带修改的主席树
怎么搞呢，由于主席树满足减法性质，且维护的是前缀信息，所以我们不难想到套一个树状数组来优化
也很好理解，对于第i个位置，修改对后面的lowbit+都修改，求和lowbit-都求和
由于修改要修改logn个树，每棵树都要开辟logS个节点，所以空间复杂度是两个log值得注意
有修改还要将修改成的数一并离散化，所以带修改的主席树是一个离线数据结构
1 type node=record 2 wh:char; 3 l,r,x:longint; 4 end; 5 point=record 6 l,r,s:longint; 7 end; 8 9 var q:array[0..10010] of node; 10 tree:array[0..3000010] of point; 11 h,c,a,w,sa,d1,d2:array[0..20010] of longint; 12 j,s,p,last,t,t1,t2,x,i,n,m:longint; 13 14 function lowbit(x:longint):longint; 15 begin 16 exit(x and (-x)); 17 end; 18 19 procedure swap(var a,b:longint); 20 var c:longint; 21 begin 22 c:=a; 23 a:=b; 24 b:=c; 25 end; 26 27 function find(x:longint):longint; 28 var l,r,m:longint; 29 begin 30 l:=1; 31 r:=p; 32 while l<=r do 33 begin 34 m:=(l+r) shr 1; 35 if sa[m]=x then exit(m); 36 if sa[m]>x then r:=m-1 else l:=m+1; 37 end; 38 end; 39 40 procedure sort(l,r: longint); 41 var i,j,x,y: longint; 42 begin 43 i:=l; 44 j:=r; 45 x:=a[(l+r) div 2]; 46 repeat 47 while a[i]<x do inc(i); 48 while x<a[j] do dec(j); 49 if not(i>j) then 50 begin 51 swap(a[i],a[j]); 52 inc(i); 53 j:=j-1; 54 end; 55 until i>j; 56 if l<j then sort(l,j); 57 if i<r then sort(i,r); 58 end; 59 60 procedure update(i:longint); 61 begin 62 tree[i].s:=tree[tree[i].l].s+tree[tree[i].r].s; 63 end; 64 65 function build(l,r:longint):longint; 66 var m,q:longint; 67 begin 68 inc(t); 69 if l=r then exit(t) 70 else begin 71 q:=t; 72 m:=(l+r) shr 1; 73 tree[q].l:=build(l,m); 74 tree[q].r:=build(m+1,r); 75 exit(q); 76 end; 77 end; 78 79 function add(l,r,y,z:longint):longint; 80 var m,q:longint; 81 begin 82 inc(t); 83 if l=r then 84 begin 85 tree[t].s:=tree[last].s+z; 86 exit(t); 87 end 88 else begin 89 q:=t; 90 m:=(l+r) shr 1; 91 if y<=m then 92 begin 93 tree[q].r:=tree[last].r; 94 last:=tree[last].l; 95 tree[q].l:=add(l,m,y,z); 96 end 97 else begin 98 tree[q].l:=tree[last].l; 99 last:=tree[last].r; 100 tree[q].r:=add(m+1,r,y,z); 101 end; 102 update(q); 103 exit(q); 104 end; 105 end; 106 107 procedure insert(x,y,z:longint); 108 begin 109 while x<=n do 110 begin 111 last:=h[x]; 112 h[x]:=add(1,p,y,z); 113 x:=x+lowbit(x); 114 end; 115 end; 116 117 function getans(l,r,x:longint):longint; 118 var m,i,s1,s2,j:longint; 119 begin 120 if l=r then exit(sa[l]) 121 else begin 122 m:=(l+r) shr 1; 123 s1:=0; 124 s2:=0; 125 for i:=1 to t1 do 126 begin 127 j:=tree[d1[i]].l; 128 s1:=s1+tree[j].s; 129 end; 130 for i:=1 to t2 do 131 begin 132 j:=tree[d2[i]].l; 133 s2:=s2+tree[j].s; 134 end; 135 if s2-s1>=x then 136 begin 137 for i:=1 to t1 do 138 d1[i]:=tree[d1[i]].l; 139 for i:=1 to t2 do 140 d2[i]:=tree[d2[i]].l; 141 exit(getans(l,m,x)); 142 end 143 else begin 144 for i:=1 to t1 do 145 d1[i]:=tree[d1[i]].r; 146 for i:=1 to t2 do 147 d2[i]:=tree[d2[i]].r; 148 x:=x-(s2-s1); 149 exit(getans(m+1,r,x)); 150 end; 151 end; 152 end; 153 154 function ask(l,r,x:longint):longint; 155 var y:longint; 156 begin 157 t1:=0; 158 t2:=0; 159 y:=l-1; 160 while y>0 do //提取区间 161 begin 162 inc(t1); 163 d1[t1]:=h[y]; 164 y:=y-lowbit(y); 165 end; 166 y:=r; 167 while y>0 do 168 begin 169 inc(t2); 170 d2[t2]:=h[y]; 171 y:=y-lowbit(y); 172 end; 173 exit(getans(1,p,x)); 174 end; 175 176 begin 177 readln(n,m); 178 s:=n; 179 for i:=1 to n do 180 begin 181 read(c[i]); 182 a[i]:=c[i]; 183 end; 184 readln; 185 for i:=1 to m do 186 begin 187 read(q[i].wh); 188 if q[i].wh='Q' then 189 readln(q[i].l,q[i].r,q[i].x) 190 else begin 191 readln(q[i].l,q[i].x); 192 inc(s); 193 a[s]:=q[i].x; 194 end; 195 end; 196 sort(1,s); 197 p:=1; 198 sa[1]:=a[1]; 199 for i:=2 to s do //离散化 200 if a[i]<>a[i-1] then 201 begin 202 inc(p); 203 sa[p]:=a[i]; 204 end; 205 206 h[0]:=build(1,p); 207 for i:=1 to n do 208 begin 209 w[i]:=find(c[i]); 210 insert(i,w[i],1); 211 end; 212 for i:=1 to m do 213 begin 214 if q[i].wh='Q' then 215 writeln(ask(q[i].l,q[i].r,q[i].x)) 216 else begin 217 x:=find(q[i].x); 218 insert(q[i].l,w[q[i].l],-1); //修改的两步 219 insert(q[i].l,x,1); 220 w[q[i].l]:=x; 221 end; 222 end; 223 end.
