[LeetCode] 164. Maximum Gap 求最大間距

 

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.

 

遇到這類問題肯定先想到的是要給數組排序，但是題目要求是要線性的時間和空間，那么只能用桶排序或者基排序。這里用桶排序 Bucket Sort 來做，首先找出數組的最大值和最小值，然后要確定每個桶的容量，即為 (最大值 - 最小值) / 個數 + 1，在確定桶的個數，即為 (最大值 - 最小值) / 桶的容量 + 1，然后需要在每個桶中找出局部最大值和最小值，而最大間距的兩個數不會在同一個桶中，而是一個桶的最小值和另一個桶的最大值之間的間距，這是因為所有的數字要盡量平均分配到每個桶中，而不是都擁擠在一個桶中，這樣保證了最大值和最小值一定不會在同一個桶中，具體的證明博主也不會，只是覺得這樣想挺有道理的，各位看官大神們若知道如何證明請務必留言告訴博主啊，參見代碼如下：

 

class Solution {
public:
    int maximumGap(vector<int>& nums) {
        if (nums.size() <= 1) return 0;
        int mx = INT_MIN, mn = INT_MAX, n = nums.size(), pre = 0, res = 0;
        for (int num : nums) {
            mx = max(mx, num);
            mn = min(mn, num);
        }
        int size = (mx - mn) / n + 1, cnt = (mx - mn) / size + 1;
        vector<int> bucket_min(cnt, INT_MAX), bucket_max(cnt, INT_MIN);
        for (int num : nums) {
            int idx = (num - mn) / size;
            bucket_min[idx] = min(bucket_min[idx], num);
            bucket_max[idx] = max(bucket_max[idx], num);
        }
        for (int i = 1; i < cnt; ++i) {
            if (bucket_min[i] == INT_MAX || bucket_max[i] == INT_MIN) continue;
            res = max(res, bucket_min[i] - bucket_max[pre]);
            pre = i;
        }
        return res;
    }
};

 

Github 同步地址：

https://github.com/grandyang/leetcode/issues/164 

 

參考資料：

https://leetcode.com/problems/maximum-gap

http://blog.csdn.net/u011345136/article/details/41963051

https://leetcode.com/problems/maximum-gap/discuss/50642/radix-sort-solution-in-java-with-explanation

https://leetcode.com/problems/maximum-gap/discuss/50643/bucket-sort-java-solution-with-explanation-on-time-and-space

 

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