1.筛法
1 var 2 n,m,i,x,tot,j :longint; 3 prime :array[0..10000050] of boolean; 4 p :array[0..10000050] of longint; 5 begin 6 read(n,m); 7 for i:=2 to n do 8 begin 9 if not prime[i] then 10 begin 11 inc(tot); 12 p[tot]:=i; 13 end; 14 for j:=1 to tot do 15 begin 16 if (i*p[j]>n) then break; 17 prime[i*p[j]]:=true; 18 if i mod p[j]=0 then break; 19 end; 20 end; 21 //for i:=1 to tot do prime[p[i]]:=true; 22 for i:=1 to m do 23 begin 24 read(x); 25 if x=1 then writeln('No') else 26 if (prime[x]) then writeln('No') else writeln('Yes'); 27 end; 28 end.
1 var 2 n,i,j,tot :longint; 3 nprime :array[0..10000050] of boolean; 4 p,phi :array[0..10000050] of int64; 5 begin 6 read(n); 7 phi[1]:=1; 8 for i:=2 to n do 9 begin 10 if not nprime[i] then 11 begin 12 phi[i]:=i-1; 13 inc(tot); 14 p[tot]:=i; 15 end; 16 for j:=1 to tot do 17 begin 18 if (i*p[j]>n) then break; 19 nprime[i*p[j]]:=true; 20 if (i mod p[j]=0) then 21 begin 22 phi[i*p[j]]:=phi[i]*p[j]; 23 break; 24 end else phi[i*p[j]]:=phi[i]*(p[j]-1); 25 end; 26 end; 27 for i:=n to n do write(phi[i],' '); 28 end.
1 var 2 n,i,j,tot :longint; 3 nprime :array[0..1000050] of boolean; 4 p,miu :array[0..1000050] of longint; 5 begin 6 read(n); 7 miu[1]:=1; 8 for i:=2 to n do 9 begin 10 if not nprime[i] then 11 begin 12 miu[i]:=-1; 13 inc(tot); 14 p[tot]:=i; 15 end; 16 for j:=1 to tot do 17 begin 18 if i*p[j]>n then break; 19 nprime[i*p[j]]:=true; 20 if (i mod p[j]=0) then 21 begin 22 miu[i*p[j]]:=0; 23 break; 24 end else miu[i*p[j]]:=-miu[i]; 25 end; 26 end; 27 for i:=1 to n do write(miu[i],' '); 28 end.
1 const maxn=2000000; 2 var 3 N,L,T,LL :int64; 4 nprime :Array[0..2000050] of boolean; 5 p :array[0..200050] of longint; 6 pre :array[0..2000050] of longint; 7 pr :array[0..2000050] of longint; 8 las,other,len :array[0..2000050] of int64; 9 la,oth,le :array[0..2000050] of longint; 10 miu :array[0..2000050] of longint; 11 phi :array[0..2000050] of int64; 12 tot,i :longint; 13 a,b :double; 14 15 procedure pred(); 16 var 17 i,j :longint; 18 begin 19 miu[1]:=1; 20 phi[1]:=1; 21 for i:=2 to maxn do 22 begin 23 if not nprime[i] then 24 begin 25 miu[i]:=-1; 26 phi[i]:=i-1; 27 inc(tot); 28 p[tot]:=i; 29 end; 30 for j:=1 to tot do 31 begin 32 if i*p[j]>maxn then break; 33 nprime[i*p[j]]:=true; 34 if i mod p[j]=0 then 35 begin 36 miu[i*p[j]]:=0; 37 phi[i*p[j]]:=int64(phi[i]*p[j]); 38 break; 39 end else 40 begin 41 miu[i*p[j]]:=-miu[i]; 42 phi[i*p[j]]:=phi[i]*(p[j]-1); 43 end; 44 end; 45 end; 46 for i:=1 to maxn do miu[i]:=miu[i-1]+miu[i]; 47 for i:=1 to maxn do phi[i]:=phi[i-1]+phi[i]; 48 end; 49 50 procedure add(u,v,r:int64); 51 begin 52 inc(L); 53 pre[L]:=las[u]; 54 las[u]:=L; 55 other[L]:=v; 56 len[L]:=r; 57 end; 58 59 function cal1(x:int64):int64; 60 var 61 ans,z,i,j,last :int64; 62 pp,q,k,di :int64; 63 begin 64 if x<=maxn then exit(phi[x]); 65 k:=x mod maxn; 66 ans:=0; 67 pp:=las[k]; 68 while pp<>0 do 69 begin 70 q:=other[pp]; 71 if q=x then exit(len[pp]); 72 pp:=pre[pp]; 73 end; 74 i:=2; 75 while i<=x do 76 begin 77 di:=x div i; 78 last:=x div di; 79 ans:=ans+(last-i+1)*cal1(di); 80 i:=last+1; 81 end; 82 ans:=int64(x*(x+1) div 2-ans); 83 add(k,x,ans); 84 exit(ans); 85 end; 86 87 procedure ad(u,v,r:longint); 88 begin 89 inc(LL); 90 pr[LL]:=la[u]; 91 la[u]:=LL; 92 oth[LL]:=v; 93 le[LL]:=r; 94 end; 95 96 function cal2(x:longint):longint; 97 var 98 last,i,di :int64; 99 ans :longint; 100 pp,q,k :longint; 101 begin 102 if x<=maxn then exit(miu[x]); 103 k:=x mod maxn; 104 ans:=0; 105 pp:=la[k]; 106 while pp<>0 do 107 begin 108 q:=oth[pp]; 109 if q=x then exit(le[pp]); 110 pp:=pr[pp]; 111 end; 112 i:=2; 113 while i<=x do 114 begin 115 di:=x div i; 116 last:=x div di; 117 ans:=ans+(last-i+1)*cal2(di); 118 i:=last+1; 119 end; 120 ans:=1-ans; 121 ad(k,x,ans); 122 exit(ans); 123 end; 124 125 begin 126 read(T); 127 pred; 128 for i:=1 to T do 129 begin 130 read(N); 131 writeln(cal1(N),' ',cal2(N)); 132 end; 133 //writeln(a); 134 end.
1 var 2 N,i,j,tot,w :longint; 3 nprime :array[0..1000050] of boolean; 4 p :array[0..1000050] of longint; 5 f,t :array[0..1000050] of int64; 6 begin 7 read(N); 8 f[1]:=1; 9 for i:=2 to N do 10 begin 11 if not nprime[i] then 12 begin 13 inc(tot); 14 p[tot]:=i; 15 f[i]:=i+1; 16 t[i]:=i; 17 end; 18 for j:=1 to tot do 19 begin 20 if i*p[j]>N then break; 21 nprime[i*p[j]]:=true; 22 if (i mod p[j]=0) then 23 begin 24 t[i*p[j]]:=t[i]*p[j]; 25 if i*p[j]=t[i*p[j]] then 26 begin 27 w:=1; 28 while w<=i*p[j] do 29 begin 30 f[i*p[j]]:=f[i*p[j]]+w; 31 w:=w*p[j]; 32 end; 33 end else f[i*p[j]]:=f[i*p[j] div t[i*p[j]]]*f[t[i*p[j]]]; 34 break; 35 end; 36 t[i*p[j]]:=p[j]; 37 f[i*p[j]]:=f[i]*f[p[j]]; 38 end; 39 end; 40 for i:=1 to N do write(f[i],' '); 41 end.
2.平衡树
1 var 2 N,i,opt,x,t,tot :longint; 3 left,right,size,key :Array[0..100050] of longint; 4 5 procedure lrot(var t:longint); 6 var 7 k :longint; 8 begin 9 k:=right[t]; 10 right[t]:=left[k]; 11 left[k]:=t; 12 size[k]:=size[t]; 13 size[t]:=size[left[t]]+size[right[t]]+1; 14 t:=k; 15 end; 16 17 procedure rrot(var t:longint); 18 var 19 k :longint; 20 begin 21 k:=left[t]; 22 left[t]:=right[k]; 23 right[k]:=t; 24 size[k]:=size[t]; 25 size[t]:=size[left[t]]+size[right[t]]+1; 26 t:=k; 27 end; 28 29 procedure maintain(var t:longint; flag:boolean); 30 begin 31 if not flag then 32 begin 33 if size[left[left[t]]]>size[right[t]] then rrot(t) else 34 if size[right[left[t]]]>size[right[t]] then 35 begin 36 lrot(left[t]); 37 rrot(t); 38 end else exit; 39 end else 40 begin 41 if size[right[right[t]]]>size[left[t]] then lrot(t) else 42 if size[left[right[t]]]>size[left[t]] then 43 begin 44 rrot(right[t]); 45 lrot(t); 46 end else exit; 47 end; 48 maintain(left[t],false); 49 maintain(right[t],true); 50 maintain(t,false); 51 maintain(t,true); 52 end; 53 54 procedure insert(var t:longint; v:longint); 55 begin 56 if t=0 then 57 begin 58 inc(tot); 59 t:=tot; 60 left[t]:=0; 61 right[t]:=0; 62 size[t]:=1; 63 key[t]:=v; 64 exit; 65 end; 66 inc(size[t]); 67 if v<key[t] then insert(left[t],v) else insert(right[t],v); 68 maintain(t,v>=key[t]); 69 end; 70 71 function delete(var t:longint; v:longint):longint; 72 begin 73 dec(size[t]); 74 if (v=key[t]) or ((v<key[t]) and (left[t]=0)) or ((v>key[t]) and (right[t]=0)) then 75 begin 76 delete:=key[t]; 77 if (left[t]=0) or (right[t]=0) then t:=left[t]+right[t] else key[t]:=delete(left[t],v+1); 78 end else 79 if v<key[t] then exit(delete(left[t],v)) else exit(delete(right[t],v)); 80 end; 81 82 function rank(var t:longint; v:longint):longint; 83 begin 84 if t=0 then exit(1); 85 if v<=key[t] then exit(rank(left[t],v)); 86 exit(rank(right[t],v)+size[left[t]]+1); 87 end; 88 89 function select(var t:longint; v:longint):longint; 90 begin 91 if v=size[left[t]]+1 then exit(key[t]); 92 if v<size[left[t]]+1 then exit(select(left[t],v)); 93 exit(select(right[t],v-size[left[t]]-1)); 94 end; 95 96 function pred(var t:longint; v:longint):longint; 97 begin 98 if t=0 then exit(-1); 99 if v<=key[t] then exit(pred(left[t],v)); 100 pred:=pred(right[t],v); 101 if pred=-1 then exit(key[t]); 102 end; 103 104 function succ(var t:longint; v:longint):longint; 105 begin 106 if t=0 then exit(-1); 107 if v>=key[t] then exit(succ(right[t],v)); 108 succ:=succ(left[t],v); 109 if succ=-1 then exit(key[t]); 110 end; 111 112 begin 113 read(N); 114 for i:=1 to N do 115 begin 116 read(opt,x); 117 if (opt=1) then insert(t,x) else 118 if (opt=2) then x:=delete(t,x) else 119 if (opt=3) then writeln(rank(t,x)) else 120 if (opt=4) then writeln(select(t,x)) else 121 if (opt=5) then writeln(pred(t,x)) else 122 if (opt=6) then writeln(succ(t,x)); 123 end; 124 end.
1 {$Q-} 2 {$inline on} 3 const inf=1000000000; 4 var 5 n,m,rt,tot,i,j,k,top :longint; 6 size,key,psum,ssum,msum,sum,a,st :array[0..500050] of longint; 7 son :array[0..500050,0..2] of longint; 8 lazy,tag,father :array[0..500050] of longint; 9 c1,c2,c3 :char; 10 11 function max(x,y:longint):longint;inline; 12 begin 13 if x>y then exit(x) else exit(y); 14 end; 15 16 procedure swap(var x,y:longint);inline; 17 var 18 z :longint; 19 begin 20 z:=x; 21 x:=y; 22 y:=z; 23 end; 24 25 26 function nw():longint;inline; 27 var 28 x :longint; 29 begin 30 if (top>0) then 31 begin 32 x:=st[top]; 33 dec(top); 34 end else 35 begin 36 inc(tot); 37 x:=tot; 38 end; 39 lazy[x]:=0; 40 tag[x]:=0; 41 son[x,0]:=0; 42 son[x,1]:=0; 43 exit(x); 44 end; 45 46 function which(x:longint):longint;inline; 47 begin 48 if x=son[father[x],1] then exit(1) else exit(0); 49 end; 50 51 procedure update(x:longint);inline; 52 begin 53 size[x]:=size[son[x,0]]+size[son[x,1]]+1; 54 sum[x]:=sum[son[x,0]]+sum[son[x,1]]+key[x]; 55 psum[x]:=max(psum[son[x,0]],key[x]+sum[son[x,0]]+max(0,psum[son[x,1]])); 56 ssum[x]:=max(ssum[son[x,1]],key[x]+sum[son[x,1]]+max(0,ssum[son[x,0]])); 57 msum[x]:=max(max(msum[son[x,0]],msum[son[x,1]]),max(ssum[son[x,0]],0)+max(psum[son[x,1]],0)+key[x]); 58 end; 59 60 61 procedure rot(x:longint);inline; 62 var 63 f,gf,opt :longint; 64 begin 65 f:=father[x]; 66 gf:=father[f]; 67 opt:=which(x); 68 if gf<>0 then son[gf,which(f)]:=x; 69 father[x]:=gf; 70 son[f,opt]:=son[x,opt xor 1]; 71 father[son[x,opt xor 1]]:=f; 72 son[x,opt xor 1]:=f; 73 father[f]:=x; 74 update(f); 75 update(x); 76 end; 77 78 procedure splay(x,go:longint);inline; 79 begin 80 while father[x]<>go do 81 begin 82 if (father[father[x]]<>go) then 83 begin 84 if which(x)=which(father[x]) then rot(father[x]) else rot(x); 85 end; 86 rot(x); 87 end; 88 if go=0 then rt:=x; 89 end; 90 91 procedure build(x,l,r:longint); 92 var 93 mid :longint; 94 begin 95 mid:=(l+r)>>1; 96 key[x]:=a[mid]; 97 if (l=r) then 98 begin 99 size[x]:=1; 100 sum[x]:=key[x]; 101 psum[x]:=key[x]; 102 ssum[x]:=key[x]; 103 msum[x]:=key[x]; 104 exit; 105 end; 106 if (l<mid) then 107 begin 108 son[x,0]:=nw; 109 father[son[x,0]]:=x; 110 build(son[x,0],l,mid-1); 111 end; 112 if (r>mid) then 113 begin 114 son[x,1]:=nw; 115 father[son[x,1]]:=x; 116 build(son[x,1],mid+1,r); 117 end; 118 update(x); 119 end; 120 121 procedure paint(x:longint);inline; 122 begin 123 lazy[x]:=lazy[x] xor 1; 124 swap(son[x,0],son[x,1]); 125 swap(psum[x],ssum[x]); 126 end; 127 128 procedure paintt(x,v:longint);inline; 129 begin 130 tag[x]:=1; 131 lazy[x]:=0; 132 key[x]:=v; 133 sum[x]:=size[x]*v; 134 msum[x]:=max(v,sum[x]); 135 psum[x]:=msum[x]; 136 ssum[x]:=msum[x]; 137 end; 138 139 procedure p_d(x:longint);inline; 140 begin 141 if (lazy[x]<>0) then 142 begin 143 if son[x,0]<>0 then paint(son[x,0]); 144 if son[x,1]<>0 then paint(son[x,1]); 145 lazy[x]:=0; 146 end; 147 if (tag[x]<>0) then 148 begin 149 if son[x,0]<>0 then paintt(son[x,0],key[x]); 150 if son[x,1]<>0 then paintt(son[x,1],key[x]); 151 tag[x]:=0; 152 end; 153 end; 154 155 function kth(x,k:longint):longint;inline; 156 begin 157 if x=0 then exit(-1); 158 p_d(x); 159 if (size[son[x,0]]+1=k) then exit(x); 160 if (size[son[x,0]]+1<k) then exit(kth(son[x,1],k-size[son[x,0]]-1)); 161 if (size[son[x,0]]+1>k) then exit(kth(son[x,0],k)); 162 end; 163 164 procedure ins(); 165 var 166 i,k,t,p,x :longint; 167 begin 168 read(k,t); 169 for i:=1 to t do read(a[i]); 170 p:=kth(rt,k+1); splay(p,0); 171 x:=kth(rt,k+2); splay(x,p); 172 son[x,0]:=nw; 173 father[son[x,0]]:=x; 174 build(son[x,0],1,t); 175 update(x); 176 update(p); 177 end; 178 179 procedure erase(x:longint); 180 begin 181 if x=0 then exit; 182 inc(top); 183 st[top]:=x; 184 if (son[x,0]<>0) then erase(son[x,0]); 185 if (son[x,1]<>0) then erase(son[x,1]); 186 end; 187 188 procedure del(); 189 var 190 k,t,p,x :longint; 191 begin 192 read(k,t); 193 p:=kth(rt,k); splay(p,0); 194 x:=kth(rt,k+t+1); splay(x,p); 195 erase(son[x,0]); 196 father[son[x,0]]:=0; 197 son[x,0]:=0; 198 update(x); 199 update(p); 200 end; 201 202 procedure rev(); 203 var 204 k,t,p,x :longint; 205 begin 206 read(k,t); 207 p:=kth(rt,k); splay(p,0); 208 x:=kth(rt,k+t+1); splay(x,p); 209 paint(son[x,0]); 210 update(x); 211 update(p); 212 end; 213 214 215 procedure make(); 216 var 217 k,t,v,p,x :longint; 218 begin 219 read(k,t,v); 220 p:=kth(rt,k); splay(p,0); 221 x:=kth(rt,k+t+1); splay(x,p); 222 paintt(son[x,0],v); 223 update(x); 224 update(p); 225 end; 226 227 function qsum():longint; 228 var 229 k,t,p,x :longint; 230 begin 231 read(k,t); 232 p:=kth(rt,k); splay(p,0); 233 x:=kth(rt,k+t+1); splay(x,p); 234 exit(sum[son[x,0]]); 235 end; 236 237 begin 238 //assign(input,'testdata.in');reset(input); 239 read(n,m); 240 for i:=1 to n do read(a[i+1]); 241 rt:=1; tot:=1; 242 a[1]:=-inf; a[n+2]:=-inf; psum[0]:=-inf; ssum[0]:=-inf; msum[0]:=-inf; 243 build(rt,1,n+2); 244 readln; 245 for i:=1 to m do 246 begin 247 read(c1,c2,c3); 248 if (c1='I') then 249 begin 250 while (c3<>' ') do read(c3); 251 ins(); 252 end; 253 if (c1='D') then 254 begin 255 while (c3<>' ') do read(c3); 256 del(); 257 end; 258 if (c1='R') then 259 begin 260 while (c3<>' ') do read(c3); 261 rev(); 262 end; 263 if (c3='K') then 264 begin 265 while (c3<>' ') do read(c3); 266 make(); 267 end; 268 if (c1='G') then 269 begin 270 while (c3<>' ') do read(c3); 271 writeln(qsum()); 272 end; 273 if (c3='X') then 274 begin 275 readln; 276 writeln(msum[rt]); 277 continue; 278 end; 279 readln; 280 end; 281 end.
3.线段树
1 type 2 rec =record 3 l,r :longint; 4 sum,lz,tg :int64; 5 end; 6 7 var 8 t :array[0..300050] of rec; 9 a :array[0..100050] of int64; 10 N,M,mo,i,opt,x,y :longint; 11 z :int64; 12 13 procedure build(x,l,r:longint); 14 var 15 mid :longint; 16 begin 17 t[x].l:=l; t[x].r:=r; t[x].tg:=1; 18 if (t[x].l=t[x].r) then 19 begin 20 t[x].sum:=a[l] mod mo; 21 exit; 22 end; 23 mid:=(t[x].l+t[x].r)>>1; 24 build(x*2,l,mid); 25 build(x*2+1,mid+1,r); 26 t[x].sum:=(t[x*2].sum+t[x*2+1].sum) mod mo; 27 end; 28 29 procedure update(x:longint); 30 begin 31 t[x].sum:=(t[x].sum*t[x].tg+t[x].lz*(t[x].r-t[x].l+1)) mod mo; 32 if (t[x].l=t[x].r) then 33 begin 34 t[x].tg:=1; 35 t[x].lz:=0; 36 exit; 37 end; 38 t[x*2].tg:=(t[x*2].tg*t[x].tg) mod mo; 39 t[x*2+1].tg:=(t[x*2+1].tg*t[x].tg) mod mo; 40 t[x*2].lz:=(t[x*2].lz*t[x].tg+t[x].lz) mod mo; 41 t[x*2+1].lz:=(t[x*2+1].lz*t[x].tg+t[x].lz) mod mo; 42 t[x].tg:=1; 43 t[x].lz:=0; 44 end; 45 46 procedure c_tg(x,l,r:longint; y:int64); 47 var 48 mid :longint; 49 begin 50 if (t[x].lz<>0) or (t[x].tg<>1) then update(x); 51 if (t[x].l=l) and (t[x].r=r) then 52 begin 53 t[x].tg:=(t[x].tg*y) mod mo; 54 exit; 55 end; 56 mid:=(t[x].l+t[x].r)>>1; 57 if l>mid then c_tg(x*2+1,l,r,y) else 58 if r<=mid then c_tg(x*2,l,r,y) else 59 begin 60 c_tg(x*2,l,mid,y); 61 c_tg(x*2+1,mid+1,r,y); 62 end; 63 t[x].sum:=(t[x*2].sum*t[x*2].tg+t[x*2].lz*(t[x*2].r-t[x*2].l+1)+ 64 t[x*2+1].sum*t[x*2+1].tg+t[x*2+1].lz*(t[x*2+1].r-t[x*2+1].l+1)) mod mo; 65 end; 66 67 procedure c_lz(x,l,r:longint; y:int64); 68 var 69 mid :longint; 70 begin 71 if (t[x].lz<>0) or (t[x].tg<>1) then update(x); 72 if (t[x].l=l) and (t[x].r=r) then 73 begin 74 t[x].lz:=(t[x].lz+y) mod mo; 75 exit; 76 end; 77 mid:=(t[x].l+t[x].r)>>1; 78 if l>mid then c_lz(x*2+1,l,r,y) else 79 if r<=mid then c_lz(x*2,l,r,y) else 80 begin 81 c_lz(x*2,l,mid,y); 82 c_lz(x*2+1,mid+1,r,y); 83 end; 84 t[x].sum:=(t[x*2].sum*t[x*2].tg+t[x*2].lz*(t[x*2].r-t[x*2].l+1)+ 85 t[x*2+1].sum*t[x*2+1].tg+t[x*2+1].lz*(t[x*2+1].r-t[x*2+1].l+1)) mod mo; 86 end; 87 88 function find(x,l,r:longint):int64; 89 var 90 mid :longint; 91 begin 92 if (t[x].lz<>0) or (t[x].tg<>1) then update(x); 93 if (t[x].l=l) and (t[x].r=r) then exit(t[x].sum mod mo); 94 mid:=(t[x].l+t[x].r)>>1; 95 if l>mid then exit(find(x*2+1,l,r)) else 96 if r<=mid then exit(find(x*2,l,r)) else 97 exit((find(x*2,l,mid)+find(x*2+1,mid+1,r)) mod mo); 98 end; 99 100 begin 101 read(N,M,mo); 102 for i:=1 to N do read(a[i]); 103 build(1,1,N); 104 for i:=1 to M do 105 begin 106 read(opt); 107 if opt=1 then 108 begin 109 read(x,y,z); 110 c_tg(1,x,y,z); 111 end else 112 if opt=2 then 113 begin 114 read(x,y,z); 115 c_lz(1,x,y,z); 116 end else 117 begin 118 read(x,y); 119 writeln(find(1,x,y)); 120 end; 121 end; 122 end.
4.树链剖分
1 type 2 rec =record 3 l,r :longint; 4 sum,lazy :int64; 5 end; 6 7 var 8 N,M,R,mo,i,x,y,opt,L,tot :longint; 9 z :int64; 10 t :array[0..300050] of rec; 11 a,key :array[0..100050] of int64; 12 size,num,dep,mson,top,father :array[0..100050] of longint; 13 vis :array[0..100050] of boolean; 14 pre,last,other :array[0..200050] of longint; 15 16 procedure swap(var x,y:longint); 17 var 18 z :longint; 19 begin 20 z:=x; 21 x:=y; 22 y:=z; 23 end; 24 25 procedure add(u,v:longint); 26 begin 27 inc(L); 28 pre[L]:=last[u]; 29 last[u]:=L; 30 other[L]:=v; 31 end; 32 33 procedure dfs(x,fa:longint); 34 var 35 p,q :longint; 36 begin 37 size[x]:=1; 38 p:=last[x]; 39 while p<>0 do 40 begin 41 q:=other[p]; 42 if q<>fa then 43 begin 44 father[q]:=x; 45 dfs(q,x); 46 size[x]:=size[x]+size[q]; 47 if size[q]>size[mson[x]] then mson[x]:=q; 48 end; 49 p:=pre[p]; 50 end; 51 end; 52 53 procedure make(x,depp,topp:longint); 54 var 55 p,q :longint; 56 begin 57 inc(tot); 58 num[x]:=tot; 59 a[tot]:=key[x]; 60 dep[x]:=depp; 61 top[x]:=topp; 62 if mson[x]<>0 then 63 begin 64 vis[mson[x]]:=true; 65 make(mson[x],depp,topp); 66 end; 67 p:=last[x]; 68 while p<>0 do 69 begin 70 q:=other[p]; 71 if (vis[q]) or (q=mson[x]) then 72 begin 73 p:=pre[p]; 74 continue; 75 end; 76 vis[q]:=true; 77 make(q,depp+1,q); 78 p:=pre[p]; 79 end; 80 end; 81 82 procedure build(x,l,r:longint); 83 var 84 mid :longint; 85 begin 86 t[x].l:=l; t[x].r:=r; 87 if (t[x].l=t[x].r) then 88 begin 89 t[x].sum:=a[l] mod mo; 90 exit; 91 end; 92 mid:=(t[x].l+t[x].r)>>1; 93 build(x*2,l,mid); 94 build(x*2+1,mid+1,r); 95 t[x].sum:=(t[x*2].sum+t[x*2+1].sum) mod mo; 96 end; 97 98 procedure update(x:longint); 99 begin 100 t[x].sum:=(t[x].sum+t[x].lazy*(t[x].r-t[x].l+1)) mod mo; 101 if (t[x].l=t[x].r) then 102 begin 103 t[x].lazy:=0; 104 exit; 105 end; 106 t[x*2].lazy:=(t[x*2].lazy+t[x].lazy) mod mo; 107 t[x*2+1].lazy:=(t[x*2+1].lazy+t[x].lazy) mod mo; 108 t[x].lazy:=0; 109 end; 110 111 procedure change(x,l,r:longint;y:int64); 112 var 113 mid :longint; 114 begin 115 if (t[x].l=l) and (t[x].r=r) then 116 begin 117 t[x].lazy:=(t[x].lazy+y) mod mo; 118 exit; 119 end; 120 if (t[x].lazy<>0) then update(x); 121 mid:=(t[x].l+t[x].r)>>1; 122 if l>mid then change(x*2+1,l,r,y) else 123 if r<=mid then change(x*2,l,r,y) else 124 begin 125 change(x*2,l,mid,y); 126 change(x*2+1,mid+1,r,y); 127 end; 128 t[x].sum:=(t[x*2].sum+t[x*2].lazy*(t[x*2].r-t[x*2].l+1)+t[x*2+1].sum+t[x*2+1].lazy*(t[x*2+1].r-t[x*2+1].l+1)) mod mo; 129 end; 130 131 function find(x,l,r:longint):int64; 132 var 133 mid :longint; 134 begin 135 if (t[x].lazy<>0) then update(x); 136 if (t[x].l=l) and (t[x].r=r) then exit(t[x].sum); 137 mid:=(t[x].l+t[x].r)>>1; 138 if l>mid then exit(find(x*2+1,l,r)) else 139 if r<=mid then exit(find(x*2,l,r)) else 140 exit((find(x*2,l,mid)+find(x*2+1,mid+1,r)) mod mo); 141 end; 142 143 procedure qchange(x,y:longint; z:int64); 144 begin 145 if dep[x]>dep[y] then swap(x,y); 146 while dep[y]>dep[x] do 147 begin 148 change(1,num[top[y]],num[y],z); 149 y:=father[top[y]]; 150 end; 151 while top[x]<>top[y] do 152 begin 153 change(1,num[top[x]],num[x],z); 154 change(1,num[top[y]],num[y],z); 155 x:=father[top[x]]; 156 y:=father[top[y]]; 157 end; 158 x:=num[x]; 159 y:=num[y]; 160 if x>y then swap(x,y); 161 change(1,x,y,z); 162 end; 163 164 function qfind(x,y:longint):int64; 165 var 166 sum :int64; 167 begin 168 sum:=0; 169 if dep[x]>dep[y] then swap(x,y); 170 while dep[y]>dep[x] do 171 begin 172 sum:=(sum+find(1,num[top[y]],num[y])) mod mo; 173 y:=father[top[y]]; 174 end; 175 while top[x]<>top[y] do 176 begin 177 sum:=(sum+find(1,num[top[y]],num[y])) mod mo; 178 sum:=(sum+find(1,num[top[x]],num[x])) mod mo; 179 y:=father[top[y]]; 180 x:=father[top[x]]; 181 end; 182 x:=num[x]; 183 y:=num[y]; 184 if x>y then swap(x,y); 185 exit((sum+find(1,x,y)) mod mo); 186 end; 187 188 189 begin 190 read(N,M,R,mo); 191 for i:=1 to N do read(key[i]); 192 for i:=1 to N-1 do 193 begin 194 read(x,y); 195 add(x,y); 196 add(y,x); 197 end; 198 dfs(R,0); 199 //for i:=1 to n do writeln(size[i]); 200 vis[R]:=true; 201 make(R,1,R); 202 build(1,1,N); 203 for i:=1 to M do 204 begin 205 read(opt); 206 if (opt=1) then 207 begin 208 read(x,y,z); 209 qchange(x,y,z); 210 end else 211 if (opt=2) then 212 begin 213 read(x,y); 214 writeln(qfind(x,y)); 215 end else 216 if (opt=3) then 217 begin 218 read(x,z); 219 change(1,num[x],num[x]+size[x]-1,z); 220 end else 221 begin 222 read(x); 223 writeln(find(1,num[x],num[x]+size[x]-1)); 224 end; 225 end; 226 end.
5.主席树
1 type 2 rec =record 3 l,r,sum :longint; 4 end; 5 6 var 7 N,M,i,j,x,y,z,tot :longint; 8 a,rt,reco,num,b,map :array[0..50050] of longint; 9 t :Array[0..50050*20] of rec; 10 11 procedure swap(var x,y:longint); 12 var 13 z :longint; 14 begin 15 z:=x; 16 x:=y; 17 y:=z; 18 end; 19 20 procedure sort(l,r:longint); 21 var 22 i,j,x :longint; 23 begin 24 i:=l; j:=r; x:=b[(l+r)>>1]; 25 while i<j do 26 begin 27 while b[i]<x do inc(i); 28 while b[j]>x do dec(j); 29 if i<=j then 30 begin 31 swap(b[i],b[j]); 32 swap(num[i],num[j]); 33 inc(i); 34 dec(j); 35 end; 36 end; 37 if i<r then sort(i,r); 38 if j>l then sort(l,j); 39 end; 40 41 42 function build(x,y,z,l,r:longint):longint; 43 var 44 cur,mid :longint; 45 begin 46 inc(tot); 47 cur:=tot; 48 t[cur]:=t[x]; 49 t[cur].sum:=t[x].sum+z; 50 if (l=r) then exit(cur); 51 mid:=(l+r)>>1; 52 if y>mid then t[cur].r:=build(t[cur].r,y,z,mid+1,r) else t[cur].l:=build(t[cur].l,y,z,l,mid); 53 exit(cur); 54 end; 55 56 function find(x,y,k,l,r:longint):longint; 57 var 58 mid,s :longint; 59 begin 60 if l=r then exit(l); 61 s:=t[t[y].r].sum-t[t[x].r].sum; 62 mid:=(l+r)>>1; 63 if k<=s then exit(find(t[x].r,t[y].r,k,mid+1,r)) else exit(find(t[x].l,t[y].l,k-s,l,mid)); 64 end; 65 66 67 begin 68 read(N); 69 for i:=1 to N do 70 begin 71 read(b[i]); 72 reco[i]:=b[i]; 73 num[i]:=i; 74 end; 75 sort(1,N); 76 for i:=1 to N do a[num[i]]:=i; 77 for i:=1 to N do map[a[i]]:=reco[i]; 78 for i:=1 to N do rt[i]:=build(rt[i-1],a[i],1,1,n); 79 read(M); 80 for i:=1 to M do 81 begin 82 read(x,y,z); 83 inc(x); 84 inc(y); 85 writeln(map[find(rt[x-1],rt[y],z,1,n)]); 86 end; 87 end.
6.最短路经
1 var 2 N,M,S,L,i,x,y,z,tot :longint; 3 d,heap,pl :array[0..10005] of longint; 4 pre,last,other,len :array[0..500050] of longint; 5 6 procedure swap(var x,y:longint); 7 var 8 z :longint; 9 begin 10 z:=x; 11 x:=y; 12 y:=z; 13 end; 14 15 procedure add(u,v,r:longint); 16 begin 17 inc(L); 18 pre[L]:=last[u]; 19 last[u]:=L; 20 other[L]:=v; 21 len[L]:=r; 22 end; 23 24 procedure up(x:longint); 25 var 26 i,j :longint; 27 begin 28 i:=x; 29 while i>>1>0 do 30 begin 31 j:=i>>1; 32 if d[heap[j]]<=d[heap[i]] then break; 33 swap(heap[i],heap[j]); 34 pl[heap[i]]:=i; 35 pl[heap[j]]:=j; 36 i:=j; 37 end; 38 end; 39 40 procedure down(x:longint); 41 var 42 i,j :longint; 43 begin 44 i:=x; 45 while i<<1<=tot do 46 begin 47 j:=i<<1; 48 if (j+1<=tot) and (d[heap[j+1]]<d[heap[j]]) then inc(j); 49 if d[heap[j]]>=d[heap[i]] then break; 50 swap(heap[i],heap[j]); 51 pl[heap[i]]:=i; 52 pl[heap[j]]:=j; 53 i:=j; 54 end; 55 end; 56 57 procedure delete(x:longint); 58 begin 59 heap[x]:=heap[tot]; 60 dec(tot); 61 down(x); 62 end; 63 64 procedure dij(); 65 var 66 p,q,cur :longint; 67 begin 68 for i:=1 to N do 69 begin 70 cur:=heap[1]; 71 delete(1); 72 p:=last[cur]; 73 while p<>0 do 74 begin 75 q:=other[p]; 76 if d[q]>d[cur]+len[p] then 77 begin 78 d[q]:=d[cur]+len[p]; 79 up(pl[q]); 80 end; 81 p:=pre[p]; 82 end; 83 end; 84 end; 85 86 begin 87 read(N,M,S); 88 for i:=1 to M do 89 begin 90 read(x,y,z); 91 add(x,y,z); 92 end; 93 for i:=1 to N do d[i]:=maxlongint>>1; d[S]:=0; 94 for i:=1 to N do heap[i]:=i; 95 for i:=1 to N do pl[i]:=i; 96 tot:=n; 97 up(S); 98 dij; 99 for i:=1 to N do if d[i]=maxlongint>>1 then write(maxlongint,' ') else write(d[i],' '); 100 end.
1 const mo=20000; 2 var 3 N,M,S,L,i,x,y,z :longint; 4 pre,last,other,len :array[0..5000050] of longint; 5 d,que :Array[0..200050] of longint; 6 vis :array[0..100050] of boolean; 7 8 procedure add(u,v,r:longint); 9 begin 10 inc(L); 11 pre[L]:=last[u]; 12 last[u]:=L; 13 other[L]:=v; 14 len[L]:=r; 15 end; 16 17 procedure spfa(); 18 var 19 p,q,cur,h,t :longint; 20 begin 21 for i:=1 to N do d[i]:=maxlongint>>1; d[S]:=0; 22 que[1]:=S; 23 h:=0; 24 t:=1; 25 while h<>t do 26 begin 27 h:=h mod mo+1; 28 cur:=que[h]; 29 vis[cur]:=false; 30 p:=last[cur]; 31 while p<>0 do 32 begin 33 q:=other[p]; 34 if d[q]>d[cur]+len[p] then 35 begin 36 d[q]:=d[cur]+len[p]; 37 if not vis[q] then 38 begin 39 vis[q]:=true; 40 inc(t); 41 que[t]:=q; 42 end; 43 end; 44 p:=pre[p]; 45 end; 46 end; 47 end; 48 49 50 begin 51 read(N,M,S); 52 for i:=1 to M do 53 begin 54 read(x,y,z); 55 add(x,y,z); 56 end; 57 spfa; 58 for i:=1 to N do if d[i]=maxlongint>>1 then write(maxlongint,' ') else write(d[i],' '); 59 end.
1 var 2 i,j,k,x,y,z :longint; 3 N,M,S :longint; 4 d :array[0..500,0..500] of longint; 5 6 function min(x,y:longint):longint; 7 begin 8 if x<y then exit(x) else exit(y); 9 end; 10 11 begin 12 read(N,M,S); 13 for i:=1 to N do 14 for j:=1 to N do d[i,j]:=maxlongint>>1; 15 for i:=1 to N do d[i,i]:=0; 16 for i:=1 to M do 17 begin 18 read(x,y,z); 19 d[x,y]:=min(d[x,y],z); 20 end; 21 for k:=1 to N do 22 for i:=1 to N do 23 for j:=1 to N do d[i,j]:=min(d[i,j],d[i,k]+d[k,j]); 24 for i:=1 to N do write(d[S,i],' '); 25 end.
7.网络流
1 var 2 N,M,SS,TT,i,x,y,z,L :longint; 3 ans :int64; 4 pre,last,other,len :array[0..300050] of longint; 5 d,que :array[0..10050] of longint; 6 7 function min(x,y:longint):longint; 8 begin 9 if x<y then exit(x) else exit(y); 10 end; 11 12 procedure add_double(u,v,r:longint); 13 begin 14 inc(L);pre[L]:=last[u];last[u]:=L;other[L]:=v;len[L]:=r; 15 inc(L);pre[L]:=last[v];last[v]:=L;other[L]:=u;len[L]:=0; 16 end; 17 18 function bfs():boolean; 19 var 20 h,t,p,q,cur :longint; 21 begin 22 fillchar(d,sizeof(d),0); 23 d[SS]:=1; 24 que[1]:=SS; 25 h:=0; 26 t:=1; 27 while h<t do 28 begin 29 inc(h); 30 cur:=que[h]; 31 p:=last[cur]; 32 while p<>0 do 33 begin 34 if len[p]>0 then 35 begin 36 q:=other[p]; 37 if (d[q]=0) then 38 begin 39 d[q]:=d[cur]+1; 40 inc(t); 41 que[t]:=q; 42 if q=TT then exit(true); 43 end; 44 end; 45 p:=pre[p]; 46 end; 47 end; 48 exit(false); 49 end; 50 51 function dinic(x,flow:longint):longint; 52 var 53 p,q,res,c :longint; 54 begin 55 if x=TT then exit(flow); 56 res:=flow; 57 p:=last[x]; 58 while p<>0 do 59 begin 60 q:=other[p]; 61 if (len[p]>0) and (res>0) and (d[q]=d[x]+1) then 62 begin 63 c:=dinic(q,min(len[p],res)); 64 dec(res,c); 65 dec(len[p],c); 66 inc(len[p xor 1],c); 67 if res=0 then exit(flow); 68 end; 69 p:=pre[p]; 70 end; 71 if flow=res then d[x]:=0; 72 exit(flow-res); 73 end; 74 75 begin 76 read(N,M,SS,TT); 77 L:=1; 78 for i:=1 to M do 79 begin 80 read(x,y,z); 81 add_double(x,y,z); 82 end; 83 while bfs() do ans:=ans+dinic(SS,maxlongint>>1); 84 writeln(ans); 85 end.
1 const mo=1000000; 2 var 3 N,M,SS,TT,L,i,x,y,z,w :longint; 4 pre,last,other,len,cos,next,from :Array[0..200050] of longint; 5 d :Array[0..5050] of longint; 6 vis :Array[0..5050] of boolean; 7 que :array[0..1000050] of longint; 8 9 function min(x,y:longint):longint; 10 begin 11 if x<y then exit(x) else exit(y); 12 end; 13 14 procedure add_double(u,v,r,w:longint); 15 begin 16 inc(L); pre[L]:=last[u]; last[u]:=L; other[L]:=v; len[L]:=r; cos[L]:=w; from[L]:=u; 17 inc(L); pre[L]:=last[v]; last[v]:=L; other[L]:=u; len[L]:=0; cos[L]:=-w; from[L]:=v; 18 end; 19 20 function spfa():boolean; 21 var 22 p,q,cur,h,t,inf :longint; 23 begin 24 fillchar(vis,sizeof(vis),false); 25 fillchar(d,sizeof(d),63); d[SS]:=0; inf:=d[0]; 26 que[1]:=SS; h:=0; t:=1; 27 while h<>t do 28 begin 29 h:=h mod mo+1; 30 cur:=que[h]; 31 p:=last[cur]; 32 vis[cur]:=false; 33 while p<>0 do 34 begin 35 if len[p]>0 then 36 begin 37 q:=other[p]; 38 if (d[q]>d[cur]+cos[p]) then 39 begin 40 next[q]:=p; 41 d[q]:=d[cur]+cos[p]; 42 if not vis[q] then 43 begin 44 vis[q]:=true; 45 t:=t mod mo+1; 46 que[t]:=q; 47 end; 48 end; 49 end; 50 p:=pre[p]; 51 end; 52 end; 53 exit(d[TT]<inf); 54 end; 55 56 57 procedure mcmf(); 58 var 59 p,q,sumflow,flow,sumcos :longint; 60 begin 61 sumflow:=0; 62 sumcos:=0; 63 while spfa do 64 begin 65 p:=next[TT]; 66 flow:=maxlongint; 67 while p<>0 do 68 begin 69 flow:=min(flow,len[p]); 70 p:=next[from[p]]; 71 end; 72 p:=next[TT]; 73 while p<>0 do 74 begin 75 len[p]:=len[p]-flow; 76 len[p xor 1]:=len[p xor 1]+flow; 77 p:=next[from[p]]; 78 end; 79 sumflow:=sumflow+flow; 80 sumcos:=sumcos+flow*d[TT]; 81 end; 82 writeln(sumflow,' ',sumcos); 83 end; 84 85 86 begin 87 read(N,M,SS,TT); 88 L:=1; 89 for i:=1 to M do 90 begin 91 read(x,y,z,w); 92 add_double(x,y,z,w); 93 end; 94 mcmf; 95 end.
8.树状数组
1 var 2 N,M,opt,x,y,i :longint; 3 z :int64; 4 c :Array[0..500050] of int64; 5 6 function lowbit(t:longint):longint; 7 begin 8 exit(t and (-t)); 9 end; 10 11 procedure ins(t:longint; x:int64); 12 begin 13 while t<=N do 14 begin 15 c[t]:=c[t]+x; 16 t:=t+lowbit(t); 17 end; 18 end; 19 20 function find(t:longint):int64; 21 var 22 sum :int64; 23 begin 24 sum:=0; 25 while t>0 do 26 begin 27 sum:=sum+c[t]; 28 t:=t-lowbit(t); 29 end; 30 exit(sum); 31 end; 32 33 begin 34 read(N,M); 35 for i:=1 to N do 36 begin 37 read(z); 38 ins(i,z); 39 end; 40 for i:=1 to M do 41 begin 42 read(opt); 43 if opt=1 then 44 begin 45 read(x,z); 46 ins(x,z); 47 end else 48 begin 49 read(x,y); 50 writeln(find(y)-find(x-1)); 51 end; 52 end; 53 end.
9.分块
1 type 2 block =record 3 l,r,id :longint; 4 sum,add :int64; 5 end; 6 7 var 8 N,M :longint; 9 i,j,k,opt,x,y,len,tot :longint; 10 z,ans :int64; 11 a :Array[0..100050] of int64; 12 b :array[0..10005] of block; 13 bel :array[0..100050] of longint; 14 15 begin 16 read(N,M); 17 len:=trunc(sqrt(N)); 18 while true do 19 begin 20 inc(tot); 21 b[tot].l:=b[tot-1].r+1; 22 b[tot].r:=b[tot].l+len-1; 23 if b[tot].r>=N then 24 begin 25 b[tot].r:=N; 26 break; 27 end; 28 end; 29 for i:=1 to N do read(a[i]); 30 for i:=1 to tot do 31 begin 32 for j:=b[i].l to b[i].r do 33 begin 34 bel[j]:=i; 35 b[i].sum:=b[i].sum+a[j]; 36 end; 37 end; 38 for k:=1 to M do 39 begin 40 read(opt); 41 if opt=1 then 42 begin 43 read(x,y,z); 44 for i:=bel[x]+1 to bel[y]-1 do b[i].add:=b[i].add+z; 45 if bel[x]=bel[y] then 46 begin 47 for i:=x to y do 48 begin 49 a[i]:=a[i]+z; 50 b[bel[i]].sum:=b[bel[i]].sum+z; 51 end; 52 end else 53 begin 54 for i:=x to b[bel[x]].r do 55 begin 56 a[i]:=a[i]+z; 57 b[bel[i]].sum:=b[bel[i]].sum+z; 58 end; 59 for i:=b[bel[y]].l to y do 60 begin 61 a[i]:=a[i]+z; 62 b[bel[i]].sum:=b[bel[i]].sum+z; 63 end; 64 end; 65 end else 66 begin 67 read(x,y); 68 ans:=0; 69 for i:=bel[x]+1 to bel[y]-1 do ans:=ans+b[i].sum+b[i].add*(b[i].r-b[i].l+1); 70 if (bel[x]=bel[y]) then 71 begin 72 for i:=x to y do ans:=ans+a[i]+b[bel[i]].add; 73 writeln(ans); 74 end else 75 begin 76 for i:=x to b[bel[x]].r do ans:=ans+a[i]+b[bel[i]].add; 77 for i:=b[bel[y]].l to y do ans:=ans+a[i]+b[bel[i]].add; 78 writeln(ans); 79 end; 80 end; 81 end; 82 end.
10.左偏树（可合并堆）
1 var 2 N,M,i,opt,x,y,fx,fy,rt :longint; 3 father,npl,l,r,key :array[0..100050] of longint; 4 flag :Array[0..100050] of boolean; 5 6 procedure swap(var x,y:longint); 7 var 8 z :longint; 9 begin 10 z:=x; 11 x:=y; 12 y:=z; 13 end; 14 15 function comb(r1,r2:longint):longint; 16 begin 17 if r1=0 then exit(r2); 18 if r2=0 then exit(r1); 19 if key[r1]>key[r2] then swap(r1,r2); 20 r[r1]:=comb(r[r1],r2); 21 if npl[l[r1]]<npl[r[r1]] then swap(l[r1],r[r1]); 22 npl[r1]:=npl[r[r1]]+1; 23 exit(r1); 24 end; 25 26 function gf(x:longint):longint; 27 begin 28 if father[x]=x then exit(x); 29 father[x]:=gf(father[x]); 30 exit(father[x]); 31 end; 32 33 begin 34 read(N,M); 35 for i:=1 to N do read(key[i]); 36 for i:=1 to N do father[i]:=i; 37 fillchar(flag,sizeof(flag),true); 38 for i:=1 to M do 39 begin 40 read(opt); 41 if opt=1 then 42 begin 43 read(x,y); 44 if (not flag[x]) or (not flag[y]) then continue; 45 fx:=gf(x); 46 fy:=gf(y); 47 if fx=fy then continue; 48 rt:=comb(fx,fy); 49 father[fx]:=rt; 50 father[fy]:=rt; 51 end else 52 begin 53 read(x); 54 if not flag[x] then 55 begin 56 writeln(-1); 57 continue; 58 end; 59 fx:=gf(x); 60 flag[fx]:=false; 61 writeln(key[fx]); 62 rt:=comb(l[fx],r[fx]); 63 father[l[fx]]:=rt; 64 father[r[fx]]:=rt; 65 father[fx]:=rt; 66 end; 67 end; 68 end.
11.St表
1 var 2 N,M,i,j,x,y,k,len :longint; 3 f :Array[0..100005,0..15] of longint; 4 5 function max(x,y:longint):longint; 6 begin 7 if x>y then exit(x) else exit(y); 8 end; 9 10 begin 11 read(N); 12 for i:=1 to N do read(f[i,0]); 13 for j:=1 to 14 do 14 for i:=1 to N do f[i,j]:=max(f[i,j-1],f[i+(1<<(j-1)),j-1]); 15 read(M); 16 for i:=1 to M do 17 begin 18 read(x,y); 19 inc(x); inc(y); 20 len:=y-x+1; 21 k:=trunc(ln(len)/ln(2)); 22 writeln(max(f[x,k],f[y-(1<<k)+1,k])); 23 end; 24 end.
12.Kmp
1 var 2 s1,s2 :ansistring; 3 next :Array[0..1005] of longint; 4 n,i,j,p,l1,l2 :longint; 5 begin 6 readln(s1); 7 readln(s2); 8 l1:=length(s1); 9 l2:=length(s2); 10 p:=0; 11 for i:=2 to l2 do 12 begin 13 while (p<>0) and (s2[p+1]<>s2[i]) do p:=next[p]; 14 if s2[p+1]=s2[i] then 15 begin 16 inc(p); 17 next[i]:=p; 18 end else next[i]:=0; 19 end; 20 p:=0; 21 for i:=1 to l1 do 22 begin 23 while (p<>0) and (s2[p+1]<>s1[i]) do p:=next[p]; 24 if s2[p+1]=s1[i] then inc(p); 25 if p=l2 then 26 begin 27 writeln(i-l2+1); 28 p:=next[p]; 29 end; 30 end; 31 for i:=1 to l2 do write(next[i],' '); 32 end.
1 var 2 next,ex :array[0..1000050] of longint; 3 N,i :longint; 4 ans :int64; 5 s :ansistring; 6 7 function max(x,y:longint):longint; 8 begin 9 if x>y then exit(x) else exit(y); 10 end; 11 12 procedure get_ex(); 13 var 14 i,j,p,a,k :longint; 15 begin 16 next[1]:=n; 17 a:=0; 18 p:=0; 19 for i:=2 to n do 20 begin 21 j:=next[i-a+1]; 22 if i+j>p then 23 begin 24 j:=max(0,p-i+1); 25 while (i+j<=n) and (s[i+j]=s[j+1]) do inc(j); 26 end; 27 next[i]:=j; 28 if i+j-1>p then 29 begin 30 a:=i; 31 p:=i+j-1; 32 end; 33 end; 34 a:=0; 35 p:=0; 36 for i:=1 to n do 37 begin 38 j:=next[i-a+1]; 39 if i+j>p then 40 begin 41 j:=max(0,p-i+1); 42 while (i+j<=n) and (j+1<=n) and (s[i+j]=s[j+1]) do inc(j); 43 end; 44 ex[i]:=j; 45 if i+j-1>p then 46 begin 47 a:=i; 48 p:=i+j-1; 49 end; 50 end; 51 end; 52 53 begin 54 readln(s); 55 N:=length(s); 56 get_ex; 57 for i:=1 to N do ans:=ans+ex[i]; 58 writeln(ans); 59 end.
13.String-Hash
1 const base=29; 2 var 3 T,N,i,j,L,LL,ans :longint; 4 hash,np :array[0..1000005] of qword; 5 k :qword; 6 s1,s2 :ansistring; 7 a,b :Array[0..1000005] of longint; 8 begin 9 readln(T); 10 np[0]:=1; 11 for i:=1 to 1000000 do np[i]:=np[i-1]*base; 12 while T>0 do 13 begin 14 dec(T); 15 readln(s1); L:=length(s1); 16 readln(s2); LL:=length(s2); 17 ans:=0; 18 for i:=1 to L do a[i]:=ord(s1[i])-ord('a')+1; 19 for i:=1 to LL do b[i]:=ord(s2[i])-ord('a')+1; 20 k:=0; 21 for i:=L downto 1 do k:=k*base+a[i]; 22 hash[LL+1]:=0; 23 for i:=LL downto 1 do hash[i]:=hash[i+1]*base+b[i]; 24 for i:=1 to LL do 25 begin 26 if i+L-1>LL then break; 27 j:=i+L-1; 28 if (hash[i]-hash[j+1]*np[L]=k) then inc(ans); 29 end; 30 writeln(ans); 31 end; 32 end.
14.后缀数组---最长回文子串
1 var 2 N,m,i,ans,jud :longint; 3 a,t,y,sa,height,rank,c,r :Array[0..400050] of longint; 4 s :ansistring; 5 6 function max(x,y:longint):longint; 7 begin 8 if x>y then exit(x) else exit(y); 9 end; 10 11 procedure swap(var x,y:longint); 12 var 13 z :longint; 14 begin 15 z:=x; 16 x:=y; 17 y:=z; 18 end; 19 20 function cmp(a,b,j:longint):boolean; 21 begin 22 exit((a+j<=n) and (b+j<=n) and (y[a]=y[b]) and (y[a+j]=y[b+j])); 23 end; 24 25 procedure getsa(); 26 var 27 i,j,p :longint; 28 begin 29 for i:=0 to m do c[i]:=0; 30 for i:=1 to n do begin r[i]:=a[i]; inc(c[r[i]]); end; 31 for i:=1 to m do c[i]:=c[i]+c[i-1]; 32 for i:=n downto 1 do begin sa[c[r[i]]]:=i; dec(c[r[i]]); end; 33 j:=1; 34 while j<=n do 35 begin 36 p:=0; 37 for i:=n-j+1 to n do begin inc(p); y[p]:=i; end; 38 for i:=1 to n do if sa[i]>j then begin inc(p); y[p]:=sa[i]-j; end; 39 for i:=0 to m do c[i]:=0; 40 for i:=1 to n do inc(c[r[y[i]]]); 41 for i:=1 to m do c[i]:=c[i]+c[i-1]; 42 for i:=n downto 1 do begin sa[c[r[y[i]]]]:=y[i]; dec(c[r[y[i]]]); end; 43 for i:=1 to n do swap(r[i],y[i]); 44 p:=1; 45 r[sa[1]]:=p; 46 for i:=2 to n do if (cmp(sa[i],sa[i-1],j)) then r[sa[i]]:=p else begin inc(p); r[sa[i]]:=p; end; 47 if p>=n then break; 48 m:=p; 49 j:=j<<1; 50 end; 51 end; 52 53 procedure getheight(); 54 var 55 i,j,k :longint; 56 begin 57 for i:=1 to n do rank[sa[i]]:=i; 58 k:=0; 59 for i:=1 to n do 60 begin 61 if k>0 then dec(k); 62 if rank[i]=1 then continue; 63 j:=sa[rank[i]-1]; 64 while (i+k<=n) and (j+k<=n) and (a[i+k]=a[j+k]) do inc(k); 65 height[rank[i]]:=k; 66 end; 67 end; 68 69 begin 70 readln(N); jud:=N; 71 readln(s); 72 for i:=1 to N do 73 begin 74 a[i]:=ord(s[i])-ord('a')+1; 75 m:=max(m,a[i]); 76 end; 77 a[N+1]:=0; 78 for i:=1 to n do a[n*2+2-i]:=a[i]; 79 n:=n*2+1; 80 getsa(); 81 getheight(); 82 for i:=1 to n do 83 if (height[i]>ans) and (((sa[i]>jud) and (sa[i-1]<jud)) or ((sa[i]<jud) and (sa[i-1]>jud))) then ans:=height[i]; 84 writeln(ans); 85 end.
15.FFT---大数乘法
1 type 2 cp =record 3 r,i :double; 4 end; 5 6 var 7 s1,s2 :ansistring; 8 a,b :array[0..1000050] of cp; 9 sum :array[0..1000050] of longint; 10 l1,l2,l,i,j,t :longint; 11 12 function max(x,y:longint):longint; 13 begin 14 if x>y then exit(x) else exit(y); 15 end; 16 17 function jia(a,b:cp):cp; 18 var 19 z :cp; 20 begin 21 z.r:=a.r+b.r; 22 z.i:=a.i+b.i; 23 exit(z); 24 end; 25 26 function jian(a,b:cp):cp; 27 var 28 z :cp; 29 begin 30 z.r:=a.r-b.r; 31 z.i:=a.i-b.i; 32 exit(z); 33 end; 34 35 function mul(a,b:cp):cp; 36 var 37 z :cp; 38 begin 39 z.r:=a.r*b.r-a.i*b.i; 40 z.i:=a.r*b.i+a.i*b.r; 41 exit(z); 42 end; 43 44 procedure swap(var x,y:cp); 45 var 46 z :cp; 47 begin 48 z:=x; 49 x:=y; 50 y:=z; 51 end; 52 53 procedure BRC(var a:array of cp; l:longint); 54 var 55 i,j,k :longint; 56 begin 57 k:=0; 58 for i:=1 to l-2 do 59 begin 60 j:=l>>1; 61 while k>=j do 62 begin 63 k:=k xor j; 64 j:=j>>1; 65 end; 66 k:=k or j; 67 if i<k then swap(a[i],a[k]); 68 end; 69 end; 70 71 procedure FFT(var a:array of cp; l,flag:longint); 72 var 73 i,j,h :longint; 74 wn,w,t :cp; 75 begin 76 BRC(a,l); 77 h:=2; 78 while h<=l do 79 begin 80 wn.r:=cos(flag*2*pi/h); 81 wn.i:=sin(flag*2*pi/h); 82 j:=0; 83 while j<l do 84 begin 85 w.r:=1; w.i:=0; 86 for i:=j to j+(h>>1)-1 do 87 begin 88 t:=mul(w,a[i+(h>>1)]); 89 a[i+(h>>1)]:=jian(a[i],t); 90 a[i]:=jia(a[i],t); 91 w:=mul(w,wn); 92 end; 93 j:=j+h; 94 end; 95 h:=h<<1; 96 end; 97 if flag=-1 then 98 begin 99 for i:=0 to l-1 do a[i].r:=a[i].r/l; 100 end; 101 end; 102 103 begin 104 readln(s1); l1:=length(s1); 105 readln(s2); l2:=length(s2); 106 l:=1; 107 while l<max(l1,l2)*2 do l:=l<<1; 108 for i:=1 to l1 do 109 begin 110 a[l1-i].r:=ord(s1[i])-48; 111 a[l1-i].i:=0; 112 end; 113 for i:=1 to l2 do 114 begin 115 b[l2-i].r:=ord(s2[i])-48; 116 b[l2-i].i:=0; 117 end; 118 FFT(a,l,1); 119 FFT(b,l,1); 120 for i:=0 to l-1 do a[i]:=mul(a[i],b[i]); 121 FFT(a,l,-1); 122 for i:=0 to l-1 do sum[i]:=trunc(a[i].r+0.5); 123 for i:=0 to l-1 do 124 begin 125 sum[i+1]:=sum[i+1]+(sum[i] div 10); 126 sum[i]:=sum[i] mod 10; 127 end; 128 t:=l; 129 while (sum[t]=0) and (t>0) do dec(t); 130 for i:=t downto 0 do write(sum[i]);writeln; 131 end.
16.Tarjan
1 var 2 iscut :array[0..100050] of boolean; 3 dfn,low :array[0..100050] of longint; 4 pre,last,other,len :Array[0..200050] of longint; 5 N,M,i,x,y,L,time,ans :longint; 6 7 function min(x,y:longint):longint; 8 begin 9 if x<y then exit(x) else exit(y); 10 end; 11 12 procedure add(u,v:longint); 13 begin 14 inc(L); 15 pre[L]:=last[u]; 16 last[u]:=L; 17 other[L]:=v; 18 end; 19 20 procedure tarjan(x,fa:longint); 21 var 22 tot,p,q :longint; 23 begin 24 inc(time); 25 dfn[x]:=time; 26 low[x]:=time; 27 tot:=0; 28 p:=last[x]; 29 while p<>0 do 30 begin 31 q:=other[p]; 32 if dfn[q]=0 then 33 begin 34 inc(tot); 35 tarjan(q,x); 36 low[x]:=min(low[x],low[q]); 37 if low[q]>=dfn[x] then iscut[x]:=true; 38 end else if (dfn[q]<dfn[x]) and (q<>fa) then low[x]:=min(low[x],dfn[q]); 39 p:=pre[p]; 40 end; 41 if (fa<0) and (tot=1) then iscut[x]:=false; 42 end; 43 44 begin 45 read(N,M); 46 for i:=1 to M do 47 begin 48 read(x,y); 49 add(x,y); 50 add(y,x); 51 end; 52 for i:=1 to N do if (dfn[i]=0) then tarjan(i,-1); 53 for i:=1 to N do if (iscut[i]) then inc(ans); 54 writeln(ans); 55 for i:=1 to N do if (iscut[i]) then write(i,' '); 56 end.
1 var 2 T,N,M,L,i,x,y,time,ans,cnt,k :longint; 3 pre,last,other :array[0..200050] of longint; 4 dfn,low :array[0..15050] of longint; 5 iscut :Array[0..100050] of boolean; 6 7 function min(x,y:longint):longint; 8 begin 9 if x<y then exit(x) else exit(y); 10 end; 11 12 procedure add(u,v:longint); 13 begin 14 inc(L); 15 pre[L]:=last[u]; 16 last[u]:=L; 17 other[L]:=v; 18 end; 19 20 procedure tarjan(x,fa:longint); 21 var 22 p,q :longint; 23 begin 24 inc(time); 25 dfn[x]:=time; 26 low[x]:=time; 27 p:=last[x]; 28 while p<>0 do 29 begin 30 q:=other[p]; 31 if dfn[q]=0 then 32 begin 33 tarjan(q,p); 34 low[x]:=min(low[x],low[q]); 35 if low[q]>dfn[x] then iscut[p>>1]:=true; 36 end else if ((p xor 1)<>fa) then low[x]:=min(low[x],dfn[q]); 37 p:=pre[p]; 38 end; 39 end; 40 41 42 begin 43 read(T); 44 for k:=1 to T do 45 begin 46 fillchar(dfn,sizeof(dfn),0); 47 fillchar(low,sizeof(low),0); 48 fillchar(last,sizeof(last),0); 49 fillchar(iscut,sizeof(iscut),false); 50 ans:=0; 51 time:=0; 52 L:=1; 53 read(N,M); 54 for i:=1 to M do 55 begin 56 read(x,y); 57 add(x,y); 58 add(y,x); 59 end; 60 for i:=1 to N do if (dfn[i]=0) then tarjan(i,-1); 61 for i:=1 to M do if (iscut[i]) then inc(ans); 62 writeln(ans); 63 cnt:=0; 64 for i:=1 to M do 65 begin 66 if iscut[i] then 67 begin 68 inc(cnt); 69 if cnt<>ans then write(i,' ') else writeln(i); 70 end; 71 end; 72 if k<>t then 73 begin 74 writeln; 75 end; 76 end; 77 end.
17.Hungary
1 var 2 N,M,E,i,j,vis_cnt,x,y,ans :longint; 3 son :Array[0..1005,0..1005] of longint; 4 link :Array[0..1005] of longint; 5 vis :array[0..1005] of longint; 6 7 function dfs(x:longint):boolean; 8 var 9 i,j :longint; 10 begin 11 for i:=1 to son[x,0] do 12 begin 13 if vis[son[x,i]]=vis_cnt then continue; 14 vis[son[x,i]]:=vis_cnt; 15 if (link[son[x,i]]=0) or (dfs(link[son[x,i]])) then 16 begin 17 link[son[x,i]]:=x; 18 exit(true); 19 end; 20 end; 21 exit(false); 22 end; 23 24 begin 25 read(N,M,E); 26 for i:=1 to E do 27 begin 28 read(x,y); 29 if (x>N) or (y>M) then continue; 30 inc(son[x,0]); 31 son[x,son[x,0]]:=y; 32 end; 33 for i:=1 to N do 34 begin 35 inc(vis_cnt); 36 if dfs(i) then inc(ans); 37 end; 38 writeln(ans); 39 end.
1 二分图的一些定理： 2 (1) 最小点覆盖=最大匹配 3 (2) 最小边覆盖=图中点的个数-最大匹配 4 (3) 最大独立集=图中点的个数-最大匹配 5 (4) DAG最小不相交路径覆盖=原图的节点数-新图的匹配数 （把原图中的每个点拆成Vx和Vy，如果有一条边A-->B，那么就加边Ax-->By 这样就得到一个二分图）。 6 (5) DAG最小可相交路径覆盖，先用Floyd求出原图的传递闭包，如果A,B联通，则连边A-->B，这样问题就转化成了DAG最小不相交路径覆盖问题了。
18.数论相关
中国剩余定理内容 对于同余方程组 x=ai (mod mi) 在模M=m1m2...mi 意义下有唯一解 解为x=sigma(aiMi(Mi-1)) 其中Mi=M/mi，Mi-1为Mi关于mi的逆元
c(n,m)%p = c(n%p,m%p)*c(n/p,m/p)
Millar Rabin素数测试内容： (1) 费马小定理：对于素数p和任意整数a，总有a^(p-1)=1 (mod p) 相反，若数p满足a^(p-1)=1 (mod p) 那么p也几乎是素数 (2) Miller Rabin测试：不断选取a，测试a^(p-1) ?=1 (mod p)，若选取多个a测试都成立则p是素数，若有一次不成立则p是合数。 选取前20个质数作为a进行测试就能保证在2^63范围内质数检测不出错
1 const eps=1e-8; 2 var 3 N,i,j,k,cur :longint; 4 p :double; 5 a :array[0..105,0..105] of double; 6 7 procedure swap(var x,y:double); 8 var 9 z :double; 10 begin 11 z:=x; 12 x:=y; 13 y:=z; 14 end; 15 16 begin 17 read(N); 18 for i:=1 to N do 19 for j:=1 to N+1 do read(a[i,j]); 20 for i:=1 to N do 21 begin 22 cur:=i; 23 for j:=i+1 to N do if abs(a[j,i])>abs(a[cur,i]) then cur:=j; 24 if abs(a[cur,i])<=eps then 25 begin 26 writeln('No Solution'); 27 halt; 28 end; 29 if cur<>i then for j:=i to N+1 do swap(a[i,j],a[cur,j]); 30 for j:=i+1 to N do 31 begin 32 p:=-(a[j,i]/a[i,i]); 33 for k:=i to N+1 do a[j,k]:=a[j,k]+p*a[i,k]; 34 end; 35 for j:=1 to i-1 do 36 begin 37 p:=-(a[j,i]/a[i,i]); 38 for k:=i to N+1 do a[j,k]:=a[j,k]+p*a[i,k]; 39 end; 40 end; 41 for i:=1 to n do writeln(a[i,n+1]/a[i,i] :0 :2); 42 end.
1 var 2 a,b :longint; 3 x,y :longint; 4 5 procedure exgcd(a,b:longint; var x,y:longint); 6 var 7 t :longint; 8 begin 9 if b=0 then 10 begin 11 x:=1; 12 y:=0; 13 exit; 14 end; 15 exgcd(b,a mod b,x,y); 16 t:=x; 17 x:=y; 18 y:=t-(a div b)*y; 19 end; 20 21 22 begin 23 read(a,b); 24 exgcd(a,b,x,y); 25 while x<=0 do inc(x,b); 26 writeln(x); 27 end.
19.点分治
1 var 2 n,k,x,y,z,i,l,sum,l1,l2,vis_cnt :longint; 3 ans :int64; 4 pre,last,other,len :array[0..20050] of longint; 5 vis :array[0..10050] of longint; 6 list,d,father,size :array[0..10050] of longint; 7 8 function max(x,y:longint):longint; 9 begin 10 if x>y then exit(x) else exit(y); 11 end; 12 13 procedure swap(var x,y:longint); 14 var 15 z :longint; 16 begin 17 z:=x; 18 x:=y; 19 y:=z; 20 end; 21 22 procedure add(u,v,r:longint); 23 begin 24 inc(l); 25 pre[l]:=last[u]; 26 last[u]:=l; 27 other[l]:=v; 28 len[l]:=r; 29 end; 30 31 procedure sort(l,r:longint); 32 var 33 i,j,x :longint; 34 begin 35 i:=l; j:=r; x:=d[list[(l+r)>>1]]; 36 while i<j do 37 begin 38 while d[list[i]]<x do inc(i); 39 while d[list[j]]>x do dec(j); 40 if i<=j then 41 begin 42 swap(list[i],list[j]); 43 inc(i); 44 deC(j); 45 end; 46 end; 47 if i<r then sort(i,r); 48 if j>l then sort(l,j); 49 end; 50 51 procedure dfs1(x,fa:longint); 52 var 53 p,q :longint; 54 begin 55 size[x]:=1; 56 inc(sum); 57 list[sum]:=x; 58 p:=last[x]; 59 while p<>0 do 60 begin 61 q:=other[p]; 62 if (q<>fa) and (vis[q]<>vis_cnt) then 63 begin 64 dfs1(q,x); 65 father[q]:=x; 66 size[x]:=size[x]+size[q]; 67 end; 68 p:=pre[p]; 69 end; 70 end; 71 72 73 function get_root(x,fa:longint):longint; 74 var 75 i,pl,t,dd,q,p,cur :longint; 76 begin 77 sum:=0; 78 dfs1(x,fa); 79 t:=maxlongint; 80 for i:=1 to sum do 81 begin 82 dd:=0; 83 cur:=list[i]; 84 p:=last[cur]; 85 while p<>0 do 86 begin 87 q:=other[p]; 88 if (q<>father[cur]) and (vis[q]<>vis_cnt) then dd:=max(dd,size[q]); 89 p:=pre[p]; 90 end; 91 if cur<>x then dd:=max(dd,size[x]-size[cur]); 92 if dd<t then 93 begin 94 pl:=cur; 95 t:=dd; 96 end; 97 end; 98 exit(pl); 99 end; 100 101 procedure dfs2(x,fa,w:longint); 102 var 103 p,q :longint; 104 begin 105 inc(l1); 106 list[l1]:=x; 107 d[x]:=w; 108 p:=last[x]; 109 while p<>0 do 110 begin 111 q:=other[p]; 112 if (q<>fa) and (vis[q]<>vis_cnt) then dfs2(q,x,w+len[p]); 113 p:=pre[p]; 114 end; 115 end; 116 117 function get_ans(l,r:longint):longint; 118 var 119 summ,i,j :longint; 120 begin 121 summ:=0; 122 j:=r; 123 for i:=l to r do 124 begin 125 while (d[list[i]]+d[list[j]]>k) and (j>i) do dec(j); 126 if i>=j then break; 127 summ:=summ+j-i; 128 end; 129 exit(summ); 130 end; 131 132 procedure work(x,fa:longint); 133 var 134 rt,p,q :longint; 135 begin 136 rt:=get_root(x,fa); 137 l1:=0; 138 l2:=0; 139 vis[rt]:=vis_cnt; 140 p:=last[rt]; 141 while p<>0 do 142 begin 143 q:=other[p]; 144 if vis[q]=vis_cnt then 145 begin 146 p:=pre[p]; 147 continue; 148 end; 149 l2:=l1; 150 dfs2(q,rt,len[p]); 151 sort(l2+1,l1); 152 ans:=ans-get_ans(l2+1,l1); 153 p:=pre[p]; 154 end; 155 inc(l1); 156 list[l1]:=rt; 157 d[rt]:=0; 158 sort(1,l1); 159 ans:=ans+get_ans(1,l1); 160 p:=last[rt]; 161 while p<>0 do 162 begin 163 q:=other[p]; 164 if (vis[q]<>vis_cnt) then work(q,rt); 165 p:=pre[p]; 166 end; 167 end; 168 169 begin 170 read(n,k); 171 while (n+k>0) do 172 begin 173 fillchar(last,sizeof(last),0); 174 inc(vis_cnt); 175 l:=0; ans:=0; 176 for i:=1 to n-1 do 177 begin 178 read(x,y,z); 179 add(x,y,z); 180 add(y,x,z); 181 end; 182 work(1,-1); 183 write(ans); 184 read(n,k); 185 if n+k>0 then writeln; 186 end; 187 end.