JZOJsenior2434.2017.04.08【NOIP 普及组】模拟赛C组 T3开关灯泡

Description

一个房间里有n盏灯泡，一开始都是熄着的，有1到n个时刻，每个时刻i，我们会将i的倍数的灯泡改变状态（即原本开着的现将它熄灭，原本熄灭的现将它点亮），问最后有多少盏灯泡是亮着的。

Input

一个数n

Output

m,表示最后有m盏是亮着的

Sample Input

5

Sample Output

2

Data Constraint

Hint

范围：40%的数据保证，n<=maxlongint
100%的数据保证，n<=10^200

正解高精度开方，然而那东西很烦，所以我不用了
想要看高精度开方百度，不过我不太确定看完会不会吐的更久……

思路：
直接二分查找
（二分你跟我说不会那你还是别搞OI了呗……）
不论是二分，还是开方，都是码农题，吐……

代码：

var
        n,l,r,mid:ansistring;
function add(s1,s2:ansistring):ansistring;
var
        a,b,c:array[0..10000]of longint;
        n,i,l1,l2,l3,x:longint;
        s:string;
begin
        fillchar(a,sizeof(a),0);
        fillchar(b,sizeof(b),0);
        fillchar(c,sizeof(c),0);
        x:=0;
        l1:=length(s1);
        for i:=1 to l1 do a[l1-i+1]:=ord(s1[i])-ord('0');
        l2:=length(s2);
        for i:=1 to l2 do b[l2-i+1]:=ord(s2[i])-ord('0');
        i:=1;
        while (i<=l1)or(i<=l2) do
        begin
                c[i]:=a[i]+b[i]+x;
                x:=c[i] div 10;
                c[i]:=c[i] mod 10;
                inc(i);
        end;
        if x>0 then
        begin
                l3:=i;
                c[i]:=x;
        end
        else l3:=i-1;
        add:='';
        for i:=l3 downto 1 do
                add:=add+chr(c[i]+48);
end;
function time(n1,n2:ansistring):ansistring;
var
        a,b,c:array[0..10000]of longint;
        lena,lenb,lenc,i,j,x:longint;
begin
        fillchar(a,sizeof(a),0);
        fillchar(b,sizeof(b),0);
        fillchar(c,sizeof(c),0);
        lena:=length(n1);
        lenb:=length(n2);
        for i:=1 to lena do a[lena-i+1]:=ord(n1[i])-ord('0');
        for i:=1 to lenb do b[lenb-i+1]:=ord(n2[i])-ord('0');
        for i:=1 to lena do
        begin
                x:=0;
                for j:=1 to lenb do
                begin
                        c[i+j-1]:=a[i]*b[j]+x+c[i+j-1];
                        x:=c[i+j-1]div 10;
                        c[i+j-1]:=c[i+j-1]mod 10;
                end;
                c[i+j]:=x;
        end;
        lenc:=lena+lenb;
        while (c[lenc]=0)and(lenc>1)do dec(lenc);
        time:='';
        for i:=lenc downto 1 do
                time:=time+chr(c[i]+48);
end;
function division(s:ansistring;y:longint):ansistring;
var
        a,b,c:array[0..10000]of longint;
        lena,lenb,lenc,i,j,x:longint;
begin
        fillchar(a,sizeof(a),0);
        fillchar(b,sizeof(b),0);
        fillchar(c,sizeof(c),0);
        lena:=length(s);
        for i:=1 to lena do a[lena-i+1]:=ord(s[i])-ord('0');
        x:=0;
        for i:=lena downto 1 do
        begin
                x:=x*10+a[i];
                c[i]:=x div y;
                x:=x mod y;
        end;
        lenc:=lena;
        division:='';
        while (c[lenc]=0)and(lenc>1)do dec(lenc);
        for i:=lenc downto 1 do
                division:=division+chr(c[i]+48);
end;
function smaller(s1,s2:ansistring):boolean;
begin
        if (length(s1)or(length(s1)=length(s2))and((s1<=s2))then
        exit(true)
                else exit(false);
end;
function bigger(s1,s2:ansistring):boolean;
begin
        if (length(s1)>length(s2))or(length(s1)=length(s2))and((s1>s2))then
        exit(true)
                else exit(false);
end;
function judge(s:ansistring):boolean;
begin
        if smaller(time(s,s),n) and bigger(time(add(s,'1'),add(s,'1')),n)then
        exit(true)
                else exit(false);
end;
begin
        readln(n);
        l:='1';
        r:=n;
        mid:=division(add(l,r),2);
        while true do
        begin
                if judge(mid) then
                begin
                        writeln(mid);
                        halt;
                end;
                if bigger(time(mid,mid),n)then
                begin
                        r:=mid;
                        mid:=division(add(l,r),2);
                end
                else
                if smaller(time(mid,mid),n)then
                begin
                        l:=add(mid,'1');
                        mid:=division(add(l,r),2);
                end;
        end;
end.

你看完吐了没？