括号序列的经典做法
把(看成1，）看成-1
匹配的括号序列即任意前缀和都非负
我们先解决静态的问题，给定一段括号序列求最少修改次数
我们先找出最大后缀和a和最小前缀和b
之间一定可以不相交
显然a+|b|个括号是未匹配的
显然修改即为(|b|+1) div 2+(a+1) div 2;
由于序列的变化，我们用splay维护
由于涉及到括号反转我们还要维护左最大和右最小
然后就没了
这个是bzoj2329的代码
1 var son:array[0..100010,1..2] of longint; 2 laz,lmax,rmax,lmin,rmin,size,sum,a,fa:array[0..100010] of longint; 3 cha,rev:array[0..100010] of boolean; 4 root,i,n,m,x,y,z,w:longint; 5 ch:char; 6 s:string; 7 8 function min(a,b:longint):longint; 9 begin 10 if a>b then exit(b) else exit(a); 11 end; 12 13 function max(a,b:longint):longint; 14 begin 15 if a>b then exit(a) else exit(b); 16 end; 17 18 procedure swap(var a,b:longint); 19 var c:longint; 20 begin 21 c:=a; 22 a:=b; 23 b:=c; 24 end; 25 26 procedure get(var a,b:longint); 27 var c:longint; 28 begin 29 c:=a; 30 a:=-b; 31 b:=-c; 32 end; 33 34 procedure update(x:longint); 35 var l,r:longint; 36 begin 37 l:=son[x,1]; 38 r:=son[x,2]; 39 size[x]:=size[l]+size[r]+1; 40 sum[x]:=sum[l]+sum[r]+a[x]; 41 lmax[x]:=max(lmax[l],sum[l]+a[x]+lmax[r]); 42 rmax[x]:=max(rmax[r],sum[r]+a[x]+rmax[l]); 43 lmin[x]:=min(lmin[l],sum[l]+a[x]+lmin[r]); 44 rmin[x]:=min(rmin[r],sum[r]+a[x]+rmin[l]); 45 end; 46 47 procedure replace(x,w:longint); 48 begin 49 a[x]:=w; 50 laz[x]:=w; 51 cha[x]:=false; 52 if w=-1 then 53 begin 54 sum[x]:=-size[x]; 55 lmax[x]:=0; 56 rmax[x]:=0; 57 lmin[x]:=sum[x]; 58 rmin[x]:=sum[x]; 59 end 60 else begin 61 sum[x]:=size[x]; 62 lmax[x]:=sum[x]; 63 rmax[x]:=sum[x]; 64 lmin[x]:=0; 65 rmin[x]:=0; 66 end; 67 end; 68 69 procedure reverse(x:longint); 70 begin 71 swap(son[x,1],son[x,2]); 72 swap(lmax[x],rmax[x]); 73 swap(lmin[x],rmin[x]); 74 rev[x]:=not rev[x]; 75 end; 76 77 procedure change(x:longint); 78 begin 79 a[x]:=-a[x]; 80 sum[x]:=-sum[x]; 81 get(lmax[x],lmin[x]); 82 get(rmax[x],rmin[x]); 83 cha[x]:=not cha[x]; 84 end; 85 86 procedure push(x:longint); 87 var l,r:longint; 88 begin 89 l:=son[x,1]; 90 r:=son[x,2]; 91 if laz[x]<>0 then 92 begin 93 if l<>-1 then replace(l,laz[x]); 94 if r<>-1 then replace(r,laz[x]); 95 laz[x]:=0; 96 end; 97 if cha[x] then 98 begin 99 if l<>-1 then change(l); 100 if r<>-1 then change(r); 101 cha[x]:=false; 102 end; 103 if rev[x] then 104 begin 105 if l<>-1 then reverse(l); 106 if r<>-1 then reverse(r); 107 rev[x]:=false; 108 end; 109 end; 110 111 function find(k:longint):longint; 112 var p:longint; 113 begin 114 p:=root; 115 while true do 116 begin 117 push(p); 118 if size[son[p,1]]+1=k then exit(p); 119 if size[son[p,1]]+1>k then p:=son[p,1] 120 else begin 121 k:=k-size[son[p,1]]-1; 122 p:=son[p,2]; 123 end; 124 end; 125 end; 126 127 procedure rotate(x,w:longint); 128 var y:longint; 129 begin 130 y:=fa[x]; 131 push(x); 132 if fa[y]=-1 then root:=x 133 else begin 134 if son[fa[y],1]=y then son[fa[y],1]:=x 135 else son[fa[y],2]:=x; 136 end; 137 fa[x]:=fa[y]; 138 son[y,3-w]:=son[x,w]; 139 if son[x,w]<>-1 then fa[son[x,w]]:=y; 140 son[x,w]:=y; 141 fa[y]:=x; 142 update(y); 143 end; 144 145 procedure splay(x,f:longint); 146 var y:longint; 147 begin 148 while fa[x]<>f do 149 begin 150 y:=fa[x]; 151 if fa[y]=f then 152 begin 153 if son[y,1]=x then rotate(x,2) 154 else rotate(x,1); 155 end 156 else begin 157 if son[fa[y],1]=y then 158 begin 159 if son[y,1]=x then rotate(y,2) else rotate(x,1); 160 rotate(x,2); 161 end 162 else begin 163 if son[y,1]=x then rotate(x,2) else rotate(y,1); 164 rotate(x,1); 165 end; 166 end; 167 end; 168 update(x); 169 end; 170 171 function getrange(x,y:longint):longint; 172 begin 173 x:=find(x); 174 y:=find(y+2); 175 splay(x,-1); 176 splay(y,x); 177 exit(son[y,1]); 178 end; 179 180 function build(l,r:longint):longint; 181 var m:longint; 182 begin 183 m:=(l+r) shr 1; 184 build:=m; 185 if l<=m-1 then 186 begin 187 son[m,1]:=build(l,m-1); 188 fa[son[m,1]]:=m; 189 end; 190 if m+1<=r then 191 begin 192 son[m,2]:=build(m+1,r); 193 fa[son[m,2]]:=m; 194 end; 195 update(m); 196 end; 197 198 begin 199 fillchar(fa,sizeof(fa),255); 200 fillchar(son,sizeof(son),255); 201 readln(n,m); 202 for i:=1 to n do 203 begin 204 read(ch); 205 if ch='(' then a[i]:=1 else a[i]:=-1; 206 end; 207 readln; 208 root:=build(0,n+1); 209 for i:=1 to m do 210 begin 211 read(ch); 212 s:=''; 213 while ch<>' ' do 214 begin 215 s:=s+ch; 216 read(ch); 217 end; 218 read(x,y); 219 z:=getrange(x,y); 220 if s='Query' then 221 writeln((abs(lmin[z])+1) div 2+(rmax[z]+1) div 2) 222 else if s='Invert' then 223 begin 224 if laz[z]=0 then change(z) 225 else replace(z,-laz[z]); 226 end 227 else if s='Swap' then 228 reverse(z) 229 else if s='Replace' then 230 begin 231 read(ch); 232 while not((ch='(') or (ch=')')) do read(ch); 233 if ch='(' then w:=1 234 else w:=-1; 235 replace(z,w); 236 end; 237 readln; 238 end; 239 end.
