BZOJ4348 : [POI2016]Park wodny
首先特判全部都是A或者全部都是B或者$n=1$的情况。
然后把矩阵四周都填充上A,枚举一个块,分以下情况讨论:
1.在它四周选两个块扩展,此时平方暴力枚举即可。
2.在它四周选定一个方向扩展两步。
3.选择一个角落,斜着扩展一步,再扩展另一步。
时间复杂度$O(n^2)$。
#include<cstdio> #define rep(i,l,r) for(int i=l;i<=r;i++) #define N 1010 int n,m,i,j,x,y,l,r,f[N][N],ans,t,q[10000][3],cnt;bool a[N][N];char ch[N]; struct P{int x,y,l,r,s;}s[N*N]; inline void up(int b){if(ans<b)ans=b;} inline void add(int x,int y,int z){ if(x&&x==y)return; q[++cnt][0]=x,q[cnt][1]=y,q[cnt][2]=z; } int main(){ scanf("%d",&n);gets(ch); if(n==1)return printf("1",ans),0; rep(i,1,n)for(gets(ch+1),j=1;j<=n;j++)if(ch[j]=='B')a[i][j]=1; rep(i,1,n)rep(j,1,n)if(a[i][j]&&!f[i][j]){ for(x=i;a[x][j];x++); for(y=j;a[i][y];y++); s[++m].x=i,s[m].y=--x,s[m].l=j,s[m].r=--y; up(s[m].s=(x-i+1)*(y-j+1)); rep(I,i,x)rep(J,j,y)f[I][J]=m; } if(ans==n*n)return printf("%d",ans),0; for(i=n;~i;i--)for(j=n;~j;j--)f[i+1][j+1]=f[i][j]; for(i=1;i<=m;i++)s[i].x++,s[i].y++,s[i].l++,s[i].r++; n+=2; ans=2; rep(i,1,m){ x=s[i].x,y=s[i].y,l=s[i].l,r=s[i].r,cnt=0; if(x>2)rep(j,l,r){ if(f[x-2][j])add(f[x-2][j],0,0); else{ t=s[i].s+2+s[f[x-2][j-1]].s+s[f[x-2][j+1]].s; if(f[x-2][j-1]!=f[x-1][j-1])t+=s[f[x-1][j-1]].s; if(f[x-2][j+1]!=f[x-1][j+1])t+=s[f[x-1][j+1]].s; if(x>3)t+=s[f[x-3][j]].s; up(t); } } if(y+2<=n)rep(j,l,r){ if(f[y+2][j])add(f[y+2][j],0,0); else{ t=s[i].s+2+s[f[y+2][j-1]].s+s[f[y+2][j+1]].s; if(f[y+2][j-1]!=f[y+1][j-1])t+=s[f[y+1][j-1]].s; if(f[y+2][j+1]!=f[y+1][j+1])t+=s[f[y+1][j+1]].s; if(y+3<=n)t+=s[f[y+3][j]].s; up(t); } } if(l>2)rep(j,x,y){ if(f[j][l-2])add(f[j][l-2],0,0); else{ t=s[i].s+2+s[f[j-1][l-2]].s+s[f[j+1][l-2]].s; if(f[j-1][l-2]!=f[j-1][l-1])t+=s[f[j-1][l-1]].s; if(f[j+1][l-2]!=f[j+1][l-1])t+=s[f[j+1][l-1]].s; if(l>3)t+=s[f[j][l-3]].s; up(t); } } if(r+2<=n)rep(j,x,y){ if(f[j][r+2])add(f[j][r+2],0,0); else{ t=s[i].s+2+s[f[j-1][r+2]].s+s[f[j+1][r+2]].s; if(f[j-1][r+2]!=f[j-1][r+1])t+=s[f[j-1][r+1]].s; if(f[j+1][r+2]!=f[j+1][r+1])t+=s[f[j+1][r+1]].s; if(r+3<=n)t+=s[f[j][r+3]].s; up(t); } } if(f[x-1][l-1]){ if(x>2)add(f[x-1][l-1],f[x-2][l],0); if(l>2)add(f[x-1][l-1],f[x][l-2],0); } if(f[y+1][l-1]){ if(y+2<=n)add(f[y+1][l-1],f[y+2][l],0); if(l>2)add(f[y+1][l-1],f[y][l-2],0); } if(f[x-1][r+1]){ if(x>2)add(f[x-1][r+1],f[x-2][r],0); if(r+2<=n)add(f[x-1][r+1],f[x][r+2],0); } if(f[y+1][r+1]){ if(y+2<=n)add(f[y+1][r+1],f[y+2][r],0); if(r+2<=n)add(f[y+1][r+1],f[y][r+2],0); } if(x==y){ if(l>2)add(f[x][l-2],f[x-1][l-1],f[x+1][l-1]); if(r+2<=n)add(f[x][r+2],f[x-1][r+1],f[x+1][r+1]); } if(l==r){ if(x>2)add(f[x-2][l],f[x-1][l-1],f[x-1][l+1]); if(y+2<=n)add(f[y+2][l],f[y+1][l-1],f[y+1][l+1]); } up(s[i].s+2); rep(j,1,cnt){ up(s[i].s+2+s[q[j][0]].s+s[q[j][1]].s+s[q[j][2]].s); rep(k,j+1,cnt){ t=s[i].s+2+s[q[j][0]].s+s[q[j][1]].s+s[q[j][2]].s+s[q[k][0]].s+s[q[k][1]].s+s[q[k][2]].s; if(q[k][0]==q[j][0]||q[k][0]==q[j][1]||q[k][0]==q[j][2])t-=s[q[k][0]].s; if(q[k][1]==q[j][0]||q[k][1]==q[j][1]||q[k][1]==q[j][2])t-=s[q[k][1]].s; if(q[k][2]==q[j][0]||q[k][2]==q[j][1]||q[k][2]==q[j][2])t-=s[q[k][2]].s; up(t); } } if(x>1&&l>1&&!f[x-1][l-1]){ t=s[i].s+2+s[f[x-2][l-1]].s+s[f[x-1][l-2]].s; if(x==y&&l==r){ if(f[x-1][l-2]!=f[x][l-2])up(t+s[f[x][l-2]].s+s[f[x+1][l-1]].s);else up(t+s[f[x+1][l-1]].s); if(f[x-2][l-1]!=f[x-2][l])up(t+s[f[x-2][l]].s+s[f[x-1][l+1]].s);else up(t+s[f[x-1][l+1]].s); }else{ if(f[x-1][l-2]!=f[x][l-2])up(t+s[f[x][l-2]].s); if(f[x-2][l-1]!=f[x-2][l])up(t+s[f[x-2][l]].s); } } if(x>1&&r<n&&!f[x-1][r+1]){ t=s[i].s+2+s[f[x-2][r+1]].s+s[f[x-1][r+2]].s; if(x==y&&l==r){ if(f[x-1][r+2]!=f[x][r+2])up(t+s[f[x][r+2]].s+s[f[x+1][l+1]].s);else up(t+s[f[x+1][l+1]].s); if(f[x-2][r+1]!=f[x-2][r])up(t+s[f[x-2][r]].s+s[f[x-1][l-1]].s);else up(t+s[f[x-1][l-1]].s); }else{ if(f[x-1][r+2]!=f[x][r+2])up(t+s[f[x][r+2]].s); if(f[x-2][r+1]!=f[x-2][r])up(t+s[f[x-2][r]].s); } } if(y<n&&l>1&&!f[y+1][l-1]){ t=s[i].s+2+s[f[y+2][l-1]].s+s[f[y+1][l-2]].s; if(x==y&&l==r){ if(f[y+1][l-2]!=f[y][l-2])up(t+s[f[y][l-2]].s+s[f[x-1][l-1]].s);else up(t+s[f[x-1][l-1]].s); if(f[y+2][l-1]!=f[y+2][l])up(t+s[f[y+2][l]].s+s[f[x+1][l+1]].s);else up(t+s[f[x+1][l+1]].s); }else{ if(f[y+1][l-2]!=f[y][l-2])up(t+s[f[y][l-2]].s); if(f[y+2][l-1]!=f[y+2][l])up(t+s[f[y+2][l]].s); } } if(y<n&&r<n&&!f[y+1][r+1]){ t=s[i].s+2+s[f[y+2][r+1]].s+s[f[y+1][r+2]].s; if(x==y&&l==r){ if(f[y+1][r+2]!=f[y][r+2])up(t+s[f[y][r+2]].s+s[f[x-1][l+1]].s);else up(t+s[f[x-1][l+1]].s); if(f[y+2][r+1]!=f[y+2][r])up(t+s[f[y+2][r]].s+s[f[x+1][l-1]].s);else up(t+s[f[x+1][l-1]].s); }else{ if(f[y+1][r+2]!=f[y][r+2])up(t+s[f[y][r+2]].s); if(f[y+2][r+1]!=f[y+2][r])up(t+s[f[y+2][r]].s); } } } return printf("%d",ans),0; }