【洛谷P2759】奇怪的函数

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

#include<cstdio>
#include<cstring>
#include<cmath>
using namespace std;
const int N=1000000000;
int n,l,r,mid;
int check(int x){
    if (x*(log(x)/log(10))>=n-1)
        return 1;
    return 0;
}
int main(){
    scanf("%d",&n);
    l=1;r=N;
    while (l<r){
        mid=(l+r)>>1;
        if (check(mid)) r=mid;
        else l=mid+1;
    }
    printf("%d",l);
    return 0;
}