Rectangular Covering [POJ2836] [状压DP]

题意

平面上有 n (2 ≤ n ≤ 15) 个点，现用平行于坐标轴的矩形去覆盖所有点，每个矩形至少盖两个点，矩形面积不可为0，求这些矩形的最小面积。

Input

The input consists of several test cases. Each test cases begins with a line containing a single integer n (2 ≤ n ≤ 15). Each of the next n lines contains two integers x, y (−1,000 ≤ x, y ≤ 1,000) giving the coordinates of a point. It is assumed that no two points are the same as each other. A single zero follows the last test case.

Output

Output the minimum total area of rectangles on a separate line for each test case.

Sample Input

2
0 1
1 0
0

Sample Output

1

Analysis

枚举两个个点，再算包含在这两个点的点，算进一个矩形

然后在枚举矩形，进行状压DP

Code

 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #include <vector>
 
 using std::vector;
 using std::min;
 using std::max;
 
 const int MAXN = ;
 const int INF = 0x3f3f3f3f;
 
 struct POINT
 {
     int x;
     int y;
 } p[MAXN + ];
 
 struct RECTANGLE
 {
     int area;
     int cover;
 } r[MAXN * MAXN];
 
 int n;
 int dp[ << MAXN];
 int area[MAXN + ][MAXN + ];
 int cnt;
 
 int abs(int x)
 {
     return x >  ? x : -x;
 }
 
 void Read()
 {
     for (int i = ; i < n; ++i)
     {
         scanf("%d%d", &p[i].x, &p[i].y);
     }
 }
 
 void Init()
 {
     cnt = ;
     for (int i = ; i < n; ++i)
     {
         for (int j = ; j < i; ++j)
         {
             if (j != i)
             {
                 int width = abs(p[i].x - p[j].x) ==  ?  : abs(p[i].x - p[j].x);
                 int height = abs(p[i].y - p[j].y) ==  ?  : abs(p[i].y - p[j].y);
                 r[cnt].area = width * height;
                 r[cnt].cover = ;
                 for (int k = ; k < n; ++k)
                 {
                     if (p[k].x >= min(p[i].x, p[j].x) && p[k].x <= max(p[i].x, p[j].x) &&
                             p[k].y >= min(p[i].y, p[j].y) && p[k].y <= max(p[i].y, p[j].y))
                     {
                         r[cnt].cover |= ( << k);
                     }
                 }
                 ++cnt;
             }
         }
     }
 }
 
 void Dp()
 {
     memset(dp, 0x3f, sizeof(dp));
     dp[] = ;
     for (int S = ; S < ( << n); ++S)
     {
         if (dp[S] != INF)
         {
             for (int i = ; i < cnt; ++i)
             {
                 int news = S | r[i].cover;
                 if (news != S)
                 {
                     dp[news] = min(dp[news], dp[S] + r[i].area);
                 }
             }
         }
     }
     printf("%d\n", dp[( << n) - ]);
 }
 
 int main()
 {
     while (scanf("%d", &n) ==  && n)
     {
         Read();
         Init();
         Dp();
     }
 
     return ;
 }