1069: [SCOI2007]最大土地面积 - BZOJ

Description

在某块平面土地上有N个点，你可以选择其中的任意四个点，将这片土地围起来，当然，你希望这四个点围成的多边形面积最大。
Input

第1行一个正整数N，接下来N行，每行2个数x,y，表示该点的横坐标和纵坐标。
Output

最大的多边形面积，答案精确到小数点后3位。
Sample Input
5
0 0
1 0
1 1
0 1
0.5 0.5
Sample Output
1.000

HINT

数据范围 n<=2000, |x|,|y|<=100000

 

先求凸包

然后枚举四边形的对角线，分别找到距离最远的两个点更新答案（这两个点都是单调的），总复杂度是O（n^2）的

哪里写挫了，超慢，总时间1600ms

  1 const

  2         maxn=2010;

  3 type

  4         point=record

  5           x,y:double;

  6         end;

  7 var

  8         a:array[0..maxn]of point;

  9         n:longint;

 10         min:point;

 11  

 12 function cj(a,b,c:point):double;

 13 begin

 14         exit((a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y));

 15 end;

 16  

 17 procedure swap(var x,y:point);

 18 var

 19         t:point;

 20 begin

 21         t:=x;x:=y;y:=t;

 22 end;

 23  

 24 procedure sort(l,r:longint);

 25 var

 26         i,j:longint;

 27         y:point;

 28 begin

 29         i:=l;

 30         j:=r;

 31         y:=a[(l+r)>>1];

 32         repeat

 33           while cj(y,a[i],min)<0 do

 34             inc(i);

 35           while cj(y,a[j],min)>0 do

 36             dec(j);

 37           if i<=j then

 38           begin

 39             swap(a[i],a[j]);

 40             inc(i);

 41             dec(j);

 42           end;

 43         until i>j;

 44         if i<r then sort(i,r);

 45         if j>l then sort(l,j);

 46 end;

 47  

 48 procedure init;

 49 var

 50         i:longint;

 51 begin

 52         read(n);

 53         min.x:=maxlongint;

 54         min.y:=maxlongint;

 55         for i:=1 to n do

 56           begin

 57             read(a[i].x,a[i].y);

 58             if (a[i].x<min.x) or ((a[i].x=min.x) and (a[i].y<min.y)) then min:=a[i];

 59           end;

 60         i:=n;

 61         while i>0 do

 62           begin

 63             if (a[i].x=min.x) and (a[i].y=min.y) then

 64               begin

 65                 a[i]:=a[n];

 66                 dec(n);

 67               end

 68             else dec(i);

 69           end;

 70         sort(1,n);

 71         inc(n);

 72         a[n]:=min;

 73         a[0]:=min;

 74 end;

 75  

 76 var

 77         q:array[0..maxn]of longint;

 78         f:array[0..maxn,0..1]of double;

 79         tot,lasta,lastb:longint;

 80         ans:double;

 81  

 82 function up(var x:double;y:double):boolean;

 83 begin

 84         if x<y then

 85         begin

 86           x:=y;

 87           exit(true);

 88         end;

 89         exit(false);

 90 end;

 91  

 92 function down(var x:double;y:double):boolean;

 93 begin

 94         if x>y then

 95         begin

 96           x:=y;

 97           exit(true);

 98         end;

 99         exit(false);

100 end;

101  

102 procedure work;

103 var

104         i,j:longint;

105 begin

106         for i:=1 to n do

107           begin

108             while (tot>0) and (cj(a[i],a[q[tot]],a[q[tot-1]])>=0) do

109               dec(tot);

110             inc(tot);

111             q[tot]:=i;

112           end;

113         for i:=1 to tot-1 do

114           begin

115             f[i+1,1]:=-maxlongint;

116             f[i+1,0]:=0;

117             for j:=1 to n do

118               if up(f[i+1,1],cj(a[q[i+1]],a[q[j]],a[q[i]])) then lasta:=j;

119             lastb:=i;

120             for j:=i+2 to tot do

121               begin

122                 f[j,1]:=cj(a[q[j]],a[q[lasta]],a[q[i]]);

123                 f[j,0]:=cj(a[q[j]],a[q[lastb]],a[q[i]]);

124                 while up(f[j,1],cj(a[q[j]],a[q[lasta mod tot+1]],a[q[i]])) do

125                   lasta:=lasta mod tot+1;

126                 while down(f[j,0],cj(a[q[j]],a[q[lastb mod tot+1]],a[q[i]])) do

127                   lastb:=lastb mod tot+1;

128                 up(ans,f[j,1]-f[j,0]);

129               end;

130           end;

131         writeln(ans/2:0:3);

132 end;

133  

134 begin

135         init;

136         work;

137 end.

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