NOIP模板
2024-08-28 01:00:52
快排
procedure qsort(l,r:longint);
var i,j,t,m:longint;
begin i:=l; j:=r;
m:=a[(i+j) div ];
repeat
while a[i]<m do inc(i);
while m<a[j] do dec(j);
if i<=j then
begin t:=a[i]; a[i]:=a[j]; a[j]:=t;
inc(i); dec(j); end; until i>j;
if i<r then qsort(i,r); if j>l then qsort(l,j); end;
堆
1.数组开两倍
procedure insert(x:longint);
var t,s,v:longint;
begin
len:=len+; f[len]:=x; s:=len;
while (s<>)and(f[s div ]>f[s]) do
begin
v:=f[s div ]; f[s div ]:=f[s]; f[s]:=v;
s:=s div ;
end;
end;
function get:longint;
var t,s,v:longint;
begin
get:=f[]; f[]:=f[len]; len:=len-; t:=;
while (t*<=len)or(t*+<=len) do
begin
if (t*+>len)or(f[t*]<f[t*+])
then s:=t* else s:=t*+;
if f[t]>f[s] then
begin
v:=f[t]; f[t]:=f[s]; f[s]:=v; t:=s;
end
else break;
end;
end;
欧拉函数(单个数值)
function phi(x:longint):longint;
var ans,i:longint;
begin
ans:=x;
for i:= to trunc(sqrt(x)) do
begin
if x mod i= then ans:=ans div i*(i-);
while x mod i= do x:=x div i;
end;
if x<> then ans:=ans div x*(x-);
exit(ans);
end;
欧拉函数(批量处理)
procedure work;
var i,j:longint;
begin
p:=;
for i:= to n do e[i]:=i;
for i:= to n do
if e[i]=i then
begin j:=i;
while j<=n do begin e[j]:=e[j] div i*(i-); inc(j,i); end;
end;
for i:= to n do
begin
if e[i]=i- then begin inc(p); prime[p]:=i; end;
end;
end;
质数筛法
procedure work(n:longint);
var i,j:longint;
begin
num:=;
for i:= to n do g[i]:=true;
for i:= to n do
if g[i]=true then
begin
inc(num); prime[num]:=i;
j:=i*;
while j<=n do begin g[j]:=false; j:=j+i; end;
end;
end;
质因数分解
procedure fenjie(x:longint);
var i,y:longint;
begin
t:=;y:=x;
for i:= to num do
begin
if prime[i]>y div then exit;
if x mod prime[i]= then
begin
inc(t); w[t]:=prime[i];
while x mod prime[i]= do x:=x div prime[i];
end;
if x= then break;
end;
end;
快速幂
function quick(x,n,p:qword):qword;
var ans:qword;
begin
ans:=;
while n> do
begin
if n and > then ans:=cheng(ans,x,p);
x:=cheng(x,x,p);
n:=n>>;
end;
exit(ans);
end;
快速乘
function cheng(x,n,p:qword):qword;
var ans:qword;
begin
ans:=;
while n> do
begin
if n and > then ans:=(ans+x) mod p;
x:=(x+x) mod p;
n:=n>>;
end;
exit(ans);
end;
拓扑排序
for i:= to n do if u[i]= then begin inc(t); f[t]:=i; end;
repeat
x:=f[t]; dec(t); inc(num);
new(p); p:=a[x];
while p<>nil do
begin
y:=p^.data;
dec(u[y]);
if u[y]= then
begin
inc(t); f[t]:=y;
end;
p:=p^.next;
end;
until num=n;
强连通分量tarjan
思路:dfn为遍历到各点的时间,low表示每个点能够追溯到的最早的栈中节点的次序号 instack表示结点是否在栈中。
对图遍历如果x的儿子y没访问过,则访问并用low[y]更行low[x],如果x的儿子y被访问过,则用dfn[y]更新low[x],这样就知道了x最早回溯到的点(在栈中),在栈中low[x]相等的值构成强连通分量。
procedure tarjan(x:longint);
var y:longint; p:point;
begin
inc(s); low[x]:=s; dfn[x]:=s; inc(t); q[t]:=x;
instack[x]:=true;
new(p); p:=a[x];
while p<>nil do
begin
y:=p^.x;
if dfn[y]= then begin tarjan(y); low[x]:=min(low[x],low[y]); end
else if instack[y]=true then low[x]:=min(low[x],dfn[y]);
p:=p^.next;
end;
if dfn[x]=low[x] then
begin
inc(num);
repeat
y:=q[t]; dec(t); f[y]:=x;instack[y]:=false;
until x=y;
end;
end;
主程序
for i:= to n do begin dfn[i]:=; low[i]:=; w[i]:=; instack[i]:=false; end;
s:=; t:=; num:=;
for i:= to n do if dfn[i]= then tarjan(i);
树的直径
思路:求树上最长路,对于各个点,求出它儿子中最长和次长的链相加。
procedure dfs(x,e:longint);
var p:point; y:longint;
begin
s1[x]:=x; s2[x]:=x; new(p); p:=a[x];
while p<>nil do
begin
y:=p^.x;
if y=e then begin p:=p^.next; continue; end;
dfs(y,x);
if f1[y]+p^.v>f1[x] then
begin
f2[x]:=f1[x]; s2[x]:=s1[x];
f1[x]:=f1[y]+p^.v; s1[x]:=y;
end
else
if f1[y]+p^.v>f2[x] then
begin
f2[x]:=f1[y]+p^.v; s2[x]:=y;
end;
p:=p^.next;
end;
if f1[x]+f2[x]>f1[max]+f2[max] then
max:=x;
end;
kmp算法
p[]:=; j:=;
for i:= to m do
begin
while (j>)and(b[j+]<>b[i]) do j:=p[j];
if b[j+]=b[i] then inc(j);
p[i]:=j;
end;
j:=; kmp:=;
for i:= to n do
begin
while (j>)and(b[j+]<>a[i]) do j:=p[j];
if b[j+]=a[i] then inc(j);
if j=m then begin inc(kmp); j:=p[j]; end;
end;
LCA
倍增
1.不要忘记dfs后调用work
2.注意枚举2^i时要包含0,注意顺序
procedure work;
var i,j:longint;
begin
for i:= to do
for j:= to n do
f[i+,j]:=f[i,f[i,j]];
end;
function lca(x,y:longint):longint;
var i,t:longint;
begin
if deep[x]<deep[y] then begin t:=x; x:=y; y:=t; end;
for i:= downto do
if ((deep[x]-deep[y])>>i)and = then x:=f[i,x];
if x=y then exit(x);
for i:= downto do
if f[i,x]<>f[i,y] then
begin x:=f[i,x]; y:=f[i,y]; end;
exit(f[,x]);
end;
二分图
染色
function dfs(x,color:longint):boolean;
var p:point; y:longint;
begin
new(p); p:=w[x]; g[x]:=color;
while p<>nil do
begin
y:=p^.x;
if g[y]=color then exit(false);
if (g[y]=)and(not dfs(y,-color)) then exit(false);
p:=p^.next;
end;
exit(true);
end;
function cheak(s:longint):boolean;
var i:longint;
begin
for i:= to n do g[i]:=;
for i:= to n do
if g[i]= then
if not dfs(i,) then exit(false);
exit(true);
end;
组合
费马小定理,快速求C(n,m)的值
procedure make;
var i:longint;
begin
f[]:=; g[]:=;
for i:= to n do
begin
f[i]:=(f[i-]*i) mod num;
g[i]:=g[i-]*quick(i,num-) mod num;
end;
end;
function get(x,y:int64):int64;
var i:longint; t:int64;
begin
if (x=)or(y=)or(x=y) then exit();
exit(((f[x]*g[x-y]) mod num)*g[y] mod num);
end;
同余
ax≡1(mod m)
program asdf;
var
a,m,x,y,t:longint;
function extgcd(a,b:longint;var x,y:longint):longint;
var d:longint;
begin
if b<> then begin d:=extgcd(b,a mod b,y,x); y:=y-(a div b)*x; end
else begin x:=;y:=; d:=a; end;
exit(d);
end;
begin
readln(a,m);
x:=; y:=;
t:=extgcd(a,m,x,y);
writeln((x+m) mod m);
end.
最新文章
- ecshop中foreach的详细用法归纳
- css 超过宽度显示...
- 【Java】常见的Set类型,HashSet、TreeSet、LinkedHashSet
- 朗逸2011款 1.4t 清除保养告警灯
- Vi、Vim及Gedit编辑器
- 趣解curl
- win7 64位 python3.4&;opencv3.0配置安装
- HeartBeat源码安装
- UNIX域协议(命名套接字)
- jQuery-爱奇艺图片切换
- 判断本机ip是电信还是网通
- GO语言之urfave/cli命令行解析
- shell脚本运行java程序jar
- javascript创建函数的20种方式汇总
- week5 0.1 安装materializecss
- 第四章 PCA降维
- Selenium自动化测试Python一:Selenium入门
- Crystal Reports 版权疑问
- 20145227鄢曼君《网络对抗》Web安全基础实践
- ASP.NET Core应用到Windows Service中