「模拟8.13」任(liu_runda的神题，性质分析)

考场时没有发现性质，用了个前缀和优化暴力，结果写WA了

我们发现其实联通块的个数就是点的个数-边的个数

然后我们需要维护横向上和纵向上的边的前缀和

前缀和的查询形式稍改一下

暴力

  1 #include<cstdio>
  2 #include<iostream>
  3 #include<cstdio>
  4 #include<cstring>
  5 #include<cmath>
  6 #include<algorithm>
  7 #include<set>
  8 #include<vector>
  9 #include<queue>
 10 #define int long long
 11 #define MAXN 6001
 12 using namespace std;
 13 int read()
 14 {
 15     int x=0;char cc=getchar();
 16     while(cc<'0'||cc>'9')cc=getchar();
 17     while(cc>='0'&&cc<='9'){x=(x<<1)+(x<<3)+(cc^48);cc=getchar();}
 18     return x;
 19 }
 20 char a[MAXN][MAXN];
 21 int sum[MAXN][MAXN];
 22 int c[MAXN][MAXN];
 23 int vis[MAXN][MAXN];
 24 int n,m;     queue<int>q_x;queue<int>q_y;
 25 void BFS(int top_x,int top_y)
 26 {
 27      int maxn_x=top_x,maxn_y=top_y;
 28
 29      q_x.push(top_x);q_y.push(top_y);
 30      vis[top_x][top_y]=1;
 31      //belong[top_x][top_y]=cntt;
 32      while(!q_x.empty())
 33      {
 34            int x=q_x.front();int y=q_y.front();q_x.pop();q_y.pop();
 35            //belong[x][y]=cntt;
 36            if(a[x-1][y]=='1'&&vis[x-1][y]==0)
 37            {
 38                 q_x.push(x-1);q_y.push(y);
 39                 vis[x-1][y]=1;
 40                 maxn_x=max(maxn_x,x-1);maxn_y=max(maxn_y,y);
 41            }
 42            if(a[x][y-1]=='1'&&vis[x][y-1]==0)
 43            {
 44                 q_x.push(x);q_y.push(y-1);
 45                 vis[x][y-1]=1;
 46                 maxn_x=max(maxn_x,x);maxn_y=max(maxn_y,y-1);
 47            }
 48            if(a[x+1][y]=='1'&&vis[x+1][y]==0)
 49            {
 50                 q_x.push(x+1);q_y.push(y);
 51                 vis[x+1][y]=1;
 52                 maxn_x=max(maxn_x,x+1);maxn_y=max(maxn_y,y);
 53            }
 54            if(a[x][y+1]=='1'&&vis[x][y+1]==0)
 55            {
 56                 q_x.push(x);q_y.push(y+1);
 57                 vis[x][y+1]=1;
 58                 maxn_x=max(maxn_x,x);maxn_y=max(maxn_y,y+1);
 59            }
 60      }
 61      sum[maxn_x][maxn_y]++;
 62      //mex[cntt]=maxn_x;
 63      //mey[cntt]=maxn_y;
 64 }
 65 int q;int cnt;
 66 int ans=0;
 67 int get_sum(int x1,int y1,int x2,int y2)
 68 {
 69     return sum[x2][y2]+sum[x1-1][y1-1]-sum[x2][y1-1]-sum[x1-1][y2];
 70 }
 71 int judge(int x,int y,int x1,int y1,int x2,int y2)
 72 {
 73     if(x<x1)return 0;if(x>x2)return 0;if(y<y1)return 0;if(y>y2)return 0;
 74     return 1;
 75 }
 76 void BFS_S(int top_x,int top_y,int x1,int y1,int x2,int y2)
 77 {
 78
 79     q_x.push(top_x);q_y.push(top_y);
 80     vis[top_x][top_y]=1;
 81     while(!q_x.empty())
 82     {
 83            int x=q_x.front();int y=q_y.front();q_x.pop();q_y.pop();
 84            if(a[x-1][y]=='1'&&vis[x-1][y]==0&&judge(x-1,y,x1,y1,x2,y2))
 85            {
 86                 q_x.push(x-1);q_y.push(y);
 87                 vis[x-1][y]=1;
 88            }
 89            if(a[x][y-1]=='1'&&vis[x][y-1]==0&&judge(x,y-1,x1,y1,x2,y2))
 90            {
 91                 q_x.push(x);q_y.push(y-1);
 92                 vis[x][y-1]=1;
 93            }
 94            if(a[x+1][y]=='1'&&vis[x+1][y]==0&&judge(x+1,y,x1,y1,x2,y2))
 95            {
 96                 q_x.push(x+1);q_y.push(y);
 97                 vis[x+1][y]=1;
 98            }
 99            if(a[x][y+1]=='1'&&vis[x][y+1]==0&&judge(x,y+1,x1,y1,x2,y2))
100            {
101                 q_x.push(x);q_y.push(y+1);
102                 vis[x][y+1]=1;
103            }
104     }
105 }
106 void work(int x1,int y1,int x2,int y2)
107 {
108      ans=0;
109      for(int i=x1;i<=x2;++i)
110      {
111          //printf("i=%lld y1=%lld\n",i,y1);
112          for(int j=y1;j<=y2;++j)
113          {
114               if(vis[i][j]==0&&a[i][j]=='1')
115               {
116                  BFS_S(i,j,x1,y1,x2,y2);
117                  ans++;
118               }
119          }
120          //printf("ans=%lld\n",ans);
121      }
122      for(int i=x1;i<=x2;++i)for(int j=y1;j<=y2;++j)vis[i][j]=0;
123 }
124 signed main()
125 {
126     scanf("%lld%lld%lld",&n,&m,&q);
127     for(int i=1;i<=n;++i)
128     {
129         scanf("%s",a[i]+1);
130     }
131     for(int i=1;i<=n;++i)
132     {
133         for(int j=1;j<=m;++j)
134         {
135             if(a[i][j]=='1'&&vis[i][j]==0)
136             {
137                 BFS(i,j);
138             }
139         }
140     }
141     for(int i=1;i<=n;++i)
142     {
143         for(int j=1;j<=m;++j)
144         {
145             sum[i][j]+=sum[i-1][j]+sum[i][j-1]-sum[i-1][j-1];
146         }
147     }
148     memset(vis,0,sizeof(vis));
149     for(int i=1;i<=q;++i)
150     {
151         int x1,y1,x2,y2;
152         ans=0;
153         x1=read();y1=read();x2=read();y2=read();
154         //printf("x1=%lld y1=%lld x2=%lld y2=%lld\n",x1,y1,x2,y2);
155         work(x1,y1,x2,y2);
156         printf("%lld\n",ans);
157     }
158 }

AC

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<cstdio>
 4 #include<cstring>
 5 #include<cmath>
 6 #include<algorithm>
 7 #include<set>
 8 #include<vector>
 9 #include<queue>
10 #define int long long
11 #define MAXN 6001
12 using namespace std;
13 int sum[MAXN][MAXN];
14 int vis[MAXN][MAXN];
15 int n,m;
16 char a[MAXN][MAXN];
17 int sum_lie[MAXN][MAXN],sum_hang[MAXN][MAXN];
18 int q_x[MAXN],q_y[MAXN];
19 void BFS(int top_x,int top_y)
20 {
21      int head,tail;
22      head=1;tail=1;q_x[1]=top_x;q_y[1]=top_y;
23      vis[top_x][top_y]=1;
24      while(head<=tail)
25      {
26            int x=q_x[head];int y=q_y[head];head++;
27            sum[x][y]++;//printf("add sum[%lld][%lld]=%lld\n",x,y,sum[x][y]);
28            if(a[x][y-1]=='1')sum_hang[x][y]++;
29            if(a[x-1][y]=='1')sum_lie[x][y]++;
30            if(a[x][y+1]=='1'&&vis[x][y+1]==0)
31            {
32                   vis[x][y+1]=1;q_x[++tail]=x;q_y[tail]=y+1;
33            }
34            if(a[x][y-1]=='1'&&vis[x][y-1]==0)
35            {
36                   vis[x][y-1]=1;q_x[++tail]=x;q_y[tail]=y-1;
37            }
38            if(a[x-1][y]=='1'&&vis[x-1][y]==0)
39            {
40                   vis[x-1][y]=1;q_x[++tail]=x-1;q_y[tail]=y;
41            }
42            if(a[x+1][y]=='1'&&vis[x+1][y]==0)
43            {
44                  vis[x+1][y]=1;q_x[++tail]=x+1;q_y[tail]=y;
45            }
46     }
47 }
48 int q;
49 signed main()
50 {
51     scanf("%lld%lld%lld",&n,&m,&q);
52     for(int i=1;i<=n;++i)
53     {
54         scanf("%s",a[i]+1);
55     }
56     for(int i=1;i<=n;++i)
57     {
58         for(int j=1;j<=m;++j)
59         {
60             if(vis[i][j]==0&&a[i][j]=='1')
61             BFS(i,j);
62         }
63     }
64     for(int i=1;i<=n;++i)
65     {
66         for(int j=1;j<=m;++j)
67         {
68             sum[i][j]+=sum[i-1][j]+sum[i][j-1]-sum[i-1][j-1];
69             //printf("sum[%lld][%lld]=%lld\n",i,j,sum[i][j]);
70         }
71     }
72     for(int i=1;i<=n;++i)
73     {
74         for(int j=1;j<=m;++j)
75         {
76             sum_hang[i][j]+=sum_hang[i][j-1]+sum_hang[i-1][j]-sum_hang[i-1][j-1];
77             sum_lie[i][j]+=sum_lie[i][j-1]+sum_lie[i-1][j]-sum_lie[i-1][j-1];
78         }
79     }
80     for(int i=1;i<=q;++i)
81     {
82         int x1,x2,y1,y2;
83         scanf("%lld%lld%lld%lld",&x1,&y1,&x2,&y2);
84         int tt=sum[x2][y2]+sum[x1-1][y1-1]-sum[x2][y1-1]-sum[x1-1][y2];
85         int ttt=sum_hang[x2][y2]+sum_hang[x1-1][y1]-sum_hang[x2][y1]-sum_hang[x1-1][y2];
86         int tttt=sum_lie[x2][y2]+sum_lie[x1][y1-1]-sum_lie[x2][y1-1]-sum_lie[x1][y2];
87         //printf("tt=%lld ttt=%lld\n",tt,ttt);
88         printf("%lld\n",tt-ttt-tttt);
89     }
90 }