C语言程序设计（第5版）习题解答-第6章

第六章

注：以下所有代码需要添加头文件<stdio.h>、<math.h>、<string.h>

1. 用筛选法求100之内的素数
   代码如下

void is_prime_eratosthenes();
int main()
{
    is_prime_eratosthenes();
    return 0;
}

void is_prime_eratosthenes()
{
    int data[100], count = 0;
    for(int i = 0; i < 100; i++) data[i] = i + 1;
    printf("original data:\n");
    for(int i = 0; i < 100; i++)
    {
        printf("%5d ", data[i]);
        if((i + 1) % 10 == 0) printf("\n");
    }
    printf("\n");
    data[0] = 0; // 将1挖掉
    for(int i = 1; i <= (int)sqrt(100); i++)
    {
        for(int j = i + 1; j < 100; j++)
        {
            if(data[i] != 0 && data[j] != 0)            // 选择非0的数进行判断
            {
                if(data[j] % data[i] == 0) data[j] = 0; // 如果是素数就挖掉
            }
        }
    }
    printf("after eratosthenes:\n");
    for(int i = 0; i < 100; i++)
    {
        if(data[i] != 0)
        {
            printf("%5d ", data[i]);
            count++;                                    // 计算素数的个数
            if((count) % 10 == 0) printf("\n");
        }
    }
    printf("\nnumber of primes = %d\n", count);
    printf("\n");
}

2. 用选择法对10个整数进行排序
   代码如下

void selection_sort(int a[], int n);
int main()
{
    int num[10] = {54, 23, 78, 96, 12, 46, 89, 49, 37, 64};
    printf("original data:\n");
    for(int i = 0; i < 10; i++)
    {
        printf("%d ", num[i]);
    }
    printf("\n");
    printf("after selection sort:\n");
    selection_sort(num, 10);
    for(int i = 0; i < 10; i++)
    {
        printf("%d ", num[i]);
    }
    printf("\n");
    return 0;
}

void selection_sort(int a[], int n)
{
    int temp;
    for(int i = 0; i < n - 1; i++)
    {
        for(int j = i + 1; j < n; j++)
        {
            if(a[i] > a[j])
            {
                temp = a[i];
                a[i] = a[j];
                a[j] = temp;
            }
        }
    }
}

3. 求一个3x3的整型矩阵A对角线元素之和，求矩阵的迹：tr(A)
   代码如下

void trace_matrix(int a[3][3]);
int main()
{
    int a[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    printf("matrix:\n");
    for(int i = 0; i < 3; i++)
    {
        for(int j = 0; j < 3; j++)
        {
            printf("%d ", a[i][j]);
        }
        printf("\n");
    }
    trace_matrix(a);
    return 0;
}

void trace_matrix(int a[3][3])
{
    int sum = 0;
    for(int i = 0; i < 3; i++)
    {
        sum += a[i][i];
    }
    printf("trace = %d\n", sum);
}

4. 向一个已排好序的数组中插入一个新元素
   代码如下

void insertion_sort(int a[], int n, int num);
int main()
{
    int a[11] = {1, 4, 6, 8, 12, 14, 22, 28, 32, 42};
    int num = 20;
    printf("original data:\n");
    for(int i = 0; i < 11; i++)
    {
        printf("%d ", a[i]);
    }
    printf("\n");
    printf("after insertion sort:\n");
    insertion_sort(a, 11, num);
    for(int i = 0; i < 11; i++)
    {
        printf("%d ", a[i]);
    }
    printf("\n");
    return 0;
}

5. 将一个数组中的值按逆序重新存放
   代码如下

void reverse_sort(int a[], int n);
int main()
{
    int a[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
    printf("original data:\n");
    for(int i = 0; i < 10; i++)
    {
        printf("%d ", a[i]);
    }
    printf("\n");
    printf("after reverse sort:\n");
    reverse_sort(a, 10);
    return 0;
}

void reverse_sort(int a[], int n)
{
    int temp;
    for(int i = 0; i < n / 2; i++)
    {
        temp = a[i];
        a[i] = a[n - 1 - i];
        a[n - 1 - i] = temp;
    }
    for(int i = 0; i < 10; i++)
    {
        printf("%d ", a[i]);
    }
    printf("\n");
}

6. 输出10行的pascal’s triangle
   代码如下

void print_pascal_triangle();
int main()
{
    print_pascal_triangle();
    return 0;
}

void print_pascal_triangle()
{
    int a[10][10];
    for(int i = 0; i < 10; i++)
    {
        a[i][i] = 1;
        a[i][0] = 1;
    }
    for(int i = 2; i < 10; i++)
    {
        for(int j = 1; j <= i - 1; j++)
        {
            a[i][j] = a[i - 1][j - 1] + a[i - 1][j];
        }
    }
    for(int i = 0; i < 10; i++)
    {
        for(int j = 0; j <= i; j++)
        {
            printf("%d ", a[i][j]);
        }
        printf("\n");
    }
    printf("\n");
}

7. 输出魔方阵，每一行、每一列和对角线之和均相等
   代码如下

void magic_square(int num);
int main()
{
    magic_square(3);
    return 0;
}

void magic_square(int num)
{
    int a[num][num], row = 0, col = num / 2;
    for(int i = 0; i < num; i++)
    {
        for (int j = 0; j < num; j++)
        {
            a[i][j] = 0;    // 将矩阵初始化为0
        }
    }
    a[row][col] = 1;        // 将1放在矩阵第一行的中间
    for(int i = 2; i <= num * num; i++)
    {
        int next_row = (row + num - 1) % num;   // 计算下一个数的行，这里+num再取模是为了防止出现负数
        int next_col = (col + 1) % num;         // 计算下一个数的列，这里+1再取模是为了防止溢出
        if(a[next_row][next_col] != 0)          // 如果下一个数的位置已有数，则把下一个数放在前一个数的下面
        {
            row = (row + 1) % num;
        }
        else
        {
            row = next_row;                     // 更新当前行
            col = next_col;                     // 更新当前列
        }
        a[row][col] = i;                        // 更新数据
    }
    for(int i = 0; i < num; i++)
    {
        for(int j = 0; j < num; j++)
        {
            printf("%3d ", a[i][j]);
        }
        printf("\n");
    }
}

8. 找出一个二维数组中的鞍点，鞍点就是该元素在该行上值最大，在该列上值最小
   代码如下

void find_saddle_point(int a[3][4]);
int main()
{
    int array[3][4] = {{1, 2, 3, 11}, {5, 6, 7, 12}, {9, 10, 11, 4}};
    find_saddle_point(array);
    return 0;
}

void find_saddle_point(int a[3][4])
{
    int max, max_row, max_col, state;   // state作状态机用
    for(int i = 0; i < 3; i++)
    {
        max = a[i][0];
        max_row = i;
        max_col = 0;
        for(int j = 0; j < 4; j++)      // 找出一行中值最大的元素
        {
            if(a[i][j] > max)
            {
                max = a[i][j];
                max_col = j;
            }
        }
        state = 1;
        for(int k = 0; k < 3; k++)      // 检查该元素是否为该列值最小
        {
            if(a[k][max_col] < max)
            {
                state = 0;
            }
        }
        if(state)
        {
            printf("(%d, %d) is a saddle point\n", max_row + 1, max_col + 1);
            break;
        }
        
    }
    if(!state) printf("there is no saddle point\n");
}

9. 有15个数按由大到小顺序存放在一个数组中，输入一个数，要求用二分法查找该数是否存在于数组中
   代码如下

void binary_search(int a[], int len, int target);
int main()
{
    int a[6] = {1, 5, 7, 23, 45, 67};
    binary_search(a, 6, 8);   
    return 0;
}

void binary_search(int a[], int len, int target)
{
    int left = 0, right = len - 1;
    while(left <= right)
    {
        int mid = left + ((right - left) >> 1);
        if(a[mid] == target)
        {
            printf("%d is in the array\n", target);
            printf("the index is %d\n", mid);
            break;
        }
        else if (a[mid] < target) left = mid + 1;
        else right = mid - 1;
    }
    printf("%d is not in the array\n", target);
}

10. 分别统计一篇文章中的大小写字母、数字、空格和其他字符的个数
    代码如下

void count_char(char txt[3][80]);
int main()
{
    char txt[3][80];
    for(int i = 0; i < 3; i++)
    {
        printf("txt[%d] = ", i);
        fgets(txt[i], sizeof(txt[i]), stdin);
    }
    count_char(txt);
    return 0;
}

void count_char(char txt[3][80])
{
    int upp, low, dig, spa, oth;
    for(int i = 0; i < 3; i++)
    {
        for(int j = 0; j < 80 && txt[i][j] != '\0'; j++)
        {
            if(txt[i][j] >= 'A' && txt[i][j] <= 'Z') upp++;
            else if(txt[i][j] >= 'a' && txt[i][j] <= 'z') low++;
            else if(txt[i][j] >= '0' && txt[i][j] <= '9') dig++;
            else if(txt[i][j] == ' ') spa++;
            else oth++;
        }
    }
    printf("upper = %d\n", upp);
    printf("lower = %d\n", low);
    printf("digit = %d\n", dig);
    printf("space = %d\n", spa);
    printf("other = %d\n", oth);
}

11. 输出一个平行四边形图案
    代码如下

void print_parallel_polygon();
int main()
{
    print_parallel_polygon();
    return 0;
}

void print_parallel_polygon()
{
    char space = ' ', a[5] = {'*', '*', '*', '*', '*'};
    for(int i = 0; i < 5; i++)
    {
        printf("\n");
        for(int j = 0; j <= i; j++) printf("%c", space);
        for(int k = 0; k < 5; k++) printf("%c", a[k]);
    }
    printf("\n");
}

12. 将电文译码
    代码如下

void decode(char txt[80]);
int main()
{
    char str[80];
    decode(str);
    return 0;
}

void decode(char txt[80])
{
    printf("input cipher code:\n");
    fgets(txt, 80, stdin);
    int i =0;
    while(txt[i] != '\0')
    {
        if(txt[i] >= 'A' && txt[i] <= 'Z') txt[i] = 155 - txt[i];
        else if(txt[i] >= 'a' && txt[i] <= 'z') txt[i] = 219 - txt[i];
        else txt[i] = txt[i];
        i++;
    }
    puts("decode:\n");
    puts(txt);
}

13. 将两个字符串连接起来，不使用strcat()函数
    代码如下

void concat(char s1[], char s2[]);
int main()
{
    char s1[80] = "hello";
    char s2[20] = "world";
    concat(s1, s2);
    return 0;
}

void concat(char s1[], char s2[])
{
    int i = 0, j = 0;
    while(s1[i] != '\0') i++;
    while(s2[j] != '\0') s1[i++] = s2[j++];
    s1[i] = '\0';
    puts(s1);
}

14. 必将两个字符串，若s1>s2，输出一个正数；若s1<s2，输出一个负数；若s1=s2，输出0。不使用strcmp()函数
    代码如下

int compare_str(char s1[], char s2[]);
int main()
{
    char s1[80] = "Aid";
    char s2[20] = "And";
    printf("%d\n", compare_str(s1, s2));
    return 0;
}

int compare_str(char s1[], char s2[])
{
    int i = 0;
    while(s1[i] == s2[i] && s1[i] != '\0') i++;
    if(s1[i] == s2[i]) return 0;
    else return (s1[i] - s2[i]);
}

15. 将一个字符数组中的全部字符复制到另一个字符数组中，不使用strcpy()函数
    代码如下

void copy_str(char s1[], char s2[]);
int main()
{
    char s1[80] = "hello";
    char s2[40] = "world";
    copy_str(s1, s2);
    return 0;
}

void copy_str(char s1[], char s2[])
{
    int i = 0;
    while(s1[i] != '\0') s2[i++] = s1[i];
    s2[i] = '\0';
    puts(s2);
}