vijos P1134 矩形覆盖 题解

4000

#include <stdio.h>
#include <stdlib.h>
#include <limits.h>

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))

typedef struct
{
short isEmpty;
int l, r, t, b; //left, right, top, bottom
} RECT;
typedef struct
{
int x, y;
} POINT;

int numPoint, numRect;
int minArea = LONG_MAX;
POINT point[55];
RECT rect[5];

void dfs(int index, int area);
int intersect(RECT a, RECT b);
int verify();

int main()
{
int i;
scanf("%d %d", &numPoint, &numRect);
for(i=0; i<numPoint; i++)
scanf("%d %d", &point[i].x, &point[i].y);
for(i=0; i<numRect; i++)
rect[i].isEmpty = 1;
//printf("%d",minArea);
dfs(0, 0);
printf("%d\n", minArea);

return 0;
}
int intersect(RECT a, RECT b)  //see: http://blog.csdn.net/yahohi/article/details/7927158 {
int dx, dy;
dx = abs((a.r+a.l) - (b.r+b.l));
dy = abs((a.t+a.b) - (b.t+b.b));
if(dx <= a.r-a.l + b.r-b.l && dy <= a.t-a.b + b.t-b.b)
return 1;
return 0;
}
int verify()  //if any two rectangles intersect, return false
{
int i, k;
for(i=0; i<numRect; i++)
{
if(rect[i].isEmpty)
continue;
for(k=i+1; k<numRect; k++)
{
if(rect[k].isEmpty)
continue;
if(intersect(rect[i], rect[k]))
return 0;
}
}
return 1;
}
void dfs(int index, int area)
{
int i, delta;
RECT tmp;
if(area >= minArea)
return;
if(index == numPoint)
{
for(i=0; i<numRect; i++)
{
if(rect[i].isEmpty)
return;
}
minArea = area;
return;
}
for(i=0; i<numRect; i++)
{
tmp = rect[i];
if(rect[i].isEmpty)
{
rect[i].l = rect[i].r = point[index].x;
rect[i].b = rect[i].t = point[index].y;
rect[i].isEmpty = 0;
}else
{
rect[i].l = MIN(rect[i].l, point[index].x);
rect[i].r = MAX(rect[i].r, point[index].x);
rect[i].b = MIN(rect[i].b, point[index].y);
rect[i].t = MAX(rect[i].t, point[index].y);
}
if(verify())
{
delta = (rect[i].r-rect[i].l) * (rect[i].t-rect[i].b);  //new area
delta -= (tmp.r-tmp.l) * (tmp.t-tmp.b);  //-= original area
dfs(index+1, area+delta);
}
rect[i] = tmp;
}
}

这题就是最简单的dfs

用dfs 搜索每一个点所在的矩形 然后对矩形的面积进行改变（也可以不改变）

numRect 表示使用的矩形个数

rect[].isEmpty 记录矩形是否被使用

rect[].l,r,t,b 表示矩形的左边界 右边界 上边界 下边界

verify() 函数和intersect()函数是用于判断矩形是否有交叉部分