P1034 矩形覆盖（dfs，剪枝）_矩形覆盖p1034python-优快云博客

本文链接：https://blog.youkuaiyun.com/qq_44765711/article/details/99880445

不想写题意描述了，看链接吧。。。

题目分析

由于数据范围较小（ $k < 5, n < 50$ ）所以考虑直接搜索，通过搜索来确定每个点是否能放进一个矩形中，状态记录当前点被矩形覆盖后的总面积.

程序实现

#include<bits/stdc++.h>
#define inf 0x3f3f3f3f
using namespace std;
struct Node{
	int x,y;
}node[55];
struct square{
	int x1,y1,x3,y3;
}sqr[6];
int n,k,ans,tot,maxn=inf;
bool check(int now,int sq){//check函数用来检查该点放入该矩形是否合法
	if(sqr[sq].x1 ==0&&sqr[sq].y1 ==0&&sqr[sq].x3 ==0&&sqr[sq].y3 ==0){
		sqr[sq].x1 =sqr[sq].x3 =node[now].x ;
		sqr[sq].y1 =sqr[sq].y3 =node[now].y ;
	}//矩形赋初值
	if(node[now].x <sqr[sq].x1 ) sqr[sq].x1 =node[now].x ;
	if(node[now].y <sqr[sq].y1 ) sqr[sq].y1 =node[now].y ;
	if(node[now].x >sqr[sq].x3 ) sqr[sq].x3 =node[now].x ;
	if(node[now].y >sqr[sq].y3 ) sqr[sq].y3 =node[now].y ;//已有初值，矩形大小改变
	for(int i=1;i<=k;i++){
		if(i==sq)continue;
		if(sqr[sq].x1 <=sqr[i].x3 &&sqr[sq].y1 <=sqr[i].y3 &&sqr[i].x3 <=sqr[sq].x3 &&sqr[i].y3 <=sqr[sq].y3 )return false;
		if(sqr[sq].x1 <=sqr[i].x1 &&sqr[sq].y1 <=sqr[i].y1 &&sqr[i].x1 <=sqr[sq].x3 &&sqr[i].y1 <=sqr[sq].y3 )return false;
		if(sqr[sq].y1 <=sqr[i].y1 &&sqr[i].y1 <=sqr[sq].y3 &&sqr[sq].x1 <=sqr[i].x1 &&sqr[i].x1 <=sqr[sq].x3 )return false;
		if(sqr[sq].y1 <=sqr[i].y3 &&sqr[i].y3 <=sqr[sq].y3 &&sqr[sq].x1 <=sqr[i].x3 &&sqr[i].x3 <=sqr[sq].x3 )return false;//判断矩形重合（不包括点和边）
		if(sqr[sq].x1 ==sqr[i].x1 &&sqr[sq].y1 ==sqr[i].y1 )return false;
		if(sqr[sq].x3 ==sqr[i].x3 &&sqr[sq].y3 ==sqr[i].y3 )return false;
		if(sqr[sq].x3 ==sqr[i].x1 &&sqr[sq].y1 ==sqr[i].y3 )return false;
		if(sqr[sq].x1 ==sqr[i].x3 &&sqr[sq].y3 ==sqr[i].y1 )return false;//没写这个特判就只剩80了，判断边点重合
	}
	return true;//没有以上情况，可以放入该矩形
}
void dfs(int now){
	if(now>n&&tot<maxn){
		maxn=tot;//用maxn表示最小值，我是不是有点毛病……凑合看吧
		return ;
	}
	if(now>n||tot>=maxn)return ;//函数递归的三种情况：已超出n，还没到n矩形面积和就比当前最小面积和大了，或者是已经放不进任何一个矩形了
	for(int i=1;i<=k;i++){
		int a=sqr[i].x1 ,b=sqr[i].y1 ,c=sqr[i].x3 ,d=sqr[i].y3 ;
		if(check(now,i)){
			int sum=(sqr[i].x3 -sqr[i].x1 )*(sqr[i].y3 -sqr[i].y1 )-(c-a)*(d-b);
			tot+=sum;
			dfs(now+1);
			tot-=sum;
		}
		sqr[i].x1 =a,sqr[i].y1 =b,sqr[i].x3 =c,sqr[i].y3 =d;//记得开临时数存先前状态
	}
	return ;
}
int main(){
	scanf("%d%d",&n,&k);
	for(int i=1;i<=n;i++){
		scanf("%d%d",&node[i].x ,&node[i].y );
	}
	dfs(1);
	printf("%d\n",maxn);
	return 0;
}