四边形的问题可以转化为三角形处理
穷举对角线，然后处理上下两个三角形，旋转卡壳
1 var x,y:array[0..5010] of double; 2 q:array[0..5010] of longint; 3 l,r,i,j,k,t,n:longint; 4 ans:double; 5 6 function max(a,b:double):double; 7 begin 8 if a>b then exit(a) else exit(b); 9 end; 10 11 function cross(i,j,k,r:longint):double; 12 begin 13 exit((x[i]-x[j])*(y[k]-y[r])-(x[k]-x[r])*(y[i]-y[j])); 14 end; 15 16 procedure swap(var a,b:double); 17 var c:double; 18 begin 19 c:=a; 20 a:=b; 21 b:=c; 22 end; 23 24 procedure sort(l,r: longint); 25 var i,j: longint; 26 p,q:double; 27 28 begin 29 i:=l; 30 j:=r; 31 p:=x[(l+r) shr 1]; 32 q:=y[(l+r) shr 1]; 33 repeat 34 while (x[i]<p) or (x[i]=p) and (y[i]<q) do inc(i); 35 while (p<x[j]) or (p=x[j]) and (q<y[j]) do dec(j); 36 if not(i>j) then 37 begin 38 swap(x[i],x[j]); 39 swap(y[i],y[j]); 40 inc(i); 41 j:=j-1; 42 end; 43 until i>j; 44 if l<j then sort(l,j); 45 if i<r then sort(i,r); 46 end; 47 48 begin 49 readln(n); 50 for i:=1 to n do 51 readln(x[i],y[i]); 52 sort(1,n); 53 q[1]:=1; 54 t:=1; 55 for i:=2 to n do 56 begin 57 while (t>1) and (cross(q[t],q[t-1],i,q[t-1])<=0) do dec(t); 58 inc(t); 59 q[t]:=i; 60 end; 61 k:=t; 62 for i:=n-1 downto 1 do 63 begin 64 while (t>k) and (cross(q[t],q[t-1],i,q[t-1])<=0) do dec(t); 65 inc(t); 66 q[t]:=i; 67 end; 68 for i:=2 to t-1 do 69 q[i+t-1]:=q[i]; 70 for i:=1 to t-1 do 71 begin 72 l:=i+1; 73 r:=i+3; 74 while (r<i+t-2) and (cross(q[i+2],q[i],q[r],q[i])<cross(q[i+2],q[i],q[r+1],q[i])) do inc(r); 75 ans:=max(ans,cross(q[i+1],q[i],q[i+2],q[i])+cross(q[i+2],q[i],q[r],q[i])); 76 for j:=i+3 to i+t-2 do 77 begin 78 while (l<j-1) and (cross(q[l+1],q[i],q[j],q[i])>cross(q[l],q[i],q[j],q[i])) do inc(l); 79 while (r<i+t-2) and (cross(q[j],q[i],q[r+1],q[i])>cross(q[j],q[i],q[r],q[i])) do inc(r); 80 ans:=max(ans,cross(q[l],q[i],q[j],q[i])+cross(q[j],q[i],q[r],q[i])); 81 end; 82 end; 83 ans:=ans/2; 84 writeln(ans:0:3); 85 end.
