UVa 10107 What is the Median?_uva10107-优快云博客

本文链接：https://blog.youkuaiyun.com/synapse7/article/details/12249627

本文介绍了一种在线求中位数的算法实现，通过不断调整输入整数的位置来维持有序状态，进而快速找出中位数。该算法适用于整数序列，并能够处理最多10000个元素。

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10107 - What is the Median?

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=24&page=show_problem&problem=1048

The Problem

Median plays an important role in the world of statistics. By definition, it is a value which divides an array into two equal parts. In this problem you are to determine the current median of some long integers.

Suppose, we have five numbers {1,3,6,2,7}. In this case, 3 is the median as it has exactly two numbers on its each side. {1,2} and {6,7}.

If there are even number of values like {1,3,6,2,7,8}, only one value cannot split this array into equal two parts, so we consider the average of the middle values {3,6}. Thus, the median will be (3+6)/2 = 4.5. In this problem, you have to print only the integer part, not the fractional. As a result, according to this problem, the median will be 4!

Input

The input file consists of series of integers X ( 0 <= X < 2^31 ) and total number of integers N is less than 10000. The numbers may have leading or trailing spaces.

Output

For each input print the current value of the median.

Sample Input

Sample Output

完整代码：

/*0.035s*/

#include<cstdio>

int a[10010];

int main()
{
	int i, x, cnt = 0, m;
	while (~scanf("%d", &x))
	{
		for (i = cnt; i; i--)
		{
			if (a[i] > x) a[i + 1] = a[i];
			else break;
		}
		a[i + 1] = x;
		++cnt;
		m = cnt >> 1;
		printf("%d\n", (cnt & 1 ? a[m + 1] : (a[m] + a[m + 1]) >> 1));
	}
	return 0;
}

PS：使用 Treap 复杂度更低。