【带权中位数】【120715测试】【朱全明NOIP模拟题】YL杯超级篮球赛

 样例输入输出
ball.in
　　1
　　1
　　0 0
ball.out
　　0.00

 

这是一道有关带权中位数（http://www.cnblogs.com/oijzh/articles/2647134.html）的题

分析题目不难发现，xy坐标是不相关的，所以应该离散化分开来，并且最终的目标位置必定在某一个人的点上（如果不在某一个点上，那么必定可以把这个点向左或向右移来找到一个更优的位置！）

了解了带权中位数，这道题就很好做了

Pascal Code

program ball;

type
  arr=array[0..500000+10] of longint;

var
  n,total:longint;
  w,oldw,x,y:arr;

procedure init;
begin
  assign(input,'ball.in');
  assign(output,'ball.out');
  reset(input);
  rewrite(output);
end;
procedure outit;
begin
  close(input);
  close(output);
  halt;
end;

procedure readdata;
var
  i:longint;
begin
  read(n);
  for i:=1 to n do
  begin
    read(w[i]);
    inc(total,w[i]);
  end;
  for i:=1 to n do read(x[i],y[i]);
end;

procedure swap(var a,b:longint);
var t:longint;
begin
  t:=a;a:=b;b:=t;
end;

procedure qs(var a:arr;l,r:longint);
var
  i,j,x:longint;
begin
  i:=l;j:=r;x:=a[i+(j-i)div 2];
  repeat
    while a[i]<x do inc(i);
    while a[j]>x do dec(j);
    if i<=j then
    begin
      swap(a[i],a[j]);
      swap(w[i],w[j]);
      inc(i);dec(j);
    end;
  until i>j;
  if i<r then qs(a,i,r);
  if l<j then qs(a,l,j);
end;

function workx:double;
var
  i,tx:longint;
  sum:double;
begin
  sum:=0;
  for i:=1 to n do
  begin
    sum:=sum+w[i];
    if sum>total/2 then
    begin
      tx:=x[i];
      break;
    end;
  end;
  sum:=0;
  for i:=1 to n do
  begin
    if x[i]=tx then continue;
    sum:=sum+w[i]*abs(x[i]-tx);
  end;
  exit(sum);
end;

function worky:double;
var
  i,ty:longint;
  sum:double;
begin
  sum:=0;
  for i:=1 to n do
  begin
    sum:=sum+w[i];
    if sum>total/2 then
    begin
      ty:=y[i];
      break;
    end;
  end;
  sum:=0;
  for i:=1 to n do
  begin
    if y[i]=ty then continue;
    sum:=sum+w[i]*abs(y[i]-ty);
  end;
  exit(sum);
end;

procedure main;
var
  xx,yy:double;
begin
  oldw:=w;
  qs(x,1,n);
  xx:=workx;
  w:=oldw;//这个一定不能忘了 因为前面排序x的时候已经打乱了w的值!!!
  qs(y,1,n);
  yy:=worky;
  writeln(xx+yy:0:2);
end;

begin
  init;
  readdata;
  main;
  outit;
end.