164. Maximum Gap

• Difficulty: Hard

• Topics: Sort

• Similar Questions:

Problem:

Given an unsorted array, find the maximum difference between the successive elements in its sorted form.

Return 0 if the array contains less than 2 elements.

Example 1:

Input: [3,6,9,1]
Output: 3
Explanation: The sorted form of the array is [1,3,6,9], either
             (3,6) or (6,9) has the maximum difference 3.

Example 2:

Input: [10]
Output: 0
Explanation: The array contains less than 2 elements, therefore return 0.

Note:

• You may assume all elements in the array are non-negative integers and fit in the 32-bit signed integer range.
• Try to solve it in linear time/space.

Solutions:

class Solution {
public:
    int maximumGap(vector<int>& nums) {
        if (nums.size() < 2)    return 0;

        int n = nums.size();

        int minElement = INT_MAX;
        int maxElement = INT_MIN;

        for (auto num : nums) {
            minElement = min(minElement, num);
            maxElement = max(maxElement, num);
        }

        int bucketSize = (maxElement - minElement + 1 + n - 1 ) / n;
        vector<int> bucketMax (n, INT_MIN);
        vector<int> bucketMin (n, INT_MAX);

        for (auto num : nums) {
            int index = (num - minElement) / bucketSize;
            bucketMax[index] = max(bucketMax[index], num);
            bucketMin[index] = min(bucketMin[index], num);
        }

        int max_gap = 0;
        int prev_max = bucketMax[0];
        for (int i = 1; i < n; ++i) {
            if (bucketMin[i] != INT_MAX) {
                max_gap = max(max_gap, bucketMin[i] - prev_max);
                prev_max = bucketMax[i];
            }
        }

        return max_gap;

    }
};