使用c++完成(1) 从键盘输入两个矩阵，并输出结果矩阵。矩阵的输入输出要求行列对齐。 (2) 把矩阵相乘写成函数形式，在主函数中完成矩阵的输入输出。 (3) 对下标越界作出异常处理。

注：由于机器学习等领域需要使用大量矩阵计算，本题仅考察基本算法实现，不考虑使用库函数。

1. 完成从键盘输入两个矩阵，并输出结果矩阵。矩阵的输入输出要求行列对齐。

#include <stdio.h>

#define MAX_ROW 10
#define MAX_COL 10

int main() {
  int a[MAX_ROW][MAX_COL], b[MAX_ROW][MAX_COL], c[MAX_ROW][MAX_COL];
  int m, n, p, q;

  printf("Input the dimensions of matrix A (m, n): ");
  scanf("%d, %d", &m, &n);
  printf("Input the elements of matrix A:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      scanf("%d", &a[i][j]);
    }
  }

  printf("Input the dimensions of matrix B (p, q): ");
  scanf("%d, %d", &p, &q);
  printf("Input the elements of matrix B:\n");
  for (int i = 0; i < p; i++) {
    for (int j = 0; j < q; j++) {
      scanf("%d", &b[i][j]);
    }
  }

  if (n != p) {
    printf("Error: the number of columns in A must equal the number of rows in B.\n");
    return 1;
  }

  printf("A:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      printf("%5d ", a[i][j]);
    }
    printf("\n");
  }

  printf("B:\n");
  for (int i = 0; i < p; i++) {
    for (int j = 0; j < q; j++) {
      printf("%5d ", b[i][j]);
    }
    printf("\n");
  }

  for (int i = 0; i < m; i++) {
    for (int j = 0; j < q; j++) {
      int sum = 0;
      for (int k = 0; k < n; k++) {
        sum += a[i][k] * b[k][j];
      }
      c[i][j] = sum;
    }
  }

  printf("C = A * B:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < q; j++) {
      printf("%5d ", c[i][j]);
    }
    printf("\n");
  }

  return 0;
}

2. 把矩阵相乘写成函数形式，在主函数中完成矩阵的输入输出。

#include <stdio.h>

#define MAX_ROW 10
#define MAX_COL 10

void matrix_multiply(int a[][MAX_COL], int b[][MAX_COL], int c[][MAX_COL], int m, int n, int q) {
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < q; j++) {
      int sum = 0;
      for (int k = 0; k < n; k++) {
        sum += a[i][k] * b[k][j];
      }
      c[i][j] = sum;
    }
  }
}

int main() {
  int a[MAX_ROW][MAX_COL], b[MAX_ROW][MAX_COL], c[MAX_ROW][MAX_COL];
  int m, n, p, q;

  printf("Input the dimensions of matrix A (m, n): ");
  scanf("%d, %d", &m, &n);
  printf("Input the elements of matrix A:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      scanf("%d", &a[i][j]);
    }
  }

  printf("Input the dimensions of matrix B (p, q): ");
  scanf("%d, %d", &p, &q);
  printf("Input the elements of matrix B:\n");
  for (int i = 0; i < p; i++) {
    for (int j = 0; j < q; j++) {
      scanf("%d", &b[i][j]);
    }
  }

  if (n != p) {
    printf("Error: the number of columns in A must equal the number of rows in B.\n");
    return 1;
  }

  printf("A:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      printf("%5d ", a[i][j]);
    }
    printf("\n");
  }

  printf("B:\n");
  for (int i = 0; i < p; i++) {
    for (int j = 0; j < q; j++) {
      printf("%5d ", b[i][j]);
    }
    printf("\n");
  }

  matrix_multiply(a, b, c, m, n, q);

  printf("C = A * B:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < q; j++) {
      printf("%5d ", c[i][j]);
    }
    printf("\n");
  }

  return 0;
}

3. 对下标越界作出异常处理。

#include <stdio.h>
#include <stdlib.h>

#define MAX_ROW 10
#define MAX_COL 10

void matrix_multiply(int a[][MAX_COL], int b[][MAX_COL], int c[][MAX_COL], int m, int n, int q) {
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < q; j++) {
      int sum = 0;
      for (int k = 0; k < n; k++) {
        sum += a[i][k] * b[k][j];
      }
      c[i][j] = sum;
    }
  }
}

int main() {
  int a[MAX_ROW][MAX_COL], b[MAX_ROW][MAX_COL], c[MAX_ROW][MAX_COL];
  int m, n, p, q;

  printf("Input the dimensions of matrix A (m, n): ");
  scanf("%d, %d", &m, &n);
  printf("Input the elements of matrix A:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      if (scanf("%d", &a[i][j]) != 1) {
        printf("Error: invalid input.\n");
        return 1;
      }
    }
  }

  printf("Input the dimensions of matrix B (p, q): ");
  scanf("%d, %d", &p, &q);
  printf("Input the elements of matrix B:\n");
  for (int i = 0; i < p; i++) {
    for (int j = 0; j < q; j++) {
      if (scanf("%d", &b[i][j]) != 1) {
        printf("Error: invalid input.\n");
        return 1;
      }
    }
  }

  if (n != p) {
    printf("Error: the number of columns in A must equal the number of rows in B.\n");
    return 1;
  }

  printf("A:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < n; j++) {
      printf("%5d ", a[i][j]);
    }
    printf("\n");
  }

  printf("B:\n");
  for (int i = 0; i < p; i++) {
    for (int j = 0; j < q; j++) {
      printf("%5d ", b[i][j]);
    }
    printf("\n");
  }

  matrix_multiply(a, b, c, m, n, q);

  printf("C = A * B:\n");
  for (int i = 0; i < m; i++) {
    for (int j = 0; j < q; j++) {
      printf("%5d ", c[i][j]);
    }
    printf("\n");
  }

  return 0;
}