平成18年度秋季基本情報午後問3

H18年秋季基本情報技術者試験の午後の問3*1(n元1次方程式・ガウスの消去法)を解いてみました。

/*
 * H18秋午後 問3
 */
#include <stdio.h>

void gauss(int n, double *a[], double *b, double *x);
void answer_print(int n, double *x);

int main()
{
  int i, j, n;
  double **a;
  double  *b;
  double  *x;

  printf("n元1次方程式 => n = "); scanf("%d", &n);
  a = (double **)malloc(sizeof(double *) * n);
  b = (double *)malloc(sizeof(double) * n);
  x = (double *)malloc(sizeof(double) * n);
  if (a == NULL || b == NULL || x == NULL) {
    printf("error: malloc\n");
    exit(1);
  }
  for (i = 0; i < n; i++) {
    a[i] = (double *)malloc(sizeof(double) * n);
    if (a[i] == NULL) {
      printf("error: malloc\n");
      exit(1);
    }
  }
  
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      printf("a[%d][%d] = ", i + 1, j + 1); scanf("%lf", &a[i][j]);
    }
    printf("b[%d] = ", i + 1); scanf("%lf", &b[i]);
  }

  gauss(n, a, b, x);
  answer_print(n, x);

  for (i = 0; i < n; i++) {
    free(a[i]);
  }
  free(a); free(b); free(x);

  return 0;
}

void gauss(int n, double *a[], double *b, double *x)
{
  int k, i, j;
  double pivot, factor, sum;

  /* 前進消去 */
  for (k = 0; k < n - 1; k++) {	
    pivot = a[k][k];
    for (i = k + 1; i < n; i++) {
      factor = a[i][k] / pivot;
      for (j = k + 1; j < n; j++) {
	a[i][j] = a[i][j] - a[k][j] * factor;
      }
      b[i] = b[i] - b[k] * factor;
    }
  }
  /* 後退代入 */
  x[n - 1] = b[n - 1] / a[n - 1][n - 1];
  for (i = n - 1; i >= 0; i--) {
    sum = 0.0;
    for (j = i + 1; j < n; j++) {
      sum += a[i][j] * x[j];
    }
    x[i] = (b[i] - sum) / a[i][i];
  }
}

void answer_print(int n, double *x)
{
  int i;
  printf("\n------ Answer ------\n");
  for (i = 0; i < n; i++) {
    printf("x[%d] = %.2f\n", i + 1, x[i]);
  }
}

を実行すると以下のようになります。

% ./gauss
n元1次方程式 => n = 3
a[1][1] = 2.0
a[1][2] = 1.0
a[1][3] = 2.0
b[1] = 2.0
a[2][1] = 3.0
a[2][2] = 2.0
a[2][3] = 1.0
b[2] = 6.0
a[3][1] = 2.0
a[3][2] = 4.0
a[3][3] = 1.0
b[3] = 9.0
 ------ Answer ------
x[1] = 1.00
x[2] = 2.00
x[3] = -1.00

*1:https://www.jitec.ipa.go.jp/1_04hanni_sukiru/mondai_kaitou_2006h18_2/2006h18a_fe_pm_qs.pdf#page=9