9-28 解题报告

第一题：fibo矩阵快速幂

无压力，给信心的

type
matrix=array[1..2,1..2] of qword;
var
c,cc:matrix;
t,bili:longint;
n,p:int64;
function multiply(x,y:matrix):matrix;
var
temp:matrix;
begin
temp[1,1]:=(x[1,1]*y[1,1]+x[1,2]*y[2,1]) mod p;
temp[1,2]:=(x[1,1]*y[1,2]+x[1,2]*y[2,2]) mod p;
temp[2,1]:=(x[2,1]*y[1,1]+x[2,2]*y[2,1]) mod p;
temp[2,2]:=(x[2,1]*y[1,2]+x[2,2]*y[2,2]) mod p;
exit(temp);
end;

function getcc(n:int64):matrix;
var
temp:matrix;
t:int64;
begin
if n=1 then exit(c);
t:=n div 2;
temp:=getcc(t);
temp:=multiply(temp,temp);
if odd(n) then exit(multiply(temp,c))
else exit(temp);
end;

procedure init;
begin
readln(n,p);
c[1,1]:=1;
c[1,2]:=1;
c[2,1]:=1;
c[2,2]:=0;
if n=0 then
begin
writeln(0);
exit;
end;
if n=1 then
begin
writeln(1 mod p);
exit;
end;
if n=2 then
begin
writeln(1 mod p);
exit;
end;
cc:=getcc(n-2);
end;

procedure work;
begin
writeln((cc[1,1]+cc[1,2]) mod p);
end;

begin
assign(input,'eins.in');
reset(input);
assign(output,'eins.out');
rewrite(output);
readln(t);
for bili:=1 to t do
begin
init;
if (n>2) then work;
end;
close(input);
close(output);
end.

第二题：树状数组
把求和变成求xor，剩下模板，再给信心

var
a,f:array[0..200010] of longint;
l,r,x,y,z,m,n,i,j:longint;

function lowbit(x:longint):longint;
begin
exit(x and (-x));
end;

procedure build(pos,x:longint);
var i:longint;
begin
i:=pos;
while i<=n do
begin
f[i]:=f[i] xor x;
inc(i,lowbit(i));
end;
end;

function sum(x:longint):longint;
var
tail,s:longint;
begin
tail:=x;
s:=0;
while tail>0 do
begin
s:=s xor f[tail];
dec(tail,lowbit(tail));
end;
sum:=s;
end;

procedure change(x,y:longint);
var p:longint;
begin
p:=x;
while p<=n do
begin
f[p]:=f[p] xor a[x] xor y;
inc(p,Lowbit(p));
end;
a[x]:=y;
end;

begin
assign(input,'zwei.in');
reset(input);
assign(output,'zwei.out');
rewrite(output);
readln(n,m);
for i:=1 to n do
begin
read(a[i]);
build(i,a[i]);
end;

for i:=1 to m do
begin
read(z,x,y);
if z=0 then change(x,y);
if z=1 then writeln(sum(y) xor sum(x-1));
end;
close(input);
close(output);
end.

第三题：
欧拉函数，写了好几次才过，后来发现快速幂写错了（捂脸= =）

var
i,t,n,mo,ans,k:int64;
bilibili:longint;

function gcd(x,y:int64):int64;
begin
if y=0 then exit(x);
exit(gcd(y,x mod y));
end;

function phi(k:int64):int64;
var i,ret:int64;
begin
ret:=1;
i:=2;
while i*i<=k do
begin
if k mod i=0 then
begin
ret:=ret*(i-1);
k:=k div i;
while k mod i=0 do begin ret:=ret*i; k:=k div i; end;
end;
inc(i);
end;
if k>1 then ret:=ret*(k-1);
exit(ret);
end;

function pow(a,b:int64):int64;
var ret,i:int64;
begin
ret:=1;
while b<>0 do
begin
if b and 1<>0 then begin ret:=(ret*a) mod mo;

end;
a:=(a*a) mod mo;
b:=b>>1;
end;
exit(ret mod mo);
end;

begin
assign(input,'drei.in');
reset(input);
assign(output,'drei.out');
rewrite(output);
readln(t);
for bilibili:=1 to t do
begin
readln(n,mo);
if mo=1 then begin writeln(-1); continue; end;
if n=0 then begin writeln(-1); continue; end;
if n=1 then begin writeln(1); continue; end;
if gcd(n,mo)>1 then begin writeln(-1); continue; end;
ans:=phi(mo);
k:=ans;
i:=2;
while i*i<=k do
begin
if k mod i=0 then
begin
if (pow(n,i)=1) and (i<ans) then ans:=i;
if (pow(n,k div i)=1) and (k div i<ans) then ans:=k div i;
end;
inc(i);
end;
writeln(ans);
end;
close(input);
close(output);
end.

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