leetcode[164] Maximum Gap

梅西刚梅开二度，我也记一题。

在一个没排序的数组里，找出排序后的相邻数字的最大差值。

要求用线性时间和空间。

如果用nlgn的话，直接排序然后判断就可以了。so easy

class Solution {
public:
    int maximumGap(vector<int> &num) {
        if (num.size() < 2) return 0;
        sort(num.begin(), num.end());
        int maxm = -1;
        for (int i = 1; i < num.size(); i++)
        {
            if (abs(num[i] - num[i-1]) > maxm)
                maxm = abs(num[i] - num[i-1]);
        }
        return maxm;
    }
};

但我们要的是线性时间。

其实这个思想在算法课上有讲过。用桶的思想。把数组分成几个桶，然后判断相邻桶的最大与最小之间的差值。关键是要知道每个桶的长度，已经桶的个数。

class Solution {
public:
    int maximumGap(vector<int> &num) {
        if (num.size() < 2) return 0;
        int Max = num[0], Min = Max, ans = 0;
        for (int i = 1; i < num.size(); i++)
        {
            if (num[i] < Min)
                Min = num[i];
            if (num[i] > Max)
                Max = num[i];
        }
        if (Max == Min) return 0;

        int bucketGap = (Max - Min)/num.size() + 1; // 桶的间隔是关键
        int bucketLen = (Max - Min)/bucketGap + 1; // 举个 1，2，3的例子就知道了
        vector<int> MinMax(2, INT_MAX);
        MinMax[1] = INT_MIN;
        vector<vector<int> > bucket(bucketLen, MinMax);

        for (int i = 0; i < num.size(); i++)
        {
            int ind = (num[i] - Min)/bucketGap;
            if (num[i] < bucket[ind][0])
                bucket[ind][0] = num[i];
            if (num[i] > bucket[ind][1])
                bucket[ind][1] = num[i];
        }

        int first = bucket[0][1], second;
        for (int i = 1; i < bucketLen; i++)
        {
            if (bucket[i][0] == INT_MAX) continue;
            second = bucket[i][0];
            int tmpmax = second - first;
            ans = tmpmax > ans ? tmpmax : ans;
            first = bucket[i][1];
        }

        return ans;
    }
};

最后附上官网的解法说明：

Suppose there are N elements and they range from A to B.

Then the maximum gap will be no smaller than ceiling[(B - A) / (N - 1)]

Let the length of a bucket to be len = ceiling[(B - A) / (N - 1)], then we will have at most num = (B - A) / len + 1 of bucket

for any number K in the array, we can easily find out which bucket it belongs by calculating loc = (K - A) / len and therefore maintain the maximum and minimum elements in each bucket.

Since the maximum difference between elements in the same buckets will be at most len - 1, so the final answer will not be taken from two elements in the same buckets.

For each non-empty buckets p, find the next non-empty buckets q, then q.min - p.max could be the potential answer to the question. Return the maximum of all those values.