C. Score matrix question description and solution; score matrix question Solution

C. Score matrix question description and solution; score matrix question Solution
Score MatrixDescription

We define the following matrix:

1/1 1/2 1/3

1/2 1/1 1/2

1/3 1/2 1/1

The elements on the diagonal line of the matrix are always 1/1, and the denominator of the scores on both sides of the diagonal line increases one by one.

The sum of the requested matrices.

Input

Given an integer N (N <50000) in each row, the matrix is N * N. When N is 0, the input ends.

Output

Output answer, retain 2 decimal places.

Sample Input

1

2

3

4

0

Sample Output

1.00

3.00

5.67

8.83

Ideas:

Matrix summation, not the summation of the determinant;

Expand the right side and bottom side to make full use of the preceding calculation results;

Code

#includeusing namespace std;
double temp=1;
double func(int n)
{
    temp+=1.0/n;
    return temp;
}
int main()
{
    double a[50005];
    a[1]=1;
    for(int i=2;i<=50000;i++)
        a[i]=a[i-1]+2*func(i)-1;

    int n;
    while(scanf("%d",&n),n){
        printf("%.2f\n",a[n]);
    }
    return 0;
}