小学数学

这个作业属于哪个课程	作业课程
这个作业要求在哪里	作业要求
这个作业的目标	实现一个自动生成小学四则运算题目的命令行程序

成员：3123004217蔡宜桓
我的github：github仓库

一.PSP表格

PSP2.1	Personal Software Process Stages	预估耗时（分钟）	实际耗时（分钟）
Planning	计划	35	30
Estimate	估计这个任务需要多少时间	15	30
Development	开发	185	200
Analysis	需求分析 (包括学习新技术)	75	80
Design Spec	生成设计文档	25	20
Design Review	设计复审	35	30
Coding Standard	代码规范 (为目前的开发制定合适的规范)	30	25
Design	具体设计	35	40
Coding	具体编码	75	70
Code Review	代码复审	25	45
Test	测试（自我测试，修改代码，提交修改）	35	30
Reporting	报告	15	20
Test Repor	测试报告	25	15
Size Measurement	计算工作量	5	20
Postmortem & Process Improvement Plan	事后总结, 并提出过程改进计划	35	30
	合计	650	685

二.代码展示

点击查看代码

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <stdbool.h>

#define MAX_QUESTIONS 10000
#define MAX_EXPR_LEN 100

typedef struct {
    int numerator;
    int denominator;
} Fraction;

typedef struct {
    char expression[MAX_EXPR_LEN];
    Fraction answer;
} Question;

// 最大公约数
int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
}

// 约分分数
void simplify(Fraction *f) {
    int common = gcd(abs(f->numerator), abs(f->denominator));
    f->numerator /= common;
    f->denominator /= common;
    if (f->denominator < 0) {
        f->numerator *= -1;
        f->denominator *= -1;
    }
}

// 生成随机分数
Fraction random_fraction(int range) {
    Fraction f;
    f.denominator = rand() % (range - 1) + 2; // 分母至少为2
    f.numerator = rand() % (f.denominator * (range - 1)) + 1;
    simplify(&f);
    return f;
}

// 生成随机自然数或分数
Fraction random_number(int range, bool allow_fraction) {
    if (allow_fraction && rand() % 4 == 0) { // 25%概率生成分数
        return random_fraction(range);
    } else {
        Fraction f;
        f.numerator = rand() % range;
        f.denominator = 1;
        return f;
    }
}

// 分数转字符串
void fraction_to_str(Fraction f, char *str) {
    if (f.denominator == 1) {
        sprintf(str, "%d", f.numerator);
    } else if (abs(f.numerator) > f.denominator) {
        int whole = f.numerator / f.denominator;
        int remainder = abs(f.numerator) % f.denominator;
        sprintf(str, "%d'%d/%d", whole, remainder, f.denominator);
    } else {
        sprintf(str, "%d/%d", f.numerator, f.denominator);
    }
}

// 字符串转分数
Fraction str_to_fraction(const char *str) {
    Fraction f;
    int whole = 0, numerator = 0, denominator = 1;
    
    if (strchr(str, '\'') != NULL) {
        sscanf(str, "%d'%d/%d", &whole, &numerator, &denominator);
        f.numerator = whole * denominator + (whole >= 0 ? numerator : -numerator);
        f.denominator = denominator;
    } else if (strchr(str, '/') != NULL) {
        sscanf(str, "%d/%d", &numerator, &denominator);
        f.numerator = numerator;
        f.denominator = denominator;
    } else {
        sscanf(str, "%d", &numerator);
        f.numerator = numerator;
        f.denominator = 1;
    }
    
    simplify(&f);
    return f;
}

// 分数加法
Fraction add(Fraction a, Fraction b) {
    Fraction result;
    result.numerator = a.numerator * b.denominator + b.numerator * a.denominator;
    result.denominator = a.denominator * b.denominator;
    simplify(&result);
    return result;
}

// 分数减法
Fraction subtract(Fraction a, Fraction b) {
    Fraction result;
    result.numerator = a.numerator * b.denominator - b.numerator * a.denominator;
    result.denominator = a.denominator * b.denominator;
    simplify(&result);
    return result;
}

// 分数乘法
Fraction multiply(Fraction a, Fraction b) {
    Fraction result;
    result.numerator = a.numerator * b.numerator;
    result.denominator = a.denominator * b.denominator;
    simplify(&result);
    return result;
}

// 分数除法
Fraction divide(Fraction a, Fraction b) {
    Fraction result;
    result.numerator = a.numerator * b.denominator;
    result.denominator = a.denominator * b.numerator;
    simplify(&result);
    return result;
}

// 生成表达式和答案
void generate_expression(Question *q, int range, int operators_left, bool in_parentheses) {
    if (operators_left == 0) {
        Fraction num = random_number(range, true);
        char num_str[20];
        fraction_to_str(num, num_str);
        strcat(q->expression, num_str);
        q->answer = num;
        return;
    }

    bool use_parentheses = in_parentheses ? false : (rand() % 2 == 0 && operators_left > 1);
    if (use_parentheses) {
        strcat(q->expression, "(");
    }

    // 左子表达式
    int left_operators = rand() % operators_left;
    if (left_operators == operators_left) left_operators--;
    generate_expression(q, range, left_operators, use_parentheses);

    // 运算符
    char op;
    Fraction temp_answer;
    switch (rand() % 4) {
        case 0: op = '+'; break;
        case 1: op = '-'; break;
        case 2: op = '*'; break;
        case 3: op = '/'; break;
    }
    
    // 处理减法和除法的限制
    bool valid = false;
    Fraction right_num;
    char right_str[20];
    int attempts = 0;
    
    do {
        attempts++;
        if (attempts > 10) { // 避免无限循环
            op = (op == '-' || op == '/') ? '+' : op;
        }
        
        // 生成右子表达式
        char temp_expr[MAX_EXPR_LEN] = "";
        Question temp_q;
        strcpy(temp_q.expression, temp_expr);
        generate_expression(&temp_q, range, operators_left - left_operators - 1, use_parentheses);
        right_num = temp_q.answer;
        strcpy(right_str, temp_q.expression);
        
        if (op == '-') {
            valid = (q->answer.numerator * right_num.denominator >= 
                    right_num.numerator * q->answer.denominator);
        } else if (op == '/') {
            valid = (right_num.numerator != 0);
        } else {
            valid = true;
        }
    } while (!valid);
    
    // 添加运算符和右子表达式
    char op_with_spaces[4] = " ";
    op_with_spaces[1] = op;
    op_with_spaces[2] = ' ';
    strcat(q->expression, op_with_spaces);
    strcat(q->expression, right_str);
    
    // 计算答案
    switch (op) {
        case '+': q->answer = add(q->answer, right_num); break;
        case '-': q->answer = subtract(q->answer, right_num); break;
        case '*': q->answer = multiply(q->answer, right_num); break;
        case '/': q->answer = divide(q->answer, right_num); break;
    }
    
    if (use_parentheses) {
        strcat(q->expression, ")");
    }
}

// 检查题目是否重复
bool is_duplicate(Question *questions, int count, Question *new_q) {
    // 简化检查：比较答案和表达式长度
    for (int i = 0; i < count; i++) {
        if (questions[i].answer.numerator == new_q->answer.numerator &&
            questions[i].answer.denominator == new_q->answer.denominator &&
            strlen(questions[i].expression) == strlen(new_q->expression)) {
            // 更复杂的检查可以在这里添加
            return true;
        }
    }
    return false;
}

// 生成题目
void generate_questions(int count, int range, const char *exercise_file, const char *answer_file) {
    Question questions[MAX_QUESTIONS];
    FILE *ef = fopen(exercise_file, "w");
    FILE *af = fopen(answer_file, "w");
    
    if (!ef || !af) {
        printf("无法打开输出文件\n");
        return;
    }
    
    srand(time(NULL));
    
    for (int i = 0; i < count; i++) {
        Question q;
        strcpy(q.expression, "");
        
        int operators = rand() % 3 + 1; // 1-3个运算符
        generate_expression(&q, range, operators, false);
        
        // 确保不重复
        while (is_duplicate(questions, i, &q)) {
            strcpy(q.expression, "");
            generate_expression(&q, range, operators, false);
        }
        
        questions[i] = q;
        
        // 写入题目文件
        fprintf(ef, "%d. %s =\n", i + 1, q.expression);
        
        // 写入答案文件
        char answer_str[20];
        fraction_to_str(q.answer, answer_str);
        fprintf(af, "%d. %s\n", i + 1, answer_str);
    }
    
    fclose(ef);
    fclose(af);
}

// 检查答案
void check_answers(const char *exercise_file, const char *answer_file, const char *grade_file) {
    FILE *ef = fopen(exercise_file, "r");
    FILE *af = fopen(answer_file, "r");
    FILE *gf = fopen(grade_file, "w");
    
    if (!ef || !af || !gf) {
        printf("无法打开输入/输出文件\n");
        return;
    }
    
    int correct_count = 0, wrong_count = 0;
    int correct_indices[MAX_QUESTIONS], wrong_indices[MAX_QUESTIONS];
    char line[256];
    int index;
    
    while (fgets(line, sizeof(line), ef)) {
        sscanf(line, "%d.", &index);
        
        char answer_line[256];
        fgets(answer_line, sizeof(answer_line), af);
        
        // 提取正确答案
        char correct_answer[20];
        sscanf(answer_line, "%*d. %s", correct_answer);
        Fraction correct = str_to_fraction(correct_answer);
        
        // 提取用户答案
        char *eq_pos = strchr(line, '=');
        if (!eq_pos || *(eq_pos + 1) == '\n') {
            // 没有答案
            wrong_indices[wrong_count++] = index;
            continue;
        }
        
        char user_answer[20];
        sscanf(eq_pos + 1, "%s", user_answer);
        Fraction user = str_to_fraction(user_answer);
        
        if (user.numerator == correct.numerator && user.denominator == correct.denominator) {
            correct_indices[correct_count++] = index;
        } else {
            wrong_indices[wrong_count++] = index;
        }
    }
    
    // 写入成绩文件
    fprintf(gf, "Correct: %d (", correct_count);
    for (int i = 0; i < correct_count; i++) {
        fprintf(gf, "%d", correct_indices[i]);
        if (i < correct_count - 1) fprintf(gf, ", ");
    }
    fprintf(gf, ")\n");
    
    fprintf(gf, "Wrong: %d (", wrong_count);
    for (int i = 0; i < wrong_count; i++) {
        fprintf(gf, "%d", wrong_indices[i]);
        if (i < wrong_count - 1) fprintf(gf, ", ");
    }
    fprintf(gf, ")\n");
    
    fclose(ef);
    fclose(af);
    fclose(gf);
}

// 打印帮助信息
void print_help() {
    printf("使用方法:\n");
    printf("生成题目: program -n <题目数量> -r <数值范围>\n");
    printf("检查答案: program -e <题目文件> -a <答案文件>\n");
}

int main(int argc, char *argv[]) {
    if (argc < 2) {
        print_help();
        return 1;
    }
    
    if (strcmp(argv[1], "-n") == 0 && argc >= 5 && strcmp(argv[3], "-r") == 0) {
        int count = atoi(argv[2]);
        int range = atoi(argv[4]);
        
        if (count <= 0 || range <= 0) {
            printf("无效的参数值\n");
            return 1;
        }
        
        generate_questions(count, range, "Exercises.txt", "Answers.txt");
        printf("已生成 %d 道题目，范围在 %d 以内\n", count, range);
    } else if (strcmp(argv[1], "-e") == 0 && argc >= 5 && strcmp(argv[3], "-a") == 0) {
        check_answers(argv[2], argv[4], "Grade.txt");
        printf("已检查答案，结果保存在 Grade.txt\n");
    } else {
        print_help();
        return 1;
    }
    
    return 0;
}