洛谷 - P1034 - 矩形覆盖 - dfs

https://www.luogu.org/problemnew/show/P1034

可能是数据太水了瞎搞都可以过。

判断两个平行于坐标轴的矩形相交（含顶点与边相交）的代码一并附上。

记得这里的xy和udlr是指数学上的坐标轴。

#include<bits/stdc++.h>
using namespace std;
#define ll long long

struct Point{
    int x,y;
    Point(int x=0,int y=0){
        this->x=x,this->y=y;
    }
}p[51];

struct Rectangle{
    int u,d,l,r;
    Rectangle(){
        u=d=l=r=-1;
    }
    bool inside(Point p){
        if(p.x>=l&&p.x<=r&&p.y>=d&&p.y<=u)
            return true;
        return false;
    }
    bool intersect_help(Rectangle r2){
        Point r1p1(l,u);
        if(r2.inside(r1p1))
            return 1;
        Point r1p2(r,u);
        if(r2.inside(r1p2))
            return 1;
        Point r1p3(r,d);
        if(r2.inside(r1p3))
            return 1;
        Point r1p4(l,d);
        if(r2.inside(r1p4))
            return 1;
        return 0;
    }

    bool intersect(Rectangle r2){
        if(u==-1||r2.u==-1)
            return 0;
        if(intersect_help(r2))
            return 1;
        if(r2.intersect_help(*this))
            return 1;
        if(l<=r2.l&&r>=r2.r&&u<=r2.u&&d>=r2.d)
            return 1;
        if(r2.l<=l&&r2.r>=r&&r2.u<=u&&r2.d>=d)
            return 1;
        return 0;
    }

    int area(){
        return (r-l)*(u-d);
    }

    void extend(Point p){
        if(u==-1){
            l=r=p.x;
            u=d=p.y;
            return;
        }
        else{
            l=min(l,p.x);
            r=max(r,p.x);
            u=max(u,p.y);
            d=min(d,p.y);
            return;
        }
    }

    void show(){
        printf("  u=%d d=%d l=%d r=%d\n",u,d,l,r);
    }
};

int n,k;
int ans=0x3f3f3f3f;
void dfs4(int id,Rectangle r1,Rectangle r2,Rectangle r3,Rectangle r4){
    //r1.show(),r2.show(),r3.show(),r4.show();
    //printf("---------\n");

    if(id>n){
        ans=min(ans,r1.area()+r2.area()+r3.area()+r4.area());
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi)||r2.inside(pi)||r3.inside(pi)||r4.inside(pi))
        dfs4(id+1,r1,r2,r3,r4);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        if(rr1.intersect(r2)||rr1.intersect(r3)||rr1.intersect(r4))
            ;
        else{
            dfs4(id+1,rr1,r2,r3,r4);
        }

        Rectangle rr2=r2;
        rr2.extend(pi);
        if(rr2.intersect(r1)||rr2.intersect(r3)||rr2.intersect(r4))
            ;
        else{
            dfs4(id+1,r1,rr2,r3,r4);
        }

        Rectangle rr3=r3;
        rr3.extend(pi);
        if(rr3.intersect(r1)||rr3.intersect(r2)||rr3.intersect(r4))
            ;
        else{
            dfs4(id+1,r1,r2,rr3,r4);
        }

        Rectangle rr4=r4;
        rr4.extend(pi);
        if(rr4.intersect(r1)||rr4.intersect(r2)||rr4.intersect(r3))
            ;
        else{
            dfs4(id+1,r1,r2,r3,rr4);
        }
    }
}


void dfs3(int id,Rectangle r1,Rectangle r2,Rectangle r3){
    //r1.show(),r2.show(),r3.show();
    //printf("---------\n");

    if(id>n){
        ans=min(ans,r1.area()+r2.area()+r3.area());
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi)||r2.inside(pi)||r3.inside(pi))
        dfs3(id+1,r1,r2,r3);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        if(rr1.intersect(r2)||rr1.intersect(r3))
            ;
        else{
            dfs3(id+1,rr1,r2,r3);
        }

        Rectangle rr2=r2;
        rr2.extend(pi);
        if(rr2.intersect(r1)||rr2.intersect(r3))
            ;
        else{
            dfs3(id+1,r1,rr2,r3);
        }

        Rectangle rr3=r3;
        rr3.extend(pi);
        if(rr3.intersect(r1)||rr3.intersect(r2))
            ;
        else{
            dfs3(id+1,r1,r2,rr3);
        }
    }
}


void dfs2(int id,Rectangle r1,Rectangle r2){
    if(id>n){
        //r1.show(),r2.show();
        int tans=r1.area()+r2.area();
        ans=min(ans,tans);
        //printf("tans=%d\n---------\n",tans);
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi)||r2.inside(pi))
        dfs2(id+1,r1,r2);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        if(rr1.intersect(r2))
            ;
        else{
            dfs2(id+1,rr1,r2);
        }

        Rectangle rr2=r2;
        rr2.extend(pi);
        if(rr2.intersect(r1))
            ;
        else{
            dfs2(id+1,r1,rr2);
        }
    }
}


void dfs(int id,Rectangle r1){
    //r1.show();
    //printf("---------\n");

    if(id>n){
        ans=min(ans,r1.area());
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi))
        dfs(id+1,r1);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        dfs(id+1,rr1);
    }
}

int main(){
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++){
        scanf("%d%d",&p[i].x,&p[i].y);
    }
    Rectangle r;
    switch(k){
    case 1:
        dfs(1,r);
        break;
    case 2:
        dfs2(1,r,r);
        break;
    case 3:
        dfs3(1,r,r,r);
        break;
    case 4:
        dfs4(1,r,r,r,r);
    }
    printf("%d\n",ans);
}

加入最优性剪枝：22ms，快了3倍？

#include<bits/stdc++.h>
using namespace std;
#define ll long long

struct Point{
    int x,y;
    Point(int x=0,int y=0){
        this->x=x,this->y=y;
    }
}p[51];

struct Rectangle{
    int u,d,l,r;
    Rectangle(){
        u=d=l=r=-1;
    }
    bool inside(Point p){
        if(p.x>=l&&p.x<=r&&p.y>=d&&p.y<=u)
            return true;
        return false;
    }
    bool intersect_help(Rectangle r2){
        Point r1p1(l,u);
        if(r2.inside(r1p1))
            return 1;
        Point r1p2(r,u);
        if(r2.inside(r1p2))
            return 1;
        Point r1p3(r,d);
        if(r2.inside(r1p3))
            return 1;
        Point r1p4(l,d);
        if(r2.inside(r1p4))
            return 1;
        return 0;
    }

    bool intersect(Rectangle r2){
        if(u==-1||r2.u==-1)
            return 0;
        if(intersect_help(r2))
            return 1;
        if(r2.intersect_help(*this))
            return 1;
        if(l<=r2.l&&r>=r2.r&&u<=r2.u&&d>=r2.d)
            return 1;
        if(r2.l<=l&&r2.r>=r&&r2.u<=u&&r2.d>=d)
            return 1;
        return 0;
    }

    int area(){
        return (r-l)*(u-d);
    }

    void extend(Point p){
        if(u==-1){
            l=r=p.x;
            u=d=p.y;
            return;
        }
        else{
            l=min(l,p.x);
            r=max(r,p.x);
            u=max(u,p.y);
            d=min(d,p.y);
            return;
        }
    }

    void show(){
        printf("  u=%d d=%d l=%d r=%d\n",u,d,l,r);
    }
};

int n,k;
int ans=0x3f3f3f3f;
void dfs4(int id,Rectangle r1,Rectangle r2,Rectangle r3,Rectangle r4){
    //r1.show(),r2.show(),r3.show(),r4.show();
    //printf("---------\n");
    int tans=r1.area()+r2.area()+r3.area()+r4.area();
    if(tans>=ans)
        return;
    if(id>n){
        ans=min(ans,tans);
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi)||r2.inside(pi)||r3.inside(pi)||r4.inside(pi))
        dfs4(id+1,r1,r2,r3,r4);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        if(rr1.intersect(r2)||rr1.intersect(r3)||rr1.intersect(r4))
            ;
        else{
            dfs4(id+1,rr1,r2,r3,r4);
        }

        Rectangle rr2=r2;
        rr2.extend(pi);
        if(rr2.intersect(r1)||rr2.intersect(r3)||rr2.intersect(r4))
            ;
        else{
            dfs4(id+1,r1,rr2,r3,r4);
        }

        Rectangle rr3=r3;
        rr3.extend(pi);
        if(rr3.intersect(r1)||rr3.intersect(r2)||rr3.intersect(r4))
            ;
        else{
            dfs4(id+1,r1,r2,rr3,r4);
        }

        Rectangle rr4=r4;
        rr4.extend(pi);
        if(rr4.intersect(r1)||rr4.intersect(r2)||rr4.intersect(r3))
            ;
        else{
            dfs4(id+1,r1,r2,r3,rr4);
        }
    }
}


void dfs3(int id,Rectangle r1,Rectangle r2,Rectangle r3){
    //r1.show(),r2.show(),r3.show();
    //printf("---------\n");
    int tans=r1.area()+r2.area()+r3.area();
    if(tans>=ans)
        return;

    if(id>n){
        ans=min(ans,tans);
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi)||r2.inside(pi)||r3.inside(pi))
        dfs3(id+1,r1,r2,r3);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        if(rr1.intersect(r2)||rr1.intersect(r3))
            ;
        else{
            dfs3(id+1,rr1,r2,r3);
        }

        Rectangle rr2=r2;
        rr2.extend(pi);
        if(rr2.intersect(r1)||rr2.intersect(r3))
            ;
        else{
            dfs3(id+1,r1,rr2,r3);
        }

        Rectangle rr3=r3;
        rr3.extend(pi);
        if(rr3.intersect(r1)||rr3.intersect(r2))
            ;
        else{
            dfs3(id+1,r1,r2,rr3);
        }
    }
}


void dfs2(int id,Rectangle r1,Rectangle r2){
    int tans=r1.area()+r2.area();
    if(tans>=ans)
        return;

    if(id>n){
        //r1.show(),r2.show();
        ans=min(ans,tans);
        //printf("tans=%d\n---------\n",tans);
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi)||r2.inside(pi))
        dfs2(id+1,r1,r2);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        if(rr1.intersect(r2))
            ;
        else{
            dfs2(id+1,rr1,r2);
        }

        Rectangle rr2=r2;
        rr2.extend(pi);
        if(rr2.intersect(r1))
            ;
        else{
            dfs2(id+1,r1,rr2);
        }
    }
}


void dfs(int id,Rectangle r1){
    //r1.show();
    //printf("---------\n");
    int tans=r1.area();
    if(tans>=ans)
        return;

    if(id>n){
        ans=min(ans,r1.area());
        return;
    }

    Point pi=p[id];
    if(r1.inside(pi))
        dfs(id+1,r1);
    else{
        Rectangle rr1=r1;
        rr1.extend(pi);
        dfs(id+1,rr1);
    }
}

int main(){
    scanf("%d%d",&n,&k);
    for(int i=1;i<=n;i++){
        scanf("%d%d",&p[i].x,&p[i].y);
    }
    Rectangle r;
    switch(k){
    case 1:
        dfs(1,r);
        break;
    case 2:
        dfs2(1,r,r);
        break;
    case 3:
        dfs3(1,r,r,r);
        break;
    case 4:
        dfs4(1,r,r,r,r);
    }
    printf("%d\n",ans);
}