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 }