题目描述
- 如何得到一个数据流中的中位数?如果从数据流中读出奇数个数值,那么中位数就是所有数值排序之后位于中间的数值。如果从数据流中读出偶数个数值,那么中位数就是所有数值排序之后中间两个数的平均值。
算法分析
- 为了保证插入新数据和取中位数的时间效率都高效,这里使用大顶堆+小顶堆的容器,并且满足:两个堆中的数据数目差不能超过1,这样可以使中位数只会出现在两个堆的交接处;大顶堆的所有数据都小于小顶堆,这样就满足了排序要求。
提交代码(模拟最大最小堆,其实是实现了priority_queue):
class Solution {
public:
void Insert(int num)
{
int length = maxHeap.size() + minHeap.size();
// 奇数个插入max
if ((length & 1) == 1)
{
// 如果插入最大堆中的数比最小堆的最小值要大
if (!minHeap.empty() && num > minHeap[0])
{
minHeap.push_back(num);
push_heap(minHeap.begin(), minHeap.end(), greater<int>());
num = minHeap[0];
pop_heap(minHeap.begin(), minHeap.end(), greater<int>());
minHeap.pop_back();
}
maxHeap.push_back(num);
push_heap(maxHeap.begin(), maxHeap.end(), less<int>());
}
else
{
if (!maxHeap.empty() && num < maxHeap[0])
{
maxHeap.push_back(num);
push_heap(maxHeap.begin(), maxHeap.end(), less<int>());
num = maxHeap[0];
pop_heap(maxHeap.begin(), maxHeap.end(), less<int>());
maxHeap.pop_back();
}
minHeap.push_back(num);
push_heap(minHeap.begin(), minHeap.end(), greater<int>());
}
}
double GetMedian()
{
int length = maxHeap.size() + minHeap.size();
if (length == 0)
return 0;
return (length & 1) == 1 ? minHeap[0]
: (maxHeap[0] + minHeap[0]) / 2.0;
}
private:
// 奇数时插入
vector<int> maxHeap;
// 偶数时插入
vector<int> minHeap;
};
测试代码:
// ====================测试代码====================
void Test(char* testName, Solution numbers, double expected)
{
if (testName != nullptr)
printf("%s begins: ", testName);
if (abs(numbers.GetMedian() - expected) < 0.0000001)
printf("Passed.\n");
else
printf("FAILED.\n");
}
int main(int argc, char* argv[])
{
Solution numbers;
printf("Test1 begins: ");
try
{
numbers.GetMedian();
printf("Passed.\n");
}
catch (const exception&)
{
printf("FAILED.\n");
}
numbers.Insert(5);
Test("Test2", numbers, 5);
numbers.Insert(2);
Test("Test3", numbers, 3.5);
numbers.Insert(3);
Test("Test4", numbers, 3);
numbers.Insert(4);
Test("Test6", numbers, 3.5);
numbers.Insert(1);
Test("Test5", numbers, 3);
numbers.Insert(6);
Test("Test7", numbers, 3.5);
numbers.Insert(7);
Test("Test8", numbers, 4);
numbers.Insert(0);
Test("Test9", numbers, 3.5);
numbers.Insert(8);
Test("Test10", numbers, 4);
return 0;
}