洛谷P2759奇怪的函数

Posted 2020-08-16 Absolutezero

x^x>=10^(n-1)

lg x^x>=n-1

x*lg x>=n-1

x*(log2 x/log2 10)>=n-1

左边单调递增，二分x即可

 1 #include<cstdio>
 2 #include<cstring>
 3 #include<cmath>
 4 using namespace std;
 5 const int N=1000000000;
 6 int n,l,r,mid;
 7 int check(int x){
 8     if (x*(log(x)/log(10))>=n-1)
 9         return 1;
10     return 0;
11 }
12 int main(){
13     scanf("%d",&n);
14     l=1;r=N;
15     while (l<r){
16         mid=(l+r)>>1;
17         if (check(mid)) r=mid;
18         else l=mid+1;
19     }
20     printf("%d",l);
21     return 0;
22 }

STD