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http://acm.sgu.ru/problem.php?contest=0&problem=114

114. Telecasting station

time limit per test: 0.50 sec.
memory limit per test: 4096 KB

Every city in Berland is situated on Ox axis. The government of the country decided to build new telecasting station. After many experiments Berland scientists came to a conclusion that in any city citizens displeasure is equal to product of citizens amount in it by distance between city and TV-station. Find such point on Ox axis for station so that sum of displeasures of all cities is minimal.

Input

Input begins from line with integer positive number N (0<N<15000) – amount of cities in Berland. Following N pairs (X, P) describes cities (0<X, P<50000), where X is a coordinate of city and P is an amount of citizens. All numbers separated by whitespace(s).

Output

Write the best position for TV-station with accuracy 10^-5.

Sample Input

4
1 3
2 1
5 2
6 2

Sample Output

3.00000

带权中位数的题目,利用带权中位数的性质就可以解出来.

题目中的人口就是权值.按位置排序后,设要求的地点为 x_k ,那 x_k 必须满足|x_k-x₀|*w₀ + |x_k-x₁|*w₁ + … + |x_k-x_n-1)|*w_n-1 的值最小，令W = sigma(w_i)，则带权中位数x_k满足:

sigma(w_i)(x_i < x_k) <= W/2

sigma(w_i)(x_i > x_k) <= W/2

CODE

#include
#include
#include
using namespace std;
struct node
{
  double x;
  long long p;
}D[15005];
bool cmp(node a,node b)
{
  return (a.x=mid) break;
  }
  printf("%.5lfn",D[i].x);
  return 0;
}