noip基本算法网络版.docx
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noip基本算法网络版
生成序列
01序列
Procedurepoducer1（n:
integer）;
VarI,j:
integer;
B:
array[0..100]ofinteger;
Begin
B[0]:
=0;
Whileb[0]=0do
Begin
I:
=n;
Whileb[i]=1dodec（i）;
B[i]:
=1;
Forj:
=I+1tondo
B[j]:
=0;
End;
End;
全排列
Procedureproducer2（n:
integer）;
Varx,I,j,p,min:
integer;
B:
array[0..100]ofinteger;
Begin
Fori:
=1tondo
B[i]:
=I;
B[0]:
=0;
Whileb[0]=0do
Begin
I:
=n;
Whileb[i]Ifi=0thenbreak;
Min:
=n+1;p:
=0;
Forj:
=itondo
If（min>b[j]）and（b[j]>b[i-1]）then
Begin
P:
=j;min:
=b[j];
End;
X:
=b[p];b[p]:
=b[i-1];b[i-1]:
=x;
Forj:
=Ito（n+i）div2do
Begin
X:
=b[j];b[j]:
=b[n+i-j];b[n+i-j]:
=x;
End;
End;
End;
组合
Procedureproducer3（n,m:
integer）;
VarI,j:
integer;
B:
array[0..100]ofinteger;
Begin
Fori:
=1tomdo
B[i]:
=I;
B[0]:
=0;
Whileb[0]=0do
Begin
I:
=m;
Whileb[i]=n+i-mdodec（i）;
Ifi=0thenbreak;
Inc（b[i]）;
Forj:
=I+1tomdo
B[j]:
=b[j-1]+1;
End;
End;
数论
素数的判断
朴素算法
Functionisprime（n:
longint）:
boolean;
Vari:
longint;
Begin
Isprime:
=true;
Fori:
=2totrunc（sqrt（n））do
Ifnmodi=0then
Begin
Isprime:
=false;
Exit;
End;
Ifi=1thenisprime:
=false;
End;
Miller_Rabbin
Functionmiller_rabbin（p:
longint）:
boolean;;
VarI,x:
longint;
Begin
Miller_rabbin:
=true;
Randomize;
Fori:
=1to30do
Begin
X:
=trunc（random*100+1）;
Ifmodular（x,p-1,p）<>1then//**a^（p-1）modp
Begin
Miller_Rabbin:
=false;
Exit;
End;
End;
Ifp=1thenmiller_rabbin:
=false;
End;
分治求a^bmodc
Functionmodular（a,b,c:
longint）:
longint;
VarI,j,len:
longint;
Bin:
array[1..50]ofinteger;
Begin
Ifb<=1then
Begin
Ifb=1thenmodular:
=amodc;
Ifb=0thenmodular:
=1;
Exit;
End;
Len:
=0;
J:
=b;
Whilej<>0do
Begin
Inc（i）;
Bin[i]:
=jand1;
Bin[i]:
=jshr1;
End;
J:
=a;
Fori:
=len-1downto1do
Begin
J:
=jmodc*jmodc;
Ifbin[i]=1thenj:
=amodc*jmodc;
End;
Modular:
=j;
End;
欧几里德辗转相除法
Functiongcd（va,vb:
longint）:
longint;
Varr:
longint;
Begin
Whilevamodvb<>0do
Begin
R:
=vamodvb;
Va:
=vb;vb:
=r;
End;
Gcd:
=vb;
End;
进制转换
Functionchange（a:
string;dx,dy:
longint）:
string;
Vartemp:
string;
Len,I,j,x,t:
longint;
Begin
T:
=0;temp:
=’’;
Len:
=length（a）;j:
=1;
Fori:
=lendownto1do
Begin
If（a[i]>=’A’）and（a[i]<=’F’）thenx:
=ord（a[i]）-55elsex:
=ord（a[i]）-48;
T:
=t+x*j;
T:
=t*dx;
End;
Whilet<>0do
Begin
X:
=tmoddy;
If（x>=10）and（x<=15）thentemp:
=temp+chr（x+55）elsetemp:
=temp+chr（x+48）;
T:
=tdivdy;
End;
Iftemp=’’thenchange:
=’0’elsechange:
=temp;
End;
高精度计算
Procedureplus_part;
Begin
Ifla>lbthenlc:
=laelselc:
=lb;
Fori:
=1tolcdo
Begin
C[i]:
=a[i]+b[i];
C[i+1]:
=c[i+1]+c[i]div1000;
C[i]:
=c[i]mod1000;
End;
End;
Procedureminus_part;
Begin
Ifla>lbthenlc:
=laelselc:
=lb;
Fori:
=1tolcdo
Begin
C[i]:
=a[i]-b[i];
Ifc[i]<0then
Begin
C[i+1]:
=c[i+1]-1;
C[i]:
=c[i]+1000;
End;
End;
End;
Proceduremult_part;
Begin
Fori:
=1tolado
Forj:
=1tolbdo
Begin
C[la+lb-1]:
=c[la+lb-1]+a[i]*b[j];
C[la+lb]:
=c[la+lb]+c[la+lb-1]div1000;
C[la+lb-1]:
=c[la+lb-1]mod1000;
End;
End;
二分法BinarySearch
Procedurebinary_search;
begin
left:
=1;right:
=n+1;c:
=0;
whileleft<=rightdo
begin
mid:
=（left+right）div2;
iff[mid]=1then
begin
right:
=mid-1;
c:
=mid;
end
else
begin
left:
=mid+1;
c:
=mid+1;
end;
end;
end;
排序
直接选择排序insertionsort
Procedureinsertion_sort;
Begin
Fori:
=1tondo
Begin
J:
=1;
While（ja[j]）doinc（j）;
X:
=a[i];
Fork:
=jtoI-1do
A[k+1]:
=a[k];
A[j]:
=x;
End;
End;
快速排序Quicksort
Procedureqsort（be,en:
longint）;
VarI,j,x,mid,temp:
longint;
Begin
I:
=be;j:
=en;mid:
=（i+j）div2;
X:
=a[mid];
Repeat
Whilex>a[i]doinc（i）;
WhilexIfi<=jthen
Begin
Temp:
=a[i];a[i]:
=a[j];a[j]:
=temp;
Inc（i）;dec（j）;
End;
Untili>j;
IfiIfbeEnd;
Procedurequicksort
Begin
Fori:
=1tondo
Read（a[i]）;
Qsort（1,n）;
End;
堆排序Heapsort
Procedureheapsort;
Begin
Heapn:
=0;
Fori:
=1tondo
Begin
read（x）;
Insert（x）;//**Heap
End;
Fori:
=1tondo
Delete
（1）;//**Heap
End;
矩阵matrix
Procedurematrix;
Begin
Fori:
=1tondo
Forj:
=1tomdo
Fork:
=1totdo
C[I,j]:
=c[I,j]+a[I,k]*b[k,j];
End;
并查集Find_UnionSet
Functionfind（x:
longint）:
longint;
Varvi,vj,sum:
longint;
Temp:
array[1..10000]oflongint;
Begin
Sum:
=0;
Inc（sum）;
Temp[sum]:
=x;
Vi:
=x;
Whilex<>sset[x]do
Begin
Inc（sum）;
Temp[sum]:
=sset[x];
X:
=sset[x];
End;
Forvj:
=1tosumdo
Sset[temp[vj]]:
=x;
Find:
=x;
End;
Procedurefind_unionset;
Begin
Iffind（x）=find（y）thenwriteln（‘YES’）
Else
Begin
X:
=find（x）;y:
=find（y）;
Sset[x]:
=sset[y];
Writeln（‘NO’）;
End;
End;
树结构
排序二叉树BST
Procedureinsert（x:
longint）;
Varp,q,s:
point;
Begin
New（p）;p:
=root;new（q）;q:
=nil;
New（s）;s^.data:
=x;s^.left:
=nil;s^.right:
=nil;
Flag:
=true;
Whileflagand（p<>nil）do
Begin
Q:
=p;
Ifp^.data>s^.datathenp:
=p^.left
Else
Ifp^.data=p^.right
Else
Begin
Flag:
=false;
Exit;
End;
End;
Ifs^.data>q^.datathenq^.right:
=selseq^.left:
=s;
Dispose（p）;dispose（q）;
End;
Procedurebst;
Begin
New（root）;
Root^.left:
=nil;root^.right:
=nil;
Read（x）;
Root^.data:
=x;
Fori:
=2ton-1do
Begin
Read（x）;
Insert（x）;
End;
End;
二叉堆Heap
Procedureinsert（x:
longint）;
VarI,j:
longint;
Begin
Inc（heapn）;
Heap[heapn]:
=x;
I:
=heapn;j:
=Idiv2;
While（j>0）and（heap[i]>heap[j]）do
Begin
Temp:
=heap[i];heap[i]:
=heap[j];heap[j]:
=temp;
I:
=j;j:
=jdiv2;
End;
End;
Proceduredelete（k:
longint）;
VarI,j:
longint;
Begin
Heap[k]:
=heap[heapn];
Dec（heapn）;
I:
=k;j:
=k*2;
If（j+1<=heapn）and（heap[j]While（j<=heapn）and（heap[i]Begin
Temp:
=heap[i];heap[i]:
=heap[j];heap[j]:
=temp;
I:
=j;j:
=j*2;
If（j+1<=heapn）and（heap[j]End;
End;
Procedureheap;
Begin
Heapn:
=0;
fori:
=1tondo
begin
readln（x）;
insert（x）;
end;
fori:
=ndownto1do
delete（i）;
end;
图论
最短路径Floyed
Procedurefloyed;
Begin
Fork:
=1tondo
Fori:
=1tondo
Forj:
=1tondo
If（i<>j）and（i<>k）and（k<>j）and（g[i,k]+g[k,j]G[I,j]:
=g[I,k]+g[k,j];
End;
最短路径Dijkstra
Proceduredijkstra;
Begin
Fork:
=1ton-1do
Begin
I:
=0;min:
=maxlongint;
Forj:
=1tondo
If（hash[j]=0）and（dis[j]Begin
Min:
=dis[j];
I:
=j;
End;
Ifi=0thenexit;
Hash[i]:
=1;
Forj:
=1tondo
If（hash[j]=0）and（dis[i]+g[I,j]Dis[j]:
=dis[i]+g[I,j];
End;
End;
最短路径Bellman_Ford
Procedurebellmanford;
Begin
Repeat
Flag:
=true;
Fori:
=1tomdo
Begin
X:
=line[i].x;y:
=line[i].y;w:
=line[i].w;
Ifdis[x]+wBegin
Dis[y]:
=dis[x]+w;
Flag:
=false;
End;
End;
Untilflag;
End;
最短路径SPFA
Procedurespfa;
Begin
Front:
=0;rear:
=1;
Q[1]:
=s;hash[s]:
=1;
Whilefront<>reardo
Begin
X:
=q[（front+1）modmaxn];
Ifstartv[x]<>0then
Fori:
=startv[x]toendv[x]do
Begin
Y:
=line[i].y;w:
=line[i].w;
Ifdis[x]>dis[y]+wthen
Begin
Dis[x]:
=dis[y]+w;
Ifhash[y]=0then
Begin
Hash[y]:
=1;
Rear:
=（rear+1）modmaxn;
Q[rear]:
=y;
End;
End;
End;
Front:
=（front+1）modmaxn;
Hash[x]:
=0;
End;
End;
MST问题Prim
Procedureprim;
Begin
fori:
=1ton-1do
begin
line[i].x:
=1;line[i].y:
=i+1;line[i].w:
=g[1,i+1];
end;
fork:
=1ton-1do
begin
min:
=maxlongint;i:
=0;
forj:
=ktondo
ifline[j].wbegin
min:
=line[j].w;i:
=j;
end;
ifi=0thenexit;
temp:
=line[i];line[i]:
=line[k];line[k]:
=temp;
x:
=line[k].y;
forj:
=k+1ton-1do
begin
y:
=line[j].y;w:
=g[x,y];
ifwbegin
line[i].w:
=w;
line[i].x:
=x;
end;
end;
end;
End;
MST问题Kruscal
Procedurekruscal;
Begin
Qsort（1,m）;//**Quicksort
Sum:
=0;count:
=0;
Forj:
=1tomdo
Begin
X:
=find（line[i].x）;y:
=find（line[i].y）;
Ifx<>ythen
Begin
Sset[x]:
=sset[y];//**Find_UnionSet
Inc（count,line[i].w）;
Inc（sum）;
Ifsum=n-1thenbreak;
End;
End;
End;
Euler图
Procedurefind（x:
longint）;
VarI:
longint;
Begin
Ifoutdegree[x]=0then
Begin
Inc（sum）;
Cnt[sum]:
=x;
End
Else
Begin
Fori:
=1tondo
Ifg[x,i]<>0then
Begin
G[x,i]:
=0;
Dec（outdegree[x]）;
Find（i）;
End;
Inc（sum）;
Cnt[sum]:
=x;
End;
End;
Procedureeuler;
Begin
Sum:
=0;
Fori:
=1tondo
Ifodd（outdegree[i]）thenbeginfind（i）;exit;end;
Find
（1）;
End;
AOV网（topo_sort）
Proceduretopo_sort;
Begin
Front:
=1;rear:
=0;
fori:
=1tondo
Ifindegree[i]=0then
Begin
Inc（rear）;
Q[rear]:
=I;
End;
Whilefront<=reardo
Begin
X:
=q[front];
Fori:
=1tondo
Ifg[x,i]<>0then
Begin
Dec（indegree[i]）;
Ifindegree[i]=0then
Begin
Inc（rear）;
Q[rear]:
=I;
End;
End’
Inc（front）;
End;
End;
AOE网
ProcedureAOE;
Begin
line1:
=line;
front:
=1;rear:
=0;
fori:
=1tondo
ifindegree[i]=0then
begin
inc（rear）;
q[rear]:
=i;
early[i]:
=0;
end;
whilefront<=reardo
begin
x:
=q[front];
ifstartv[x]<>0then
fori:
=startv[x]toendv[x]do
begin
y:
=line[i].y;
w:
=line[i].w;
dec（indeg[y]）;
ifindeg[y]=0then
begin
inc（rear）;
q[rear]:
=y;
end;
ifearly[y]early[y]:
=early[x]+w;
end;
inc（front）;
end;
line:
=line1;
fori:
=1tondo
last[i]:
=maxint;
last[q[rear]]:
=early[q[rear]];
fori:
=rear-1downto1do
begin
x:
=q[i];
ifstartv[x]<>0then
forj:
=startv[x]toendv[x]do
iflast[x]>last[line[j].y]-line[j].wthen
last[x]:
=last[line[j].y]-line[j].w;
end;
end;
网络流Ford_Fulkson
Functionfindpath:
boolean;
vari,x:
longint;
begin
can:
=0;
hash[s]:
=maxint;
q[1]:
=s;front:
=1;rear:
=1;
whilefront<=reardo
begin
x:
=q[front];
fori:
=1tondo
if（hash[i]=0）and（c[x,i]-f[x,i]>0）and（min（hash[x],c[x,i]-f[x,i]）>hash[i]）then
begin
in
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