hdu--1542&&1255&1828--线段树<扫描线>

所谓扫描线一般按照习惯上就是说从左到右或者是从下到上

这2题都是这样的运用但除此也还有别的方法可以过

我们将下边标记为1 上边标记为-1 这是自下而上的扫描如果是从左到右那么自然是左边为1 右边为-1

这边当然要进行离散化了。因为是数据蛮大的浮点数嘛~

这步真的很重要= =

然后注意下 unique去重或者自己手写for遍历一遍我就懒的写了

直接Lower_bound就可以了因为这些数据肯定能找到的嘛

这边线段树的建树需要注意下因为我们的叶子结点是 1-2 2-3这样的元线段所以这边我们建立的不是通常我们所建立的1-1 2-2这样的。

其实我还是没有说到重点就是对于该节点所表示的区间被覆盖一次 2次及以上没覆盖或者到达了叶子节点我们究竟为什么是采取这些操作~

我们先来讲1542-求出矩形覆盖的所有面积<一个区域被覆盖2次只计算一次>

艹。。。还是自己画图吧。。

但是有什么不清楚的可以留言= =

  1 #include <iostream>
  2 #include <cstring>
  3 #include <algorithm>
  4 #include <iomanip>
  5 using namespace std;
  6 
  7 int cnt;
  8 const int size = 220;
  9 struct data
 10 {
 11     int L , R;
 12     double x1 , x2 , y;
 13     double sum;
 14     int flag;
 15     data(){};
 16     data( double u , double v , double w , int p ):x1(u),x2(v),y(w),flag(p){};
 17 }tree[size*4] , mat[size];
 18 double w[size];
 19 
 20 bool cmp( const data p , const data q )
 21 {
 22     return p.y < q.y;
 23 }
 24 
 25 void pushUp( int rt )
 26 {
 27     if( tree[rt].flag )
 28         tree[rt].sum = w[ tree[rt].R ] - w[ tree[rt].L ];
 29     else if( tree[rt].L+1==tree[rt].R )
 30         tree[rt].sum = 0;
 31     else
 32         tree[rt].sum =  tree[rt<<1].sum + tree[rt<<1|1].sum;
 33 }
 34 
 35 void build( int rt , int L , int R )
 36 {
 37     int M = ( L + R ) >> 1;
 38     tree[rt].L = L;
 39     tree[rt].R = R;
 40     tree[rt].sum = 0;
 41     tree[rt].flag = 0;
 42     if( L+1==R )
 43     {
 44         return ;
 45     }
 46     build( rt<<1 , L , M );
 47     build( rt<<1|1 , M , R );
 48 }
 49 
 50 void update( int rt , int L , int R , int var )//var区别是上边还是下边
 51 {
 52     int M = ( tree[rt].L + tree[rt].R ) >> 1;
 53     if( tree[rt].L == L && tree[rt].R == R )
 54     {
 55         tree[rt].flag += var;
 56         pushUp( rt );
 57         return ;
 58     }
 59     if( R<=M )
 60         update( rt<<1 , L , R , var );
 61     else if( L>=M )
 62         update( rt<<1|1 , L , R , var );
 63     else
 64     {
 65         update( rt<<1 , L , M , var );
 66         update( rt<<1|1 , M , R , var );
 67     }
 68     pushUp( rt );
 69 }
 70 
 71 int main()
 72 {
 73     int Case = 1 , n;
 74     double x1 , y1 , x2 , y2;
 75     double ans;
 76     while( cin >> n && n )
 77     {
 78         cnt = 1;
 79         for( int i = 0 ; i<n ; i++ )
 80         {
 81             cin >> x1 >> y1 >> x2 >> y2;
 82             w[cnt] = x1;
 83             mat[cnt++] = data( x1 , x2 , y1 , 1 );
 84             w[cnt] = x2;
 85             mat[cnt++] = data( x1 , x2 , y2 , -1 );
 86         }
 87         sort( w+1 , w+cnt );//离散化x轴坐标 
 88         sort( mat+1 , mat+cnt , cmp );//按y的高低来排 
 89         cnt = unique( w+1 , w+cnt ) - w;
 90         build( 1 , 1 , cnt-1 );
 91         ans = 0;
 92         for( int i = 1 ; i<(n<<1) ; i++ )
 93         {
 94             int L = lower_bound( w+1 , w+cnt , mat[i].x1 ) - w;
 95             int R = lower_bound( w+1 , w+cnt , mat[i].x2 ) - w;    
 96             update( 1 , L , R , mat[i].flag );
 97             ans += tree[1].sum * ( mat[i+1].y - mat[i].y );
 98         }
 99         cout << "Test case #" << Case++ << endl;
100         cout << "Total explored area: ";
101         cout << setiosflags(ios::fixed);
102         cout << setprecision(2) << ans << endl << endl;
103     }
104     return 0;
105 }

View Code

  1 #include <iostream>
  2 #include <cstring>
  3 #include <algorithm>
  4 #include <iomanip>
  5 using namespace std;
  6 
  7 int cnt;
  8 const int size = 2200;
  9 struct data
 10 {
 11     int L , R;
 12     double x1 , x2 , y;
 13     double onceSum;
 14     double twiceSum;
 15     int flag;
 16     data(){};
 17     data( double u , double v , double w , int p ):x1(u),x2(v),y(w),flag(p){};
 18 }tree[size*4] , mat[size];
 19 double w[size];
 20 
 21 bool cmp( const data p , const data q )
 22 {
 23     return p.y < q.y;
 24 }
 25 
 26 void push( int rt )
 27 {
 28     if( tree[rt].flag )
 29         tree[rt].onceSum = w[ tree[rt].R ] - w[ tree[rt].L ];
 30     else if( tree[rt].L +1 == tree[rt].R )
 31         tree[rt].onceSum = 0;
 32     else
 33         tree[rt].onceSum = tree[rt<<1].onceSum + tree[rt<<1|1].onceSum;
 34 }
 35 
 36 void pushUp( int rt )
 37 {
 38     if( tree[rt].flag>=2 )
 39         tree[rt].twiceSum = w[ tree[rt].R ] - w[ tree[rt].L ];
 40     else if( tree[rt].L +1 == tree[rt].R )
 41         tree[rt].twiceSum = 0;
 42     else if( tree[rt].flag==1 )
 43         tree[rt].twiceSum = tree[rt<<1].onceSum + tree[rt<<1|1].onceSum;
 44     else
 45         tree[rt].twiceSum =  tree[rt<<1].twiceSum + tree[rt<<1|1].twiceSum;
 46 }
 47 
 48 void build( int rt , int L , int R )
 49 {
 50     int M = ( L + R ) >> 1;
 51     tree[rt].L = L;
 52     tree[rt].R = R;
 53     tree[rt].onceSum = tree[rt].twiceSum = 0;
 54     tree[rt].flag = 0;
 55     if( L+1==R )
 56     {
 57         return ;
 58     }
 59     build( rt<<1 , L , M );
 60     build( rt<<1|1 , M , R );
 61 }
 62 
 63 void update( int rt , int L , int R , int var )//var区别是上边还是下边
 64 {
 65     int M = ( tree[rt].L + tree[rt].R ) >> 1;
 66     if( tree[rt].L == L && tree[rt].R == R )
 67     {
 68         tree[rt].flag += var;
 69         push( rt );
 70         pushUp( rt );
 71         return ;
 72     }
 73     if( R<=M )
 74         update( rt<<1 , L , R , var );
 75     else if( L>=M )
 76         update( rt<<1|1 , L , R , var );
 77     else
 78     {
 79         update( rt<<1 , L , M , var );
 80         update( rt<<1|1 , M , R , var );
 81     }
 82     push( rt );
 83     pushUp( rt );
 84 }
 85 
 86 int main()
 87 {
 88     int n , T;
 89     double x1 , y1 , x2 , y2;
 90     double ans;
 91     while( ~scanf("%d",&T) )
 92     {
 93         while( T-- )
 94         {
 95             cnt = 1;
 96             scanf("%d",&n);
 97             for( int i = 0 ; i<n ; i++ )
 98             {
 99                 scanf("%lf %lf %lf %lf",&x1,&y1,&x2,&y2);
100                 w[cnt] = x1;
101                 mat[cnt++] = data( x1 , x2 , y1 , 1 );
102                 w[cnt] = x2;
103                 mat[cnt++] = data( x1 , x2 , y2 , -1 );
104             }
105             sort( w+1 , w+cnt );//离散化x轴坐标 
106             sort( mat+1 , mat+cnt , cmp );//按y的高低来排 
107             cnt = unique( w+1 , w+cnt ) - w;
108             build( 1 , 1 , cnt-1 );
109             ans = 0;
110             for( int i = 1 ; i<(n<<1) ; i++ )
111             {
112                 int L = lower_bound( w+1 , w+cnt , mat[i].x1 ) - w;
113                 int R = lower_bound( w+1 , w+cnt , mat[i].x2 ) - w;    
114                 update( 1 , L , R , mat[i].flag );
115                 ans += tree[1].twiceSum * ( mat[i+1].y - mat[i].y );
116             }
117             //cout << setiosflags(ios::fixed);
118             //cout << setprecision(2) << ans << endl;
119             printf("%.2lf
",ans);
120         }
121     }
122     return 0;
123 }

View Code

1828 矩形周长并。。我觉得比上面2个难多了

这题的话可以不使用离散化了因为都是 int数而且范围不大是从[-10000,10000]

我还是贴下离散化的好了

  1 #include <iostream>
  2 #include <algorithm>
  3 using namespace std;
  4 
  5 const int size = 5020;
  6 int cnt;
  7 struct data
  8 {
  9     int x1 , x2 , x , y , L , R;
 10     int flag , sum , num;
 11     bool Lflag , Rflag;
 12     data(){};
 13     data( int u , int v , int w , int p ):x1(u),x2(v),y(w),flag(p){};
 14     
 15 }tree[size<<2] , mat[size*2];
 16 int w[size*2];
 17 
 18 int Abs( int x )
 19 {
 20     return x > 0 ? x : -x;
 21 }
 22 
 23 bool cmp( const data p , const data q )
 24 {
 25     return p.y < q.y;
 26 }
 27 
 28 void pushUp( int rt )
 29 {
 30     if( tree[rt].flag )
 31     {
 32         tree[rt].sum = w[ tree[rt].R ] - w[ tree[rt].L ];
 33         tree[rt].Lflag = tree[rt].Rflag = 1;
 34         tree[rt].num = 1;
 35     }
 36     else if( tree[rt].L +1 ==tree[rt].R )
 37     {
 38         tree[rt].sum = tree[rt].num = 0;
 39         tree[rt].Lflag = tree[rt].Rflag = 0;
 40     }
 41     else
 42     {
 43         tree[rt].sum = tree[rt<<1].sum + tree[rt<<1|1].sum;
 44         tree[rt].Lflag = tree[rt<<1].Lflag;
 45         tree[rt].Rflag = tree[rt<<1|1].Rflag;
 46         tree[rt].num = tree[rt<<1].num + tree[rt<<1|1].num- tree[rt<<1].Rflag*tree[rt<<1|1].Lflag;
 47     }
 48 }
 49                                     
 50 void build( int rt , int L , int R )
 51 {
 52     int M = (L+R) >> 1;
 53     tree[rt].L = L;
 54     tree[rt].R = R;
 55     tree[rt].flag = tree[rt].sum = tree[rt].num = 0;
 56     tree[rt].Lflag = tree[rt].Rflag = 0;
 57     if( L+1 == R )
 58     {
 59         return ;
 60     }
 61     build( rt<<1 , L , M );
 62     build( rt<<1|1 , M , R );
 63 }
 64 
 65 void update( int rt , int L , int R , int var )
 66 {
 67     int M = ( tree[rt].L + tree[rt].R ) >> 1;
 68     if( tree[rt].L == L && tree[rt].R == R )
 69     {
 70         tree[rt].flag += var;
 71         pushUp( rt );
 72         return ;
 73     }
 74     if( R<=M )
 75         update( rt<<1 , L , R , var );
 76     else if( L>=M )
 77         update( rt<<1|1 , L , R , var );
 78     else
 79     {
 80         update( rt<<1 , L , M , var );
 81         update( rt<<1|1 , M , R , var );
 82     }
 83     pushUp( rt );
 84 }
 85 
 86 int main()
 87 {
 88     cin.sync_with_stdio(false);
 89     int n , pre , ans , L , R;
 90     int x1 , x2 , y1 , y2;
 91     while( cin >> n )
 92     {
 93         cnt = 1;
 94         for( int i = 0 ; i<n ; i++ )
 95         {
 96             cin >> x1 >> y1 >> x2 >> y2;
 97             w[cnt] = x1;
 98             mat[cnt++] = data( x1 , x2 , y1 , 1 );
 99             w[cnt] = x2;
100             mat[cnt++] = data( x1 , x2 , y2 , -1 );
101         }
102         sort( w+1 , w+cnt );
103         sort( mat+1 , mat+cnt , cmp );
104         cnt = unique( w+1 , w+cnt ) - w;
105         build( 1 , 1 , cnt-1 );
106         ans = pre = 0;
107         for( int i = 1 ; i<(n<<1); i++ )
108         {
109             L = lower_bound( w+1 , w+cnt , mat[i].x1 ) - w;
110             R = lower_bound( w+1 , w+cnt , mat[i].x2 ) - w;
111             update( 1 , L , R , mat[i].flag );
112             ans += Abs( tree[1].sum - pre );
113             pre = tree[1].sum;
114             ans += tree[1].num * ( mat[i+1].y - mat[i].y ) * 2;
115         }
116         ans += mat[n<<1].x2 - mat[n<<1].x1;
117         cout << ans << endl;
118     }
119     return 0;
120 }

View Code

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原文地址：https://www.cnblogs.com/radical/p/4149197.html