【桶排序】求无序数组中最大的“Gap"

标签：c++   程序员   面试   桶排序   

题目：leetcode

Given an unsorted array, find the maximum difference between the successive elements in its sorted form.
Try to solve it in linear time/space.
Return 0 if the array contains less than 2 elements.
You may assume all elements in the array are non-negative integers and fit in the 32-bit signed integer range.

提示：

假设题目中的排序数组是升序。

运用桶排序，把数组平均分成len组（len是数组元素个数），每组前闭后开，其中最后一组只有一个元素——最大值。

则最大的gap的来源有两种可能：1、每个桶内的最大最小值之差；2、两个相邻非空的桶之间，“大桶最小值”减去“小桶最大值”之差。

//返回值第一个是数组最小值，第二个数是数组最大值
pair<int, int> minmax(const vector<int> &s)
{
	int rmin = INT_MAX, rmax = -1;
	for (size_t i = 0; i < s.size(); i++)
	{
		rmin = min(rmin, s[i]);
		rmax = max(rmax, s[i]);
	}
	pair<int, int> res = { rmin, rmax };
	return res;
}

//求三个数中最大那个数
int maxnum(const int &a, const int &b, const int &c)
{
	int temp = max(a, b);
	temp = max(temp, c);
	return temp;
}

//把数组s的元素平均分成s.size()组，每组前闭后开，即类似 [a,b)
vector<vector<int>> bucketsort(const vector<int> &s, const int size)
{
	pair<int, int> r = minmax(s);
	vector<vector<int>> bucket(size);
	for (size_t i = 0; i < s.size(); i++)
	{
		int index = (s[i] - r.first) / size;
		bucket[index].push_back(s[i]);
	}
	return bucket;
}

int FindMaxGap(const vector<int> &s)
{
	if (s.size() < 2)
		return 0;
	vector<vector<int>> bucket = bucketsort(s,s.size());
	int gap, premax;
	//初始化gap和premax
	if (bucket[0].size() >= 2)
	{
		auto t = minmax(bucket[0]);
		gap = t.second - t.first;
		premax = t.second;
	}
	else if (bucket[0].empty())
	{
		gap = -1;
		premax = 0;
	}
	else
	{
		gap = -1;
		premax = bucket[0][0];
	}
	
	for (size_t i = 1; i < bucket.size(); i++)
	{
		if (bucket[i].empty())
			continue;
		if (bucket[i].size() == 1)
		{
			gap = max(gap, bucket[i][0] - premax);
			premax = bucket[i][0];
			continue;
		}			
		pair<int, int> t = minmax(bucket[i]);
		gap = maxnum(gap, t.second - t.first, t.first - premax);
		premax = t.second;
	}
	return gap;
}


//测试代码
srand((unsigned)time(NULL));
vector<int> n;
for (int i = 0; i < 10; i++)
{
	int t = rand() % 100 + 1;
	n.push_back(t);
	cout << t << "\t";
}
cout << endl;
cout << FindMaxGap(n) << endl;
sort(n.begin(), n.end());
for (int i = 0; i < 10; i++)
{
	cout << n[i] << "\t";
}

【桶排序】求无序数组中最大的“Gap"

标签：c++   程序员   面试   桶排序   

原文地址：http://blog.csdn.net/bupt8846/article/details/44096117