SWUST0249 （凸包面积）

type node=record x,y:longint; end;
const maxn=3008;
var k,q,qq:longint;
    sum:double;
    f,g:array[0..maxn] of node;
    m,i,j,a,b:longint;
    stack:array[0..maxn] of longint;
    nm:longint;
function dis(a,b:node):double;
begin
    exit(sqrt(sqr(a.x-b.x)+sqr(a.y-b.y)));
end;
procedure swap(var a,b:node); inline;
var c:node;
begin
    c:=a; a:=b; b:=c;
end;
function dig(a,b:node):longint; inline;
begin
    exit(a.x*b.y-a.y*b.x);
end;
function mk(a,b:node):node; inline;
begin
    mk.x:=b.x-a.x;
    mk.y:=b.y-a.y;
end;
function cmp(a,b:node):boolean; inline;
var p1,p2:node;
begin
    p1:=mk(f[1],a);
    p2:=mk(f[1],b);
    if dig(P1,P2)<0 then exit(true);
    if dig(P1,P2)=0 then
        if dis(f[1],a)>dis(f[1],b) then
            exit(true);
    exit(false);
end;
procedure sort(l,r:longint);
var i,j:longint;
    x:node;
begin
    i:=l; j:=r; x:=f[(l+r) div 2];
    while i<=j do
    begin
        while cmp(f[i],x) do inc(i);
        while cmp(x,f[j]) do dec(j);
        if i<=j then
        begin
            swap(f[i],f[j]);
            inc(i); dec(j);
        end;
    end;
    if l<j then sort(l,j);
    if i<r then sort(i,r);
end;
begin
    readln(q);
    for qq:=1 to q do
    begin
        readln(m);
        for i:=1 to m do readln(f[i].x,f[i].y);
        if m=2 then begin writeln('0.0'); continue; end;
        j:=1;
        for i:=2 to m do
            if (f[i].y<f[j].y) or (f[i].y=f[j].y) and (f[i].x<f[j].x) then
                j:=i;
        swap(f[1],f[j]);
        sort(2,m);
        k:=2;
        g[1]:=f[1]; g[2]:=f[2];
        for i:=3 to m do
            if dig(mk(f[1],f[i]),mk(f[1],f[i-1]))<>0 then
            begin
                inc(k);
                g[k]:=f[i];
            end;
        nm:=3;
        stack[1]:=1; stack[2]:=2; stack[3]:=3;
        for i:=4 to k do
        begin
            a:=stack[nm-1];
            b:=stack[nm];
            while dig(mk(g[a],g[b]),mk(g[a],g[i]))>0 do
            begin
                dec(nm);
                a:=stack[nm-1];
                b:=stack[nm];
            end;
            inc(nm);
            stack[nm]:=i;
        end;
        sum:=0;
        while nm>=3 do
        begin
            a:=stack[nm];
            b:=stack[nm-1];
            sum:=sum+abs(dig(mk(g[1],g[b]),mk(g[1],g[a])))/2;
            dec(nm);
        end;
        writeln(sum:0:1);
    end;
end.