C++ 初级实战案例：20 个经典编程练习 | 极客日志

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C++ 初级实战案例：20 个经典编程练习

包含 20 个 C++ 初级实战案例，涵盖温度转换、闰年判断、阶乘计算、素数筛选、数组排序、字符串处理、斐波那契数列、简易计算器、猜数字游戏、矩阵运算、成绩统计、进制转换、日期计算、汉诺塔递归及字符画图形绘制等内容。每个案例提供完整代码与运行示例，旨在帮助初学者巩固基础语法、掌握常用算法及逻辑结构。

黑客帝国发布于 2026/3/28更新于 2026/4/164 浏览

案例 1：温度转换器

案例描述

实现摄氏度与华氏度之间的相互转换。

知识点

基本输入输出
数学运算
函数封装

完整代码

#include <iostream>
#include 
  std;


{
     celsius *  /  + ;
}


{
     (fahrenheit - ) *  / ;
}

{
     choice;
     temp, result;
    cout <<  << endl;
    cout <<  << endl;
    cout <<  << endl;
    cout << ;
    cin >> choice;
     (choice == ) {
        cout << ;
        cin >> temp;
        result = (temp);
        cout << fixed << ();
        cout << temp <<  << result <<  << endl;
    }   (choice == ) {
        cout << ;
        cin >> temp;
        result = (temp);
        cout << fixed << ();
        cout << temp <<  << result <<  << endl;
    }  {
        cout <<  << endl;
    }
     ;
}

========== 温度转换器 ==========
1. 摄氏度转华氏度
2. 华氏度转摄氏度
请选择 (1/2): 1
请输入摄氏度：25
25.00°C = 77.00°F

#include <iostream>
using namespace std;

bool isLeapYear(int year) {
    // 闰年条件：能被 4 整除但不能被 100 整除，或能被 400 整除
    return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
}

int main() {
    int year;
    cout << "请输入年份：";
    cin >> year;
    if (isLeapYear(year)) {
        cout << year << "年是闰年" << endl;
    } else {
        cout << year << "年不是闰年" << endl;
    }
    // 扩展：判断多个年份
    cout << "\n近 10 年的闰年有：" << endl;
    for (int i = year; i < year + 10; i++) {
        if (isLeapYear(i)) {
            cout << i << " ";
        }
    }
    cout << endl;
    return 0;
}

请输入年份：2024
2024 年是闰年
近 10 年的闰年有：
2024 2028 2032

#include <iostream>
using namespace std;

// 方法 1：循环实现
long long factorialLoop(int n) {
    if (n < 0) return -1; // 错误标识
    if (n == 0 || n == 1) return 1;
    long long result = 1;
    for (int i = 2; i <= n; i++) {
        result *= i;
    }
    return result;
}

// 方法 2：递归实现
long long factorialRecursive(int n) {
    if (n < 0) return -1;
    if (n == 0 || n == 1) return 1;
    return n * factorialRecursive(n - 1);
}

int main() {
    int num;
    cout << "请输入一个非负整数：";
    cin >> num;
    if (num < 0) {
        cout << "错误：阶乘不支持负数！" << endl;
        return 1;
    }
    if (num > 20) {
        cout << "警告：数字过大可能溢出，建议输入 0-20 之间的数" << endl;
    }
    long long result1 = factorialLoop(num);
    long long result2 = factorialRecursive(num);
    cout << num << "! = " << result1 << " (循环方法)" << endl;
    cout << num << "! = " << result2 << " (递归方法)" << endl;
    // 显示阶乘表
    cout << "\n阶乘表 (0-10):" << endl;
    for (int i = 0; i <= 10; i++) {
        cout << i << "! = " << factorialLoop(i) << endl;
    }
    return 0;
}

请输入一个非负整数：5
5! = 120 (循环方法)
5! = 120 (递归方法)
阶乘表 (0-10):
0! = 1
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! = 362880
10! = 3628800

#include <iostream>
#include <cmath>
#include <vector>
using namespace std;

// 判断是否为素数（优化版）
bool isPrime(int n) {
    if (n <= 1) return false;
    if (n <= 3) return true;
    if (n % 2 == 0 || n % 3 == 0) return false;
    // 只需检查到 sqrt(n)
    for (int i = 5; i * i <= n; i += 6) {
        if (n % i == 0 || n % (i + 2) == 0) {
            return false;
        }
    }
    return true;
}

// 生成指定范围内的素数
vector<int> generatePrimes(int start, int end) {
    vector<int> primes;
    for (int i = start; i <= end; i++) {
        if (isPrime(i)) {
            primes.push_back(i);
        }
    }
    return primes;
}

int main() {
    int choice;
    cout << "========== 素数工具 ==========" << endl;
    cout << "1. 判断单个数是否为素数" << endl;
    cout << "2. 生成范围内的素数" << endl;
    cout << "请选择：";
    cin >> choice;
    if (choice == 1) {
        int num;
        cout << "请输入一个数：";
        cin >> num;
        if (isPrime(num)) {
            cout << num << " 是素数" << endl;
        } else {
            cout << num << " 不是素数" << endl;
        }
    } else if (choice == 2) {
        int start, end;
        cout << "请输入范围（起始 结束）：";
        cin >> start >> end;
        vector<int> primes = generatePrimes(start, end);
        cout << start << " 到 " << end << " 之间的素数有 " << primes.size() << " 个：" << endl;
        int count = 0;
        for (int prime : primes) {
            cout << prime << " ";
            count++;
            if (count % 10 == 0) cout << endl; // 每行显示 10 个
        }
        cout << endl;
    }
    return 0;
}

========== 素数工具 ==========
1. 判断单个数是否为素数
2. 生成范围内的素数
请选择：2
请输入范围（起始 结束）: 1 50
1 到 50 之间的素数有 15 个：
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

#include <iostream>
#include <algorithm>
using namespace std;

// 打印数组
void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;
}

// 冒泡排序
void bubbleSort(int arr[], int n) {
    for (int i = 0; i < n - 1; i++) {
        bool swapped = false;
        for (int j = 0; j < n - i - 1; j++) {
            if (arr[j] > arr[j + 1]) {
                swap(arr[j], arr[j + 1]);
                swapped = true;
            }
        }
        // 如果没有发生交换，说明已经有序
        if (!swapped) break;
    }
}

// 选择排序
void selectionSort(int arr[], int n) {
    for (int i = 0; i < n - 1; i++) {
        int minIdx = i;
        for (int j = i + 1; j < n; j++) {
            if (arr[j] < arr[minIdx]) {
                minIdx = j;
            }
        }
        if (minIdx != i) {
            swap(arr[i], arr[minIdx]);
        }
    }
}

// 插入排序
void insertionSort(int arr[], int n) {
    for (int i = 1; i < n; i++) {
        int key = arr[i];
        int j = i - 1;
        // 将大于 key 的元素向后移动
        while (j >= 0 && arr[j] > key) {
            arr[j + 1] = arr[j];
            j--;
        }
        arr[j + 1] = key;
    }
}

int main() {
    int arr[] = {64, 34, 25, 12, 22, 11, 90};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "原始数组：";
    printArray(arr, n);
    // 测试冒泡排序
    int arr1[] = {64, 34, 25, 12, 22, 11, 90};
    bubbleSort(arr1, n);
    cout << "冒泡排序：";
    printArray(arr1, n);
    // 测试选择排序
    int arr2[] = {64, 34, 25, 12, 22, 11, 90};
    selectionSort(arr2, n);
    cout << "选择排序：";
    printArray(arr2, n);
    // 测试插入排序
    int arr3[] = {64, 34, 25, 12, 22, 11, 90};
    insertionSort(arr3, n);
    cout << "插入排序：";
    printArray(arr3, n);
    return 0;
}

原始数组：64 34 25 12 22 11 90
冒泡排序：11 12 22 25 34 64 90
选择排序：11 12 22 25 34 64 90
插入排序：11 12 22 25 34 64 90

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

// 方法 1：使用双指针
void reverseString1(string& str) {
    int left = 0;
    int right = str.length() - 1;
    while (left < right) {
        swap(str[left], str[right]);
        left++;
        right--;
    }
}

// 方法 2：使用 STL 的 reverse 函数
void reverseString2(string& str) {
    reverse(str.begin(), str.end());
}

// 方法 3：递归方法
void reverseString3(string& str, int left, int right) {
    if (left >= right) return;
    swap(str[left], str[right]);
    reverseString3(str, left + 1, right - 1);
}

// 反转单词顺序（保持单词内部字符顺序）
string reverseWords(const string& str) {
    string result = "";
    string word = "";
    for (int i = str.length() - 1; i >= 0; i--) {
        if (str[i] == ' ') {
            if (!word.empty()) {
                reverse(word.begin(), word.end());
                result += word + " ";
                word = "";
            }
        } else {
            word += str[i];
        }
    }
    if (!word.empty()) {
        reverse(word.begin(), word.end());
        result += word;
    }
    return result;
}

int main() {
    string str1 = "Hello World";
    string str2 = "Hello World";
    string str3 = "Hello World";
    string str4 = "Hello World from C++";
    cout << "原始字符串：" << str1 << endl;
    reverseString1(str1);
    cout << "方法 1（双指针）：" << str1 << endl;
    reverseString2(str2);
    cout << "方法 2（STL）：" << str2 << endl;
    reverseString3(str3, 0, str3.length() - 1);
    cout << "方法 3（递归）：" << str3 << endl;
    cout << "\n原始句子：" << str4 << endl;
    cout << "反转单词顺序：" << reverseWords(str4) << endl;
    return 0;
}

原始字符串：Hello World
方法 1（双指针）：dlroW olleH
方法 2（STL）：dlroW olleH
方法 3（递归）：dlroW olleH
原始句子：Hello World from C++
反转单词顺序：C++ from World Hello

#include <iostream>
#include <climits>
using namespace std;

struct MinMax {
    int minValue;
    int maxValue;
    int minIndex;
    int maxIndex;
};

MinMax findMinMax(int arr[], int n) {
    MinMax result;
    result.minValue = INT_MAX;
    result.maxValue = INT_MIN;
    result.minIndex = -1;
    result.maxIndex = -1;
    for (int i = 0; i < n; i++) {
        if (arr[i] < result.minValue) {
            result.minValue = arr[i];
            result.minIndex = i;
        }
        if (arr[i] > result.maxValue) {
            result.maxValue = arr[i];
            result.maxIndex = i;
        }
    }
    return result;
}

// 查找第二大的数
int findSecondMax(int arr[], int n) {
    if (n < 2) return -1;
    int max1 = INT_MIN, max2 = INT_MIN;
    for (int i = 0; i < n; i++) {
        if (arr[i] > max1) {
            max2 = max1;
            max1 = arr[i];
        } else if (arr[i] > max2 && arr[i] < max1) {
            max2 = arr[i];
        }
    }
    return (max2 == INT_MIN) ? -1 : max2;
}

int main() {
    int arr[] = {45, 23, 67, 12, 89, 34, 78, 56};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "数组元素：";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << endl;
    MinMax result = findMinMax(arr, n);
    cout << "\n最小值：" << result.minValue << " (位置：" << result.minIndex << ")" << endl;
    cout << "最大值：" << result.maxValue << " (位置：" << result.maxIndex << ")" << endl;
    int secondMax = findSecondMax(arr, n);
    if (secondMax != -1) {
        cout << "第二大的数：" << secondMax << endl;
    }
    cout << "数值范围：" << result.maxValue - result.minValue << endl;
    return 0;
}

数组元素：45 23 67 12 89 34 78 56
最小值：12 (位置：3)
最大值：89 (位置：4)
第二大的数：78
数值范围：77

#include <iostream>
#include <vector>
using namespace std;

// 方法 1：递归（效率低）
long long fibRecursive(int n) {
    if (n <= 1) return n;
    return fibRecursive(n - 1) + fibRecursive(n - 2);
}

// 方法 2：迭代（效率高）
long long fibIterative(int n) {
    if (n <= 1) return n;
    long long a = 0, b = 1;
    for (int i = 2; i <= n; i++) {
        long long temp = a + b;
        a = b;
        b = temp;
    }
    return b;
}

// 方法 3：使用数组存储（动态规划）
vector<long long> fibArray(int n) {
    vector<long long> fib(n + 1);
    fib[0] = 0;
    if (n > 0) fib[1] = 1;
    for (int i = 2; i <= n; i++) {
        fib[i] = fib[i - 1] + fib[i - 2];
    }
    return fib;
}

int main() {
    int n;
    cout << "请输入要生成的斐波那契数列项数：";
    cin >> n;
    if (n < 0) {
        cout << "错误：请输入非负整数！" << endl;
        return 1;
    }
    if (n > 50) {
        cout << "警告：数字过大可能溢出，建议输入 0-50 之间的数" << endl;
    }
    // 使用迭代方法生成数列
    cout << "\n斐波那契数列前 " << n + 1 << " 项：" << endl;
    for (int i = 0; i <= n; i++) {
        cout << "F(" << i << ") = " << fibIterative(i) << endl;
    }
    // 使用数组方法一次性生成
    cout << "\n使用数组方法：" << endl;
    vector<long long> fibSeq = fibArray(n);
    for (int i = 0; i <= n; i++) {
        cout << fibSeq[i] << " ";
        if ((i + 1) % 10 == 0) cout << endl;
    }
    cout << endl;
    return 0;
}

请输入要生成的斐波那契数列项数：10
斐波那契数列前 11 项：
F(0) = 0
F(1) = 1
F(2) = 1
F(3) = 2
F(4) = 3
F(5) = 5
F(6) = 8
F(7) = 13
F(8) = 21
F(9) = 34
F(10) = 55
使用数组方法：
0 1 1 2 3 5 8 13 21 34 55

#include <iostream>
#include <string>
#include <cctype>
using namespace std;

// 方法 1：基本判断
bool isPalindrome1(const string& str) {
    int left = 0;
    int right = str.length() - 1;
    while (left < right) {
        if (str[left] != str[right]) {
            return false;
        }
        left++;
        right--;
    }
    return true;
}

// 方法 2：忽略大小写和非字母数字字符
bool isPalindrome2(const string& str) {
    int left = 0;
    int right = str.length() - 1;
    while (left < right) {
        // 跳过非字母数字字符
        while (left < right && !isalnum(str[left])) left++;
        while (left < right && !isalnum(str[right])) right--;
        // 比较（忽略大小写）
        if (tolower(str[left]) != tolower(str[right])) {
            return false;
        }
        left++;
        right--;
    }
    return true;
}

// 找出最长回文子串
string longestPalindrome(const string& str) {
    int n = str.length();
    if (n == 0) return "";
    int maxLen = 1;
    int start = 0;
    // 检查所有子串
    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            bool isPalin = true;
            int left = i, right = j;
            while (left < right) {
                if (str[left] != str[right]) {
                    isPalin = false;
                    break;
                }
                left++;
                right--;
            }
            if (isPalin && (j - i + 1) > maxLen) {
                maxLen = j - i + 1;
                start = i;
            }
        }
    }
    return str.substr(start, maxLen);
}

int main() {
    string test1 = "racecar";
    string test2 = "hello";
    string test3 = "A man, a plan, a canal: Panama";
    string test4 = "abcbabcba";
    cout << "\"" << test1 << "\" 是回文：" << (isPalindrome1(test1) ? "是" : "否") << endl;
    cout << "\"" << test2 << "\" 是回文：" << (isPalindrome1(test2) ? "是" : "否") << endl;
    cout << "\"" << test3 << "\" 是回文（忽略符号和大小写）：" << (isPalindrome2(test3) ? "是" : "否") << endl;
    cout << "\n\"" << test4 << "\" 的最长回文子串：\"" << longestPalindrome(test4) << "\"" << endl;
    // 交互式测试
    cout << "\n请输入一个字符串：";
    string userInput;
    getline(cin, userInput);
    cout << "基本判断：" << (isPalindrome1(userInput) ? "是回文" : "不是回文") << endl;
    cout << "高级判断：" << (isPalindrome2(userInput) ? "是回文" : "不是回文") << endl;
    return 0;
}

"racecar" 是回文：是
"hello" 是回文：否
"A man, a plan, a canal: Panama" 是回文（忽略符号和大小写）：是
"abcbabcba" 的最长回文子串："abcbabcba"
请输入一个字符串：level
基本判断：是回文
高级判断：是回文

#include <iostream>
#include <string>
#include <stack>
#include <cctype>
using namespace std;

// 基础四则运算计算器
class SimpleCalculator {
private:
    // 判断运算符优先级
    int precedence(char op) {
        if (op == '+' || op == '-') return 1;
        if (op == '*' || op == '/') return 2;
        return 0;
    }

    // 执行运算
    double applyOp(double a, double b, char op) {
        switch (op) {
        case '+': return a + b;
        case '-': return a - b;
        case '*': return a * b;
        case '/':
            if (b == 0) throw runtime_error("除数不能为 0");
            return a / b;
        }
        return 0;
    }

public:
    // 计算表达式
    double evaluate(string expression) {
        stack<double> values; // 存储数字
        stack<char> operators; // 存储运算符
        for (int i = 0; i < expression.length(); i++) {
            // 跳过空格
            if (isspace(expression[i])) continue;
            // 如果是数字
            if (isdigit(expression[i]) || expression[i] == '.') {
                double val = 0;
                bool isDecimal = false;
                double decimalPlace = 0.1;
                while (i < expression.length() && (isdigit(expression[i]) || expression[i] == '.')) {
                    if (expression[i] == '.') {
                        isDecimal = true;
                    } else if (!isDecimal) {
                        val = val * 10 + (expression[i] - '0');
                    } else {
                        val += (expression[i] - '0') * decimalPlace;
                        decimalPlace *= 0.1;
                    }
                    i++;
                }
                i--;
                values.push(val);
            }
            // 如果是左括号
            else if (expression[i] == '(') {
                operators.push(expression[i]);
            }
            // 如果是右括号
            else if (expression[i] == ')') {
                while (!operators.empty() && operators.top() != '(') {
                    double val2 = values.top(); values.pop();
                    double val1 = values.top(); values.pop();
                    char op = operators.top(); operators.pop();
                    values.push(applyOp(val1, val2, op));
                }
                if (!operators.empty()) operators.pop(); // 移除'('
            }
            // 如果是运算符
            else if (expression[i] == '+' || expression[i] == '-' || expression[i] == '*' || expression[i] == '/') {
                while (!operators.empty() && precedence(operators.top()) >= precedence(expression[i])) {
                    double val2 = values.top(); values.pop();
                    double val1 = values.top(); values.pop();
                    char op = operators.top(); operators.pop();
                    values.push(applyOp(val1, val2, op));
                }
                operators.push(expression[i]);
            }
        }
        // 处理剩余的运算
        while (!operators.empty()) {
            double val2 = values.top(); values.pop();
            double val1 = values.top(); values.pop();
            char op = operators.top(); operators.pop();
            values.push(applyOp(val1, val2, op));
        }
        return values.top();
    }
};

int main() {
    SimpleCalculator calc;
    string expression;
    cout << "========== 简易计算器 ==========" << endl;
    cout << "支持 +、-、*、/、() 运算" << endl;
    cout << "输入 'quit' 退出" << endl;
    cout << "===============================" << endl;
    while (true) {
        cout << "\n请输入表达式：";
        getline(cin, expression);
        if (expression == "quit" || expression == "exit") {
            cout << "再见！" << endl;
            break;
        }
        try {
            double result = calc.evaluate(expression);
            cout << "结果 = " << result << endl;
        } catch (const exception& e) {
            cout << "错误：" << e.what() << endl;
        }
    }
    return 0;
}

========== 简易计算器 ==========
支持 +、-、*、/、() 运算
输入 'quit' 退出
===============================
请输入表达式：2 + 3 * 4
结果 = 14
请输入表达式：(2 + 3) * 4
结果 = 20
请输入表达式：10 / 2 + 3
结果 = 8
请输入表达式：quit
再见！

#include <iostream>
#include <cstdlib>
#include <ctime>
using namespace std;

class GuessGame {
private:
    int targetNumber;
    int attempts;
    int maxAttempts;
    int minRange;
    int maxRange;

public:
    GuessGame(int min = 1, int max = 100, int maxTries = 10) : minRange(min), maxRange(max), maxAttempts(maxTries), attempts(0) {
        srand(time(0));
        targetNumber = rand() % (maxRange - minRange + 1) + minRange;
    }

    void play() {
        cout << "\n========== 猜数字游戏 ==========" << endl;
        cout << "我想了一个 " << minRange << " 到 " << maxRange << " 之间的数字" << endl;
        cout << "你有 " << maxAttempts << " 次机会来猜" << endl;
        cout << "===============================" << endl;
        while (attempts < maxAttempts) {
            cout << "\n第 " << (attempts + 1) << " 次猜测，请输入：";
            int guess;
            cin >> guess;
            if (guess < minRange || guess > maxRange) {
                cout << "请输入 " << minRange << " 到 " << maxRange << " 之间的数字！" << endl;
                continue;
            }
            attempts++;
            if (guess == targetNumber) {
                cout << "恭喜你！猜对了！" << endl;
                cout << "你用了 " << attempts << " 次猜中了数字 " << targetNumber << endl;
                return;
            } else if (guess < targetNumber) {
                cout << "太小了！";
                if (targetNumber - guess > 10) {
                    cout << "（还差得远呢）";
                } else {
                    cout << "（快接近了）";
                }
                cout << endl;
            } else {
                cout << "太大了！";
                if (guess - targetNumber > 10) {
                    cout << "（还差得远呢）";
                } else {
                    cout << "（快接近了）";
                }
                cout << endl;
            }
            cout << "剩余机会：" << (maxAttempts - attempts) << endl;
        }
        cout << "\n游戏结束！正确答案是：" << targetNumber << endl;
    }
};

int main() {
    char playAgain;
    do {
        int difficulty;
        cout << "选择难度：1.简单 (1-50,15 次) 2.中等 (1-100,10 次) 3.困难 (1-200,8 次): ";
        cin >> difficulty;
        GuessGame* game;
        switch (difficulty) {
        case 1: game = new GuessGame(1, 50, 15); break;
        case 3: game = new GuessGame(1, 200, 8); break;
        default: game = new GuessGame(1, 100, 10); break;
        }
        game->play();
        delete game;
        cout << "\n再玩一次？(y/n): ";
        cin >> playAgain;
    } while (playAgain == 'y' || playAgain == 'Y');
    cout << "谢谢游玩！" << endl;
    return 0;
}

选择难度：1.简单 (1-50,15 次) 2.中等 (1-100,10 次) 3.困难 (1-200,8 次): 2
========== 猜数字游戏 ==========
我想了一个 1 到 100 之间的数字
你有 10 次机会来猜
===============================
第 1 次猜测，请输入：50
太小了！（还差得远呢）
剩余机会：9
第 2 次猜测，请输入：75
太大了！（快接近了）
剩余机会：8
第 3 次猜测，请输入：68
恭喜你！猜对了！
你用了 3 次猜中了数字 68
再玩一次？(y/n): n
谢谢游玩！

#include <iostream>
#include <iomanip>
using namespace std;

const int MAX_SIZE = 10;

// 打印矩阵
void printMatrix(int mat[][MAX_SIZE], int rows, int cols) {
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            cout << setw(4) << mat[i][j] << " ";
        }
        cout << endl;
    }
}

// 矩阵转置
void transpose(int mat[][MAX_SIZE], int result[][MAX_SIZE], int rows, int cols) {
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            result[j][i] = mat[i][j];
        }
    }
}

// 矩阵加法
bool addMatrix(int mat1[][MAX_SIZE], int mat2[][MAX_SIZE], int result[][MAX_SIZE], int rows, int cols) {
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            result[i][j] = mat1[i][j] + mat2[i][j];
        }
    }
    return true;
}

// 矩阵乘法
bool multiplyMatrix(int mat1[][MAX_SIZE], int mat2[][MAX_SIZE], int result[][MAX_SIZE], int r1, int c1, int r2, int c2) {
    if (c1 != r2) {
        return false; // 矩阵不能相乘
    }
    // 初始化结果矩阵
    for (int i = 0; i < r1; i++) {
        for (int j = 0; j < c2; j++) {
            result[i][j] = 0;
        }
    }
    // 计算乘积
    for (int i = 0; i < r1; i++) {
        for (int j = 0; j < c2; j++) {
            for (int k = 0; k < c1; k++) {
                result[i][j] += mat1[i][k] * mat2[k][j];
            }
        }
    }
    return true;
}

int main() {
    int mat1[MAX_SIZE][MAX_SIZE] = {{1, 2, 3}, {4, 5, 6}};
    int mat2[MAX_SIZE][MAX_SIZE] = {{7, 8, 9}, {10, 11, 12}};
    int mat3[MAX_SIZE][MAX_SIZE] = {{1, 2}, {3, 4}, {5, 6}};
    int result[MAX_SIZE][MAX_SIZE];
    cout << "矩阵 A (2x3):" << endl;
    printMatrix(mat1, 2, 3);
    cout << "\n矩阵 B (2x3):" << endl;
    printMatrix(mat2, 2, 3);
    cout << "\n矩阵 C (3x2):" << endl;
    printMatrix(mat3, 3, 2);
    // 转置
    cout << "\n矩阵 A 的转置:" << endl;
    transpose(mat1, result, 2, 3);
    printMatrix(result, 3, 2);
    // 加法
    cout << "\n矩阵 A + 矩阵 B:" << endl;
    addMatrix(mat1, mat2, result, 2, 3);
    printMatrix(result, 2, 3);
    // 乘法
    cout << "\n矩阵 A × 矩阵 C:" << endl;
    if (multiplyMatrix(mat1, mat3, result, 2, 3, 3, 2)) {
        printMatrix(result, 2, 2);
    } else {
        cout << "矩阵维度不匹配，无法相乘！" << endl;
    }
    return 0;
}

矩阵 A (2x3):
   1   2   3
   4   5   6
矩阵 B (2x3):
   7   8   9
  10  11  12
矩阵 C (3x2):
   1   2
   3   4
   5   6
矩阵 A 的转置:
   1   4
   2   5
   3   6
矩阵 A + 矩阵 B:
   8  10  12
  14  16  18
矩阵 A × 矩阵 C:
  22  28
  49  64

#include <iostream>
#include <iomanip>
#include <algorithm>
using namespace std;

struct ScoreStats {
    double average;
    double highest;
    double lowest;
    double passRate;
    double excellentRate;
    int passCount;
    int excellentCount;
};

ScoreStats analyzeScores(double scores[], int n) {
    ScoreStats stats;
    double sum = 0;
    stats.highest = scores[0];
    stats.lowest = scores[0];
    stats.passCount = 0;
    stats.excellentCount = 0;
    for (int i = 0; i < n; i++) {
        sum += scores[i];
        if (scores[i] > stats.highest) stats.highest = scores[i];
        if (scores[i] < stats.lowest) stats.lowest = scores[i];
        if (scores[i] >= 60) stats.passCount++;
        if (scores[i] >= 90) stats.excellentCount++;
    }
    stats.average = sum / n;
    stats.passRate = (stats.passCount * 100.0) / n;
    stats.excellentRate = (stats.excellentCount * 100.0) / n;
    return stats;
}

void printGradeDistribution(double scores[], int n) {
    int distribution[5] = {0}; // 不及格、及格、中等、良好、优秀
    for (int i = 0; i < n; i++) {
        if (scores[i] < 60) distribution[0]++;
        else if (scores[i] < 70) distribution[1]++;
        else if (scores[i] < 80) distribution[2]++;
        else if (scores[i] < 90) distribution[3]++;
        else distribution[4]++;
    }
    cout << "\n成绩分布:" << endl;
    cout << "不及格 (<60): " << distribution[0] << " 人 (" << fixed << setprecision(1) << (distribution[0] * 100.0 / n) << "% )" << endl;
    cout << "及格 (60-69): " << distribution[1] << " 人 (" << (distribution[1] * 100.0 / n) << "% )" << endl;
    cout << "中等 (70-79): " << distribution[2] << " 人 (" << (distribution[2] * 100.0 / n) << "% )" << endl;
    cout << "良好 (80-89): " << distribution[3] << " 人 (" << (distribution[3] * 100.0 / n) << "% )" << endl;
    cout << "优秀 (90-100): " << distribution[4] << " 人 (" << (distribution[4] * 100.0 / n) << "% )" << endl;
}

int main() {
    const int MAX_STUDENTS = 100;
    double scores[MAX_STUDENTS];
    int n;
    cout << "请输入学生人数：";
    cin >> n;
    if (n <= 0 || n > MAX_STUDENTS) {
        cout << "学生人数无效！" << endl;
        return 1;
    }
    cout << "请输入 " << n << " 个学生的成绩:" << endl;
    for (int i = 0; i < n; i++) {
        cout << "学生" << (i + 1) << ": ";
        cin >> scores[i];
        if (scores[i] < 0 || scores[i] > 100) {
            cout << "成绩无效，请重新输入！" << endl;
            i--;
        }
    }
    ScoreStats stats = analyzeScores(scores, n);
    cout << "\n========== 成绩统计结果 ==========" << endl;
    cout << fixed << setprecision(2);
    cout << "平均分：" << stats.average << endl;
    cout << "最高分：" << stats.highest << endl;
    cout << "最低分：" << stats.lowest << endl;
    cout << "及格人数：" << stats.passCount << " 人" << endl;
    cout << "及格率：" << stats.passRate << "%" << endl;
    cout << "优秀人数：" << stats.excellentCount << " 人" << endl;
    cout << "优秀率：" << stats.excellentRate << "%" << endl;
    printGradeDistribution(scores, n);
    // 排序后显示
    sort(scores, scores + n);
    cout << "\n成绩排序（从低到高）:" << endl;
    for (int i = 0; i < n; i++) {
        cout << scores[i] << " ";
        if ((i + 1) % 10 == 0) cout << endl;
    }
    cout << endl;
    return 0;
}

请输入学生人数：10
请输入 10 个学生的成绩:
学生 1: 85
学生 2: 92
学生 3: 78
学生 4: 65
学生 5: 88
学生 6: 76
学生 7: 95
学生 8: 58
学生 9: 82
学生 10: 90
========== 成绩统计结果 ==========
平均分：80.90
最高分：95.00
最低分：58.00
及格人数：9 人
及格率：90.00%
优秀人数：3 人
优秀率：30.00%
成绩分布:
不及格 (<60): 1 人 (10.0%)
及格 (60-69): 1 人 (10.0%)
中等 (70-79): 2 人 (20.0%)
良好 (80-89): 3 人 (30.0%)
优秀 (90-100): 3 人 (30.0%)
成绩排序（从低到高）:
58.00 65.00 76.00 78.00 82.00 85.00 88.00 90.00 92.00 95.00

#include <iostream>
#include <string>
#include <cctype>
using namespace std;

struct CharStats {
    int letters;
    int digits;
    int spaces;
    int uppercase;
    int lowercase;
    int punctuation;
    int others;
    int total;
};

CharStats analyzeString(const string& str) {
    CharStats stats = {0, 0, 0, 0, 0, 0, 0, 0};
    for (char ch : str) {
        stats.total++;
        if (isalpha(ch)) {
            stats.letters++;
            if (isupper(ch)) stats.uppercase++;
            else stats.lowercase++;
        } else if (isdigit(ch)) {
            stats.digits++;
        } else if (isspace(ch)) {
            stats.spaces++;
        } else if (ispunct(ch)) {
            stats.punctuation++;
        } else {
            stats.others++;
        }
    }
    return stats;
}

// 统计单词数量
int countWords(const string& str) {
    int count = 0;
    bool inWord = false;
    for (char ch : str) {
        if (isspace(ch)) {
            inWord = false;
        } else if (!inWord) {
            inWord = true;
            count++;
        }
    }
    return count;
}

// 查找最长单词
string findLongestWord(const string& str) {
    string longestWord = "";
    string currentWord = "";
    for (char ch : str) {
        if (isalnum(ch)) {
            currentWord += ch;
        } else {
            if (currentWord.length() > longestWord.length()) {
                longestWord = currentWord;
            }
            currentWord = "";
        }
    }
    // 检查最后一个单词
    if (currentWord.length() > longestWord.length()) {
        longestWord = currentWord;
    }
    return longestWord;
}

int main() {
    string text;
    cout << "请输入一段文本：" << endl;
    getline(cin, text);
    CharStats stats = analyzeString(text);
    cout << "\n========== 字符统计分析 ==========" << endl;
    cout << "总字符数：" << stats.total << endl;
    cout << "字母数：" << stats.letters << " (大写：" << stats.uppercase << ", 小写：" << stats.lowercase << ")" << endl;
    cout << "数字数：" << stats.digits << endl;
    cout << "空格数：" << stats.spaces << endl;
    cout << "标点符号：" << stats.punctuation << endl;
    cout << "其他字符：" << stats.others << endl;
    int wordCount = countWords(text);
    string longestWord = findLongestWord(text);
    cout << "\n单词数：" << wordCount << endl;
    cout << "最长单词：\"" << longestWord << "\" (长度：" << longestWord.length() << ")" << endl;
    // 字符频率统计
    cout << "\n字母频率统计:" << endl;
    int freq[26] = {0};
    for (char ch : text) {
        if (isalpha(ch)) {
            freq[tolower(ch) - 'a']++;
        }
    }
    for (int i = 0; i < 26; i++) {
        if (freq[i] > 0) {
            cout << char('a' + i) << ": " << freq[i] << " ";
            if ((i + 1) % 5 == 0) cout << endl;
        }
    }
    cout << endl;
    return 0;
}

请输入一段文本：
Hello World! This is a C++ programming example. Count123
========== 字符统计分析 ==========
总字符数：56
字母数：43 (大写：5, 小写：38)
数字数：3
空格数：7
标点符号：2
其他字符：1
单词数：8
最长单词："programming" (长度：11)
字母频率统计:
a: 3 c: 2 d: 1 e: 4 g: 2 h: 2 i: 3 l: 3 m: 3 n: 2 o: 4 p: 2 r: 3 s: 2 t: 2 u: 1 w: 1 x: 1

#include <iostream>
#include <string>
#include <iomanip>
using namespace std;

struct BankAccount {
    string accountNumber;
    string ownerName;
    double balance;
    string password;
};

class SimpleBankSystem {
private:
    BankAccount accounts[100];
    int accountCount;

    int findAccount(const string& accountNumber) {
        for (int i = 0; i < accountCount; i++) {
            if (accounts[i].accountNumber == accountNumber) {
                return i;
            }
        }
        return -1;
    }

public:
    SimpleBankSystem() : accountCount(0) {}

    void createAccount() {
        if (accountCount >= 100) {
            cout << "系统已满，无法创建新账户！" << endl;
            return;
        }
        BankAccount newAccount;
        cout << "\n创建新账户" << endl;
        cout << "账号：";
        cin >> newAccount.accountNumber;
        if (findAccount(newAccount.accountNumber) != -1) {
            cout << "账号已存在！" << endl;
            return;
        }
        cout << "户名：";
        cin.ignore();
        getline(cin, newAccount.ownerName);
        cout << "初始存款：";
        cin >> newAccount.balance;
        if (newAccount.balance < 0) {
            cout << "初始存款不能为负！" << endl;
            return;
        }
        cout << "设置密码：";
        cin >> newAccount.password;
        accounts[accountCount++] = newAccount;
        cout << "账户创建成功！" << endl;
    }

    void deposit() {
        string accountNumber;
        double amount;
        cout << "\n存款" << endl;
        cout << "账号：";
        cin >> accountNumber;
        int index = findAccount(accountNumber);
        if (index == -1) {
            cout << "账号不存在！" << endl;
            return;
        }
        cout << "存款金额：";
        cin >> amount;
        if (amount <= 0) {
            cout << "存款金额必须大于 0！" << endl;
            return;
        }
        accounts[index].balance += amount;
        cout << "存款成功！当前余额：" << fixed << setprecision(2) << accounts[index].balance << " 元" << endl;
    }

    void withdraw() {
        string accountNumber, password;
        double amount;
        cout << "\n取款" << endl;
        cout << "账号：";
        cin >> accountNumber;
        int index = findAccount(accountNumber);
        if (index == -1) {
            cout << "账号不存在！" << endl;
            return;
        }
        cout << "密码：";
        cin >> password;
        if (password != accounts[index].password) {
            cout << "密码错误！" << endl;
            return;
        }
        cout << "取款金额：";
        cin >> amount;
        if (amount <= 0) {
            cout << "取款金额必须大于 0！" << endl;
            return;
        }
        if (amount > accounts[index].balance) {
            cout << "余额不足！当前余额：" << fixed << setprecision(2) << accounts[index].balance << " 元" << endl;
            return;
        }
        accounts[index].balance -= amount;
        cout << "取款成功！当前余额：" << fixed << setprecision(2) << accounts[index].balance << " 元" << endl;
    }

    void checkBalance() {
        string accountNumber, password;
        cout << "\n查询余额" << endl;
        cout << "账号：";
        cin >> accountNumber;
        int index = findAccount(accountNumber);
        if (index == -1) {
            cout << "账号不存在！" << endl;
            return;
        }
        cout << "密码：";
        cin >> password;
        if (password != accounts[index].password) {
            cout << "密码错误！" << endl;
            return;
        }
        cout << "\n账户信息" << endl;
        cout << "账号：" << accounts[index].accountNumber << endl;
        cout << "户名：" << accounts[index].ownerName << endl;
        cout << "余额：" << fixed << setprecision(2) << accounts[index].balance << " 元" << endl;
    }

    void showMenu() {
        cout << "\n========== 简易银行系统 ==========" << endl;
        cout << "1. 创建账户" << endl;
        cout << "2. 存款" << endl;
        cout << "3. 取款" << endl;
        cout << "4. 查询余额" << endl;
        cout << "5. 退出" << endl;
        cout << "=================================" << endl;
        cout << "请选择：";
    }
};

int main() {
    SimpleBankSystem bank;
    int choice;
    while (true) {
        bank.showMenu();
        cin >> choice;
        switch (choice) {
        case 1: bank.createAccount(); break;
        case 2: bank.deposit(); break;
        case 3: bank.withdraw(); break;
        case 4: bank.checkBalance(); break;
        case 5: cout << "感谢使用！再见！" << endl; return 0;
        default: cout << "无效选择！" << endl;
        }
    }
    return 0;
}

========== 简易银行系统 ==========
1. 创建账户
2. 存款
3. 取款
4. 查询余额
5. 退出
=================================
请选择：1
创建新账户
账号：1001
户名：张三
初始存款：1000
设置密码：123456
账户创建成功！
========== 简易银行系统 ==========
请选择：2
存款
账号：1001
存款金额：500
存款成功！当前余额：1500.00 元
========== 简易银行系统 ==========
请选择：3
取款
账号：1001
密码：123456
取款金额：200
取款成功！当前余额：1300.00 元

#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

// 十进制转其他进制
string decimalToBase(int decimal, int base) {
    if (decimal == 0) return "0";
    string result = "";
    const char digits[] = "0123456789ABCDEF";
    bool isNegative = decimal < 0;
    decimal = abs(decimal);
    while (decimal > 0) {
        result += digits[decimal % base];
        decimal /= base;
    }
    if (isNegative) result += '-';
    reverse(result.begin(), result.end());
    return result;
}

// 其他进制转十进制
int baseToDecimal(const string& number, int base) {
    int result = 0;
    int power = 1;
    bool isNegative = (number[0] == '-');
    int startPos = isNegative ? 1 : 0;
    for (int i = number.length() - 1; i >= startPos; i--) {
        char digit = number[i];
        int value;
        if (digit >= '0' && digit <= '9') {
            value = digit - '0';
        } else if (digit >= 'A' && digit <= 'F') {
            value = digit - 'A' + 10;
        } else if (digit >= 'a' && digit <= 'f') {
            value = digit - 'a' + 10;
        } else {
            return -1; // 无效字符
        }
        if (value >= base) {
            return -1; // 数字超出进制范围
        }
        result += value * power;
        power *= base;
    }
    return isNegative ? -result : result;
}

void showConversions(int decimal) {
    cout << "\n========== 进制转换结果 ==========" << endl;
    cout << "十进制：" << decimal << endl;
    cout << "二进制：" << decimalToBase(decimal, 2) << endl;
    cout << "八进制：" << decimalToBase(decimal, 8) << endl;
    cout << "十六进制：" << decimalToBase(decimal, 16) << endl;
    cout << "================================" << endl;
}

int main() {
    int choice;
    while (true) {
        cout << "\n========== 进制转换器 ==========" << endl;
        cout << "1. 十进制转其他进制" << endl;
        cout << "2. 二进制转十进制" << endl;
        cout << "3. 八进制转十进制" << endl;
        cout << "4. 十六进制转十进制" << endl;
        cout << "5. 退出" << endl;
        cout << "===============================" << endl;
        cout << "请选择：";
        cin >> choice;
        if (choice == 5) {
            cout << "再见！" << endl;
            break;
        }
        switch (choice) {
        case 1: {
            int decimal;
            cout << "请输入十进制数：";
            cin >> decimal;
            showConversions(decimal);
            break;
        }
        case 2: {
            string binary;
            cout << "请输入二进制数：";
            cin >> binary;
            int decimal = baseToDecimal(binary, 2);
            if (decimal == -1) {
                cout << "无效的二进制数！" << endl;
            } else {
                showConversions(decimal);
            }
            break;
        }
        case 3: {
            string octal;
            cout << "请输入八进制数：";
            cin >> octal;
            int decimal = baseToDecimal(octal, 8);
            if (decimal == -1) {
                cout << "无效的八进制数！" << endl;
            } else {
                showConversions(decimal);
            }
            break;
        }
        case 4: {
            string hex;
            cout << "请输入十六进制数：";
            cin >> hex;
            int decimal = baseToDecimal(hex, 16);
            if (decimal == -1) {
                cout << "无效的十六进制数！" << endl;
            } else {
                showConversions(decimal);
            }
            break;
        }
        default: cout << "无效选择！" << endl;
        }
    }
    return 0;
}

========== 进制转换器 ==========
1. 十进制转其他进制
2. 二进制转十进制
3. 八进制转十进制
4. 十六进制转十进制
5. 退出
===============================
请选择：1
请输入十进制数：255
========== 进制转换结果 ==========
十进制：255
二进制：11111111
八进制：377
十六进制：FF
================================

#include <iostream>
using namespace std;

struct Date {
    int year;
    int month;
    int day;
};

// 判断是否为闰年
bool isLeapYear(int year) {
    return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0);
}

// 获取某月的天数
int getDaysInMonth(int year, int month) {
    int days[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
    if (month == 2 && isLeapYear(year)) {
        return 29;
    }
    return days[month];
}

// 判断日期是否有效
bool isValidDate(const Date& date) {
    if (date.year < 1 || date.month < 1 || date.month > 12 || date.day < 1) {
        return false;
    }
    int maxDay = getDaysInMonth(date.year, date.month);
    return date.day <= maxDay;
}

// 计算从公元 1 年 1 月 1 日到指定日期的天数
int dateToDays(const Date& date) {
    int days = 0;
    // 计算年份的天数
    for (int y = 1; y < date.year; y++) {
        days += isLeapYear(y) ? 366 : 365;
    }
    // 计算月份的天数
    for (int m = 1; m < date.month; m++) {
        days += getDaysInMonth(date.year, m);
    }
    // 加上日期
    days += date.day;
    return days;
}

// 计算两个日期之间的天数差
int daysBetween(const Date& date1, const Date& date2) {
    return abs(dateToDays(date1) - dateToDays(date2));
}

// 获取星期几（0=周日，1=周一，..., 6=周六）
int getDayOfWeek(const Date& date) {
    // 使用蔡勒公式
    int y = date.year;
    int m = date.month;
    int d = date.day;
    if (m < 3) {
        m += 12;
        y--;
    }
    int c = y / 100;
    y = y % 100;
    int w = (y + y / 4 + c / 4 - 2 * c + (26 * (m + 1)) / 10 + d - 1) % 7;
    return (w + 7) % 7;
}

const char* getWeekDayName(int dayOfWeek) {
    const char* names[] = {"周日", "周一", "周二", "周三", "周四", "周五", "周六"};
    return names[dayOfWeek];
}

int main() {
    Date date1, date2;
    cout << "========== 日期计算器 ==========" << endl;
    cout << "请输入第一个日期（年 月 日）：";
    cin >> date1.year >> date1.month >> date1.day;
    if (!isValidDate(date1)) {
        cout << "日期 1 无效！" << endl;
        return 1;
    }
    cout << "请输入第二个日期（年 月 日）：";
    cin >> date2.year >> date2.month >> date2.day;
    if (!isValidDate(date2)) {
        cout << "日期 2 无效！" << endl;
        return 1;
    }
    int days = daysBetween(date1, date2);
    cout << "\n========== 计算结果 ==========" << endl;
    cout << "日期 1: " << date1.year << "年" << date1.month << "月" << date1.day << "日 " << getWeekDayName(getDayOfWeek(date1)) << endl;
    cout << "日期 2: " << date2.year << "年" << date2.month << "月" << date2.day << "日 " << getWeekDayName(getDayOfWeek(date2)) << endl;
    cout << "相差天数：" << days << " 天" << endl;
    cout << "相差周数：" << days / 7 << " 周 " << days % 7 << " 天" << endl;
    return 0;
}

========== 日期计算器 ==========
请输入第一个日期（年 月 日）: 2024 1 1
请输入第二个日期（年 月 日）: 2024 12 31
========== 计算结果 ==========
日期 1: 2024 年 1 月 1 日 周一
日期 2: 2024 年 12 月 31 日 周二
相差天数：365 天
相差周数：52 周 1 天

#include <iostream>
using namespace std;

int moveCount = 0;

// 汉诺塔递归解法
void hanoi(int n, char from, char to, char aux) {
    if (n == 1) {
        moveCount++;
        cout << "第 " << moveCount << " 步：将盘子 " << n << " 从 " << from << " 移动到 " << to << endl;
        return;
    }
    // 将 n-1 个盘子从 from 移动到 aux（借助 to）
    hanoi(n - 1, from, aux, to);
    // 将第 n 个盘子从 from 移动到 to
    moveCount++;
    cout << "第 " << moveCount << " 步：将盘子 " << n << " 从 " << from << " 移动到 " << to << endl;
    // 将 n-1 个盘子从 aux 移动到 to（借助 from）
    hanoi(n - 1, aux, to, from);
}

// 计算最少步数
int minSteps(int n) {
    return (1 << n) - 1; // 2^n - 1
}

int main() {
    int n;
    cout << "========== 汉诺塔问题 ==========" << endl;
    cout << "请输入盘子数量：";
    cin >> n;
    if (n <= 0) {
        cout << "盘子数量必须大于 0！" << endl;
        return 1;
    }
    if (n > 10) {
        cout << "盘子数量过多，步骤会很多（2^" << n << "-1 = " << minSteps(n) << " 步）" << endl;
        cout << "建议输入 10 以内的数字" << endl;
        cout << "是否继续？(y/n): ";
        char choice;
        cin >> choice;
        if (choice != 'y' && choice != 'Y') {
            return 0;
        }
    }
    cout << "\n理论最少步数：" << minSteps(n) << " 步" << endl;
    cout << "\n开始移动..." << endl;
    cout << "A 柱 (起始) -> C 柱 (目标)，B 柱 (辅助)" << endl;
    cout << "==============================" << endl;
    moveCount = 0;
    hanoi(n, 'A', 'C', 'B');
    cout << "\n==============================" << endl;
    cout << "完成！总共移动了 " << moveCount << " 次" << endl;
    return 0;
}

========== 汉诺塔问题 ==========
请输入盘子数量：3
理论最少步数：7 步
开始移动...
A 柱 (起始) -> C 柱 (目标)，B 柱 (辅助)
===============================
第 1 步：将盘子 1 从 A 移动到 C
第 2 步：将盘子 2 从 A 移动到 B
第 3 步：将盘子 1 从 C 移动到 B
第 4 步：将盘子 3 从 A 移动到 C
第 5 步：将盘子 1 从 B 移动到 A
第 6 步：将盘子 2 从 B 移动到 C
第 7 步：将盘子 1 从 A 移动到 C
===============================
完成！总共移动了 7 次

#include <iostream>
#include <iomanip>
using namespace std;

void printPascalTriangle(int n) {
    int triangle[100][100] = {0};
    // 生成杨辉三角
    for (int i = 0; i < n; i++) {
        triangle[i][0] = 1; // 每行第一个数为 1
        triangle[i][i] = 1; // 对角线上的数为 1
        for (int j = 1; j < i; j++) {
            triangle[i][j] = triangle[i - 1][j - 1] + triangle[i - 1][j];
        }
    }
    // 打印杨辉三角
    cout << "\n========== 杨辉三角 ==========" << endl;
    for (int i = 0; i < n; i++) {
        // 打印前导空格，使三角形居中
        for (int k = 0; k < (n - i - 1) * 2; k++) {
            cout << " ";
        }
        for (int j = 0; j <= i; j++) {
            cout << setw(4) << triangle[i][j];
        }
        cout << endl;
    }
    cout << "=============================" << endl;
}

// 计算组合数 C(n, k) = n! / (k! * (n-k)!)
long long combination(int n, int k) {
    if (k > n - k) k = n - k; // 优化计算
    long long result = 1;
    for (int i = 0; i < k; i++) {
        result *= (n - i);
        result /= (i + 1);
    }
    return result;
}

// 使用组合数公式打印
void printPascalTriangleByFormula(int n) {
    cout << "\n使用组合数公式:" << endl;
    for (int i = 0; i < n; i++) {
        for (int k = 0; k < (n - i - 1) * 2; k++) {
            cout << " ";
        }
        for (int j = 0; j <= i; j++) {
            cout << setw(4) << combination(i, j);
        }
        cout << endl;
    }
}

// 打印特定行
void printRow(int row) {
    cout << "第 " << row + 1 << " 行：";
    for (int i = 0; i <= row; i++) {
        cout << combination(row, i) << " ";
    }
    cout << endl;
}

int main() {
    int n;
    cout << "请输入杨辉三角的行数：";
    cin >> n;
    if (n <= 0 || n > 30) {
        cout << "行数应在 1-30 之间！" << endl;
        return 1;
    }
    printPascalTriangle(n);
    cout << "\n杨辉三角的性质:" << endl;
    cout << "1. 每行首尾都是 1" << endl;
    cout << "2. 每个数等于它上方两个数之和" << endl;
    cout << "3. 第 n 行的数字是组合数 C(n-1, k)" << endl;
    cout << "4. 每行数字之和为 2^(n-1)" << endl;
    // 验证性质 4
    cout << "\n验证：第 " << n << " 行数字之和 = ";
    long long sum = 0;
    for (int i = 0; i < n; i++) {
        sum += combination(n - 1, i);
    }
    cout << sum << " = 2^" << (n - 1) << " = " << (1 << (n - 1)) << endl;
    return 0;
}

请输入杨辉三角的行数：7
========== 杨辉三角 ==========
      1
     1 1
    1 2 1
   1 3 3 1
  1 4 6 4 1
 1 5 10 10 5 1
1 6 15 20 15 6 1
=============================
杨辉三角的性质:
1. 每行首尾都是 1
2. 每个数等于它上方两个数之和
3. 第 n 行的数字是组合数 C(n-1, k)
4. 每行数字之和为 2^(n-1)
验证：第 7 行数字之和 = 64 = 2^6 = 64

#include <iostream>
using namespace std;

// 直角三角形
void printRightTriangle(int n) {
    cout << "\n直角三角形:" << endl;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= i; j++) {
            cout << "* ";
        }
        cout << endl;
    }
}

// 等腰三角形
void printIsoscelesTriangle(int n) {
    cout << "\n等腰三角形:" << endl;
    for (int i = 1; i <= n; i++) {
        // 打印空格
        for (int j = 1; j <= n - i; j++) {
            cout << " ";
        }
        // 打印星号
        for (int j = 1; j <= 2 * i - 1; j++) {
            cout << "*";
        }
        cout << endl;
    }
}

// 菱形
void printDiamond(int n) {
    cout << "\n菱形:" << endl;
    // 上半部分
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n - i; j++) {
            cout << " ";
        }
        for (int j = 1; j <= 2 * i - 1; j++) {
            cout << "*";
        }
        cout << endl;
    }
    // 下半部分
    for (int i = n - 1; i >= 1; i--) {
        for (int j = 1; j <= n - i; j++) {
            cout << " ";
        }
        for (int j = 1; j <= 2 * i - 1; j++) {
            cout << "*";
        }
        cout << endl;
    }
}

// 空心菱形
void printHollowDiamond(int n) {
    cout << "\n空心菱形:" << endl;
    // 上半部分
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n - i; j++) {
            cout << " ";
        }
        for (int j = 1; j <= 2 * i - 1; j++) {
            if (j == 1 || j == 2 * i - 1) {
                cout << "*";
            } else {
                cout << " ";
            }
        }
        cout << endl;
    }
    // 下半部分
    for (int i = n - 1; i >= 1; i--) {
        for (int j = 1; j <= n - i; j++) {
            cout << " ";
        }
        for (int j = 1; j <= 2 * i - 1; j++) {
            if (j == 1 || j == 2 * i - 1) {
                cout << "*";
            } else {
                cout << " ";
            }
        }
        cout << endl;
    }
}

// 心形
void printHeart(int n) {
    cout << "\n心形:" << endl;
    // 上半部分
    for (int i = n / 2; i < n; i += 2) {
        // 左边空格
        for (int j = 1; j < n - i; j += 2) {
            cout << " ";
        }
        // 左边的心形
        for (int j = 1; j <= i; j++) {
            cout << "*";
        }
        // 中间空格
        for (int j = 1; j <= n - i; j++) {
            cout << " ";
        }
        // 右边的心形
        for (int j = 1; j <= i; j++) {
            cout << "*";
        }
        cout << endl;
    }
    // 下半部分
    for (int i = n; i >= 1; i--) {
        for (int j = 0; j < n - i; j++) {
            cout << " ";
        }
        for (int j = 1; j <= i * 2 - 1; j++) {
            cout << "*";
        }
        cout << endl;
    }
}

// 矩形
void printRectangle(int rows, int cols) {
    cout << "\n矩形 (" << rows << "x" << cols << "):" << endl;
    for (int i = 0; i < rows; i++) {
        for (int j = 0; j < cols; j++) {
            if (i == 0 || i == rows - 1 || j == 0 || j == cols - 1) {
                cout << "* ";
            } else {
                cout << " ";
            }
        }
        cout << endl;
    }
}

int main() {
    int choice, size;
    while (true) {
        cout << "\n========== 字符画图形 ==========" << endl;
        cout << "1. 直角三角形" << endl;
        cout << "2. 等腰三角形" << endl;
        cout << "3. 菱形" << endl;
        cout << "4. 空心菱形" << endl;
        cout << "5. 心形" << endl;
        cout << "6. 矩形" << endl;
        cout << "7. 显示所有图形" << endl;
        cout << "8. 退出" << endl;
        cout << "===============================" << endl;
        cout << "请选择：";
        cin >> choice;
        if (choice == 8) {
            cout << "再见！" << endl;
            break;
        }
        if (choice == 7) {
            size = 5;
            printRightTriangle(size);
            printIsoscelesTriangle(size);
            printDiamond(size);
            printHollowDiamond(size);
            printHeart(6);
            printRectangle(5, 10);
            continue;
        }
        cout << "请输入图形大小：";
        cin >> size;
        if (size <= 0 || size > 20) {
            cout << "大小应在 1-20 之间！" << endl;
            continue;
        }
        switch (choice) {
        case 1: printRightTriangle(size); break;
        case 2: printIsoscelesTriangle(size); break;
        case 3: printDiamond(size); break;
        case 4: printHollowDiamond(size); break;
        case 5: printHeart(size); break;
        case 6: {
            int cols;
            cout << "请输入列数：";
            cin >> cols;
            printRectangle(size, cols);
            break;
        }
        default: cout << "无效选择！" << endl;
        }
    }
    return 0;
}

========== 字符画图形 ==========
1. 直角三角形
2. 等腰三角形
3. 菱形
4. 空心菱形
5. 心形
6. 矩形
7. 显示所有图形
8. 退出
===============================
请选择：3
请输入图形大小：5
菱形:
 *
***
*****
*******
*********
*******
*****
***
*

C++ 初级实战案例：20 个经典编程练习

案例 1：温度转换器

案例描述

知识点

完整代码

运行示例

案例 2：判断闰年

案例描述

知识点

完整代码

运行示例

案例 3：计算阶乘

案例描述

知识点

完整代码

运行示例

案例 4：素数判断与生成

案例描述

知识点

完整代码

运行示例

案例 5：数组排序算法

案例描述

知识点

完整代码

运行示例

案例 6：字符串反转

案例描述

知识点

完整代码

运行示例

案例 7：查找数组中的最大值和最小值

案例描述

知识点

完整代码

运行示例

案例 8：斐波那契数列

案例描述

知识点

完整代码

运行示例

案例 9：回文字符串判断

案例描述

知识点

完整代码

运行示例

案例 10：简易计算器

案例描述

知识点

完整代码

运行示例

案例 11：猜数字游戏

案例描述

知识点

完整代码

运行示例

案例 12：二维数组矩阵操作

案例描述

知识点

完整代码

运行示例

案例 13：成绩统计系统

案例描述

知识点

完整代码

运行示例

案例 14：字符串统计分析

案例描述

知识点

完整代码

运行示例

案例 15：简易银行账户系统

案例描述

知识点

完整代码

运行示例

案例 16：进制转换器

案例描述

知识点

完整代码