Description

A pointer array is simply an array whose elements are pointers.

For example, if we declare:

int *iptr[10];

then iptr is an array containing ten integer pointers. Each element of iptr points to an integer stored in another array.

Your task is to write a function max that returns the maximum integer among the elements pointed to by a pointer array.

The function definition is:

int max(int *iptr[], int n);

Example Usage

The following program shows how the max function can be used in the main function:

#include <stdio.h>
#define N 10
int max(int *iptr[], int n);

int main (void)
{
    int i;
    int array[N];
    int *iptr[N];
   
    for (i = 0; i < N; i++) {
        scanf("%d", &(array[i]));
        iptr[i] = &(array[i]);
    }
   
    printf("%d\n", max(iptr, N));
    return 0;
}

 

Input

• The input consists of N integers (where N = 10 in this problem).

• These integers are read from standard input, separated by spaces or newlines.

Output

The program outputs the maximum value among the integers pointed to by the pointer array.

Sample Input  Download

Sample Output  Download

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Description

Solve the linear system Ax = y, where:

• A is an n×n upper-triangular matrix,

• x and y are n-dimensional vectors.

To save memory, only the upper triangle of A (including the diagonal) is stored in a one-dimensional array in row-major packed order.

For 0 ≤ i ≤ j < n, the element Ai, j is stored consecutively for rows i = 0,1,…,n−1
The linear index of ​ in the packed array is:

 

Implement back-substitution 高斯消去法 in the function below:

void upper_solver(double *A, double *x, double *y, int n); 

• A points to the packed upper-triangular data of size n*(n+1)/2.

• y is the right-hand-side vector.

• x is the output vector; store the solution in x.

• You may assume all diagonal entries of A are non-zero.

Example Main Function

#include <stdio.h>
#define N 256

void upper_solver(double *A, double *x, double *y, int n);

int main(void)
{
    int i, j;
    int n;
    double A[N * (N + 1) / 2];
    double *aptr = A;
    double x[N];
    double y[N];
   
    scanf("%d", &n);
    for (i = 0; i < n; i++)
        for (j = i; j < n; j++) {
            scanf("%lf", aptr);
            aptr++;
        }
       
    for (i = 0; i < n; i++)
        scanf("%lf", &y[i]);
   
    upper_solver(A, x, y, n);
   
    for (i = 0; i < n; i++)
        printf("%f\n", x[i]);
   
    return 0;
}

Hint  back-substitution 高斯消去法

Suppose we want to solve Ax=y where A is a 3×3 upper-triangular matrix:

Step 1: Solve for the last variable x₂

From the last row:

4x₂​=8 ⇒ x₂​=2

---

Step 2: Solve for x₁​ using the second row

3x_1​+2x₂​=4

Substitute x₂=2

3x₁​+4=4 ⇒ x_1​=0

---

Step 3: Solve for x₀ using the first row

2x₀​+1⋅x₁​−1⋅x_2​=1

Substitute x₁​=0,x₂​=2:

2x₀​−2=1 ⇒ x₀​=1.5

Final Solution

 

Input

• The first line contains an integer n (0 < n ≤ 256), representing the size of the matrix.

• The next n*(n+1)/2 floating-point numbers describe the upper triangle of the n×n matrix A, stored in row-major packed order:

  • For each rowi = 0,1,…,n−1, input the elements A_i,i ,A_{i,i+1, ... ,} A_i,n-1

• The final line contains n floating-point numbers, representing the elements of the vector y.

Example

// Sample input 1

3
1.0 2.0 3.0
2.0 1.0
4.0
2.0 3.0 -4.0

Here, 

• n=3

• Upper triangle of Matrix A (packed form)：

  

• Vector y is

^​

 

Output

• Output n floating-point numbers, each on a separate line, representing the solution vector x of the system Ax=y

• Use default %f formatting (six digits after the decimal point in C).

Sample Input  Download

Sample Output  Download

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