Time Complexity: O(n log n) due to the sorting step.
Space Complexity: O(1) as no additional space is used except for variables.
1function maximumGap(nums) {
2 if (nums.length < 2) return 0;
3 nums.sort((a, b) => a - b);
4 let maxGap = 0;
5 for (let i = 1; i < nums.length; i++) {
6 maxGap = Math.max(maxGap, nums[i] - nums[i - 1]);
7 }
8 return maxGap;
9}This JavaScript solution sorts the array using sort(). It then iterates through the array to determine the maximum gap.
This approach leverages the bucket sort idea to achieve linear time complexity. By calculating the bucket size and distributing array elements across buckets, we attempt to isolate maximum differences across distinct buckets, as adjacent elements within a bucket should have a smaller difference.
Time Complexity: O(n) since the bucket placement and scanning are linear operations.
Space Complexity: O(n) for the two bucket arrays.
1The Python solution applies the bucket strategy by establishing a range-based partitioning, analyzing bucket-constrained min and max values, then finding inter-bucket gaps.