【BZOJ2329】括号修复（splay）
题意：一个左右括号组成的序列，需要维护以下操作：
1：前后翻转
2：区间值取反
3：区间修改
4：询问某一段区间最少修改几次能变成一段合法序列
n,m<=100000
思路：RYZ作业
如果把(看做1，)看做-1，询问的就是这段区间(-左端开始的最小字段和+1) div 2+（右端开始的最大字段和+1) div 2
因为有反转操作，用splay维护这些值
具体标记下穿的时候先传反转再传取反，取反的时候如果有修改标记修改标记也要取反
这个版本是左右子段不能为空
1 const oo=1000000000; 2 var t:array[0..500000,0..1]of longint; 3 sum,size,lmax,lmin,rmax,rmin,rev,tag,flp,a,fa,v:array[0..500000]of longint; 4 n,m,i,j,k,x,y,z,root,s:longint; 5 ch:ansistring; 6 7 procedure swap(var x,y:longint); 8 var t:longint; 9 begin 10 t:=x; x:=y; y:=t; 11 end; 12 13 function max(x,y:longint):longint; 14 begin 15 if x>y then exit(x); 16 exit(y); 17 end; 18 19 function min(x,y:longint):longint; 20 begin 21 if x<y then exit(x); 22 exit(y); 23 end; 24 25 procedure pushup(p:longint); 26 var l,r:longint; 27 begin 28 if p=0 then exit; 29 l:=t[p,0]; r:=t[p,1]; 30 sum[p]:=sum[l]+sum[r]+v[p]; 31 size[p]:=size[l]+size[r]+1; 32 lmax[p]:=max(lmax[l], 33 max(sum[l]+v[p], 34 sum[l]+v[p]+lmax[r])); 35 lmin[p]:=min(lmin[l], 36 min(sum[l]+v[p], 37 sum[l]+v[p]+lmin[r])); 38 rmax[p]:=max(rmax[r], 39 max(sum[r]+v[p], 40 sum[r]+v[p]+rmax[l])); 41 rmin[p]:=min(rmin[r], 42 min(sum[r]+v[p], 43 sum[r]+v[p]+rmin[l])); 44 end; 45 46 procedure dorev(p:longint); 47 var l,r:longint; 48 begin 49 l:=t[p,0]; r:=t[p,1]; 50 rev[p]:=rev[p] xor 1; 51 swap(t[p,0],t[p,1]); 52 swap(lmax[p],rmax[p]); 53 swap(lmin[p],rmin[p]); 54 end; 55 56 procedure doflp(p:longint); 57 var l,r:longint; 58 begin 59 l:=t[p,0]; r:=t[p,1]; 60 flp[p]:=flp[p] xor 1; 61 sum[p]:=-sum[p]; v[p]:=-v[p]; 62 lmax[p]:=-lmax[p]; lmin[p]:=-lmin[p]; 63 swap(lmax[p],lmin[p]); 64 rmax[p]:=-rmax[p]; rmin[p]:=-rmin[p]; 65 swap(rmax[p],rmin[p]); 66 tag[p]:=-tag[p]; 67 end; 68 69 procedure dotag(p,d:longint); 70 var l,r:longint; 71 begin 72 l:=t[p,0]; r:=t[p,1]; 73 rev[p]:=0; flp[p]:=0; 74 v[p]:=d; tag[p]:=d; sum[p]:=d*size[p]; 75 lmax[p]:=max(d,sum[p]); 76 rmax[p]:=lmax[p]; 77 lmin[p]:=min(d,sum[p]); 78 rmin[p]:=lmin[p]; 79 end; 80 81 procedure pushdown(p:longint); 82 var l,r:longint; 83 begin 84 l:=t[p,0]; r:=t[p,1]; 85 if rev[p]=1 then 86 begin 87 if l>0 then dorev(l); 88 if r>0 then dorev(r); 89 rev[p]:=0; 90 end; 91 if flp[p]=1 then 92 begin 93 if l>0 then doflp(l); 94 if r>0 then doflp(r); 95 flp[p]:=0; 96 end; 97 if tag[p]<>0 then 98 begin 99 if l>0 then dotag(l,tag[p]); 100 if r>0 then dotag(r,tag[p]); 101 tag[p]:=0; 102 end; 103 end; 104 105 procedure rotate(x:longint;var k:longint); 106 var l,r,y,z:longint; 107 begin 108 y:=fa[x]; z:=fa[y]; 109 if t[y,0]=x then l:=0 110 else l:=1; 111 r:=l xor 1; 112 if y<>k then 113 begin 114 if t[z,0]=y then t[z,0]:=x 115 else t[z,1]:=x; 116 end 117 else k:=x; 118 fa[y]:=x; fa[x]:=z; fa[t[x,r]]:=y; 119 t[y,l]:=t[x,r]; t[x,r]:=y; 120 pushup(y); 121 pushup(x); 122 end; 123 124 procedure splay(x:longint;var k:longint); 125 var y,z:longint; 126 begin 127 while x<>k do 128 begin 129 y:=fa[x]; z:=fa[y]; 130 if y<>k then 131 begin 132 if (t[y,0]=x)xor(t[z,0]=y) then rotate(x,k) 133 else rotate(y,k); 134 end 135 else k:=x; 136 rotate(x,k); 137 end; 138 end; 139 140 function kth(x,k:longint):longint; 141 var tmp:longint; 142 begin 143 pushdown(x); 144 tmp:=size[t[x,0]]+1; 145 if k=tmp then exit(x); 146 if k<tmp then exit(kth(t[x,0],k)) 147 else exit(kth(t[x,1],k-tmp)); 148 end; 149 150 function split(l,r:longint):longint; 151 var x,y:longint; 152 begin 153 x:=kth(root,l-1); y:=kth(root,r+1); 154 splay(x,root); splay(y,t[x,1]); 155 exit(t[y,0]); 156 end; 157 158 function query(l,r:longint):longint; 159 var s,x:longint; 160 begin 161 x:=split(l,r); 162 s:=(-lmin[x]+1) div 2+(rmax[x]+1) div 2; 163 exit(s); 164 end; 165 166 procedure build(l,r,x:longint); 167 var mid,last,now:longint; 168 begin 169 if l>r then exit; 170 mid:=(l+r)>>1; now:=mid; last:=x; 171 if l=r then 172 begin 173 sum[now]:=a[l]; size[now]:=1; 174 tag[now]:=0; rev[now]:=0; flp[now]:=0; 175 if a[l]>=0 then 176 begin 177 lmax[now]:=a[l]; rmax[now]:=a[l]; 178 lmin[now]:=0; rmin[now]:=0; 179 end 180 else 181 begin 182 lmax[now]:=0; rmax[now]:=0; 183 lmin[now]:=a[l]; rmin[now]:=a[l]; 184 end; 185 end 186 else 187 begin 188 build(l,mid-1,mid); 189 build(mid+1,r,mid); 190 end; 191 fa[now]:=last; v[now]:=a[mid]; 192 pushup(now); 193 if mid>=x then t[last,1]:=now 194 else t[last,0]:=now; 195 end; 196 197 procedure change(l,r,v:longint); 198 var x,y,k:longint; 199 begin 200 x:=split(l,r); y:=fa[x]; 201 dotag(x,v); 202 pushup(y); 203 pushup(fa[y]); 204 end; 205 206 procedure rever(l,r:longint); 207 var x,y:longint; 208 begin 209 x:=split(l,r); y:=fa[x]; 210 dorev(x); 211 pushup(y); 212 pushup(fa[y]); 213 end; 214 215 procedure invert(l,r:longint); 216 var x,y:longint; 217 begin 218 x:=split(l,r); y:=fa[x]; 219 doflp(x); 220 pushup(y); 221 pushup(fa[y]); 222 end; 223 224 begin 225 assign(input,'bzoj2329.in'); reset(input); 226 assign(output,'bzoj2329.out'); rewrite(output); 227 readln(n,m); 228 readln(ch); 229 for i:=1 to n do 230 if ch[i]='(' then a[i+1]:=1 231 else a[i+1]:=-1; 232 lmax[0]:=-oo; rmax[0]:=-oo; 233 lmin[0]:=oo; rmin[0]:=oo; 234 build(1,n+2,0); 235 root:=(n+3)>>1; 236 for i:=1 to m do 237 begin 238 readln(ch); k:=length(ch); s:=0; x:=0; y:=0; z:=0; 239 for j:=1 to k do 240 begin 241 if ch[j]=' ' then begin inc(s); continue; end; 242 if (ch[j]<'0')or(ch[j]>'9') then continue; 243 if s=1 then x:=x*10+ord(ch[j])-ord('0'); 244 if s=2 then y:=y*10+ord(ch[j])-ord('0'); 245 end; 246 if ch[k]='(' then z:=1 247 else z:=-1; 248 inc(x); inc(y); 249 case ch[1] of 250 'R':change(x,y,z); 251 'S':rever(x,y); 252 'I':invert(x,y); 253 'Q':writeln(query(x,y)); 254 end; 255 end; 256 close(input); 257 close(output); 258 end.
这个版本左右子段可以为空，取最值的时候还要与0比较，同时初始化也不需要，因为可以取空，初始值就是0
1 const oo=1000000000; 2 var t:array[0..500000,0..1]of longint; 3 sum,size,lmax,lmin,rmax,rmin,rev,tag,flp,a,fa,v:array[0..500000]of longint; 4 n,m,i,j,k,x,y,z,root,s:longint; 5 ch:ansistring; 6 7 procedure swap(var x,y:longint); 8 var t:longint; 9 begin 10 t:=x; x:=y; y:=t; 11 end; 12 13 function max(x,y:longint):longint; 14 begin 15 if x>y then exit(x); 16 exit(y); 17 end; 18 19 function min(x,y:longint):longint; 20 begin 21 if x<y then exit(x); 22 exit(y); 23 end; 24 25 procedure pushup(p:longint); 26 var l,r:longint; 27 begin 28 //if p=0 then exit; 29 l:=t[p,0]; r:=t[p,1]; 30 sum[p]:=sum[l]+sum[r]+v[p]; 31 size[p]:=size[l]+size[r]+1; 32 lmax[p]:=max(0,max(lmax[l],sum[l]+v[p]+lmax[r])); 33 lmin[p]:=min(0,min(lmin[l],sum[l]+v[p]+lmin[r])); 34 rmax[p]:=max(0,max(rmax[r],sum[r]+v[p]+rmax[l])); 35 rmin[p]:=min(0,min(rmin[r],sum[r]+v[p]+rmin[l])); 36 end; 37 38 procedure dorev(p:longint); 39 begin 40 rev[p]:=rev[p] xor 1; 41 swap(t[p,0],t[p,1]); 42 swap(lmax[p],rmax[p]); 43 swap(lmin[p],rmin[p]); 44 end; 45 46 procedure doflp(p:longint); 47 begin 48 flp[p]:=flp[p] xor 1; 49 sum[p]:=-sum[p]; v[p]:=-v[p]; 50 lmax[p]:=-lmax[p]; lmin[p]:=-lmin[p]; 51 swap(lmax[p],lmin[p]); 52 rmax[p]:=-rmax[p]; rmin[p]:=-rmin[p]; 53 swap(rmax[p],rmin[p]); 54 tag[p]:=-tag[p]; 55 end; 56 57 procedure dotag(p,d:longint); 58 begin 59 rev[p]:=0; flp[p]:=0; 60 v[p]:=d; tag[p]:=d; sum[p]:=d*size[p]; 61 if d>0 then 62 begin 63 lmax[p]:=sum[p]; rmax[p]:=sum[p]; 64 lmin[p]:=0; rmin[p]:=0; 65 end 66 else 67 begin 68 lmax[p]:=0; rmax[p]:=0; 69 lmin[p]:=sum[p]; rmin[p]:=sum[p]; 70 end; 71 72 end; 73 74 procedure pushdown(p:longint); 75 var l,r:longint; 76 begin 77 l:=t[p,0]; r:=t[p,1]; 78 if rev[p]=1 then 79 begin 80 if l>0 then dorev(l); 81 if r>0 then dorev(r); 82 rev[p]:=0; 83 end; 84 if flp[p]=1 then 85 begin 86 if l>0 then doflp(l); 87 if r>0 then doflp(r); 88 flp[p]:=0; 89 end; 90 if tag[p]<>0 then 91 begin 92 if l>0 then dotag(l,tag[p]); 93 if r>0 then dotag(r,tag[p]); 94 tag[p]:=0; 95 end; 96 end; 97 98 procedure rotate(x:longint;var k:longint); 99 var l,r,y,z:longint; 100 begin 101 y:=fa[x]; z:=fa[y]; 102 if t[y,0]=x then l:=0 103 else l:=1; 104 r:=l xor 1; 105 if y<>k then 106 begin 107 if t[z,0]=y then t[z,0]:=x 108 else t[z,1]:=x; 109 end 110 else k:=x; 111 fa[y]:=x; fa[x]:=z; fa[t[x,r]]:=y; 112 t[y,l]:=t[x,r]; t[x,r]:=y; 113 pushup(y); 114 pushup(x); 115 end; 116 117 procedure splay(x:longint;var k:longint); 118 var y,z:longint; 119 begin 120 while x<>k do 121 begin 122 y:=fa[x]; z:=fa[y]; 123 if y<>k then 124 begin 125 if (t[y,0]=x)xor(t[z,0]=y) then rotate(x,k) 126 else rotate(y,k); 127 end 128 else k:=x; 129 rotate(x,k); 130 end; 131 end; 132 133 function kth(x,k:longint):longint; 134 var tmp:longint; 135 begin 136 pushdown(x); 137 tmp:=size[t[x,0]]+1; 138 if k=tmp then exit(x); 139 if k<tmp then exit(kth(t[x,0],k)) 140 else exit(kth(t[x,1],k-tmp)); 141 end; 142 143 function split(l,r:longint):longint; 144 var x,y:longint; 145 begin 146 x:=kth(root,l-1); y:=kth(root,r+1); 147 splay(x,root); splay(y,t[x,1]); 148 exit(t[y,0]); 149 end; 150 151 function query(l,r:longint):longint; 152 var s,x:longint; 153 begin 154 x:=split(l,r); 155 s:=(-lmin[x]+1) div 2+(rmax[x]+1) div 2; 156 exit(s); 157 end; 158 159 procedure build(l,r,x:longint); 160 var mid,last,now:longint; 161 begin 162 if l>r then exit; 163 mid:=(l+r)>>1; now:=mid; last:=x; 164 if l=r then 165 begin 166 sum[now]:=a[l]; size[now]:=1; 167 tag[now]:=0; rev[now]:=0; flp[now]:=0; 168 if a[l]>=0 then 169 begin 170 lmax[now]:=a[l]; rmax[now]:=a[l]; 171 lmin[now]:=0; rmin[now]:=0; 172 end 173 else 174 begin 175 lmax[now]:=0; rmax[now]:=0; 176 lmin[now]:=a[l]; rmin[now]:=a[l]; 177 end; 178 end 179 else 180 begin 181 build(l,mid-1,mid); 182 build(mid+1,r,mid); 183 end; 184 fa[now]:=last; v[now]:=a[mid]; 185 pushup(now); 186 if mid>=x then t[last,1]:=now 187 else t[last,0]:=now; 188 end; 189 190 procedure change(l,r,v:longint); 191 var x,y,k:longint; 192 begin 193 x:=split(l,r); y:=fa[x]; 194 dotag(x,v); 195 pushup(y); 196 pushup(fa[y]); 197 end; 198 199 procedure rever(l,r:longint); 200 var x,y:longint; 201 begin 202 x:=split(l,r); y:=fa[x]; 203 dorev(x); 204 pushup(y); 205 pushup(fa[y]); 206 end; 207 208 procedure invert(l,r:longint); 209 var x,y:longint; 210 begin 211 x:=split(l,r); y:=fa[x]; 212 doflp(x); 213 pushup(y); 214 pushup(fa[y]); 215 end; 216 217 begin 218 219 readln(n,m); 220 readln(ch); 221 for i:=1 to n do 222 if ch[i]='(' then a[i+1]:=1 223 else a[i+1]:=-1; 224 //a[1]:=oo; a[n+2]:=-oo; 225 //lmax[0]:=-oo; rmax[0]:=-oo; 226 // lmin[0]:=oo; rmin[0]:=oo; 227 build(1,n+2,0); 228 root:=(n+3)>>1; 229 for i:=1 to m do 230 begin 231 readln(ch); k:=length(ch); s:=0; x:=0; y:=0; z:=0; 232 for j:=1 to k do 233 begin 234 if ch[j]=' ' then begin inc(s); continue; end; 235 if (ch[j]<'0')or(ch[j]>'9') then continue; 236 if s=1 then x:=x*10+ord(ch[j])-ord('0'); 237 if s=2 then y:=y*10+ord(ch[j])-ord('0'); 238 end; 239 if ch[k]='(' then z:=1 240 else z:=-1; 241 inc(x); inc(y); 242 case ch[1] of 243 'R':change(x,y,z); 244 'S':rever(x,y); 245 'I':invert(x,y); 246 'Q':writeln(query(x,y)); 247 end; 248 // for j:=1 to n+2 do// write(rev[j],' ',flp[j],' ',tag[j],' '); 249 // write(v[j],' '); 250 // writeln; 251 end; 252 253 end.
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