Question A: Score Matrix
Idea 1:
This idea is correct, but the data in the title is too large and overtime.
Time complexity O(n 2 )
#include<cstdio>
#include<cmath>
double a[50005]={
0};
int main(void)
{
int N;
int i,j;
a[1]=1;
a[2]=3;
while(1)
{
scanf("%d",&N);
for(i=3;i<=N;i++)
{
double sum=0;
for(j=1;j<=i;j++)
{
sum+=1.0/j;
}
sum=sum*4-2-2.0/(j-1);
a[i]=sum+a[i-2];
}
if(N==0)
break;
printf("%.2lf\n",a[N]);
}
return 0;
}*/
Idea 2:
Time complexity O(n)
#include<cstdio>
int main(void)
{
int N;
while(1)
{
scanf("%d",&N);
if(N==0)
break;
double sum=0;
for(int i=1;i<=N;i++)
{
sum=sum+1.0/i*(N+1-i);
}
printf("%.2lf\n",sum*2-N);
}
return 0;
}