大一MATLAB，怎么写啊

Question

大一MATLAB题，总共十一道，实在是做得焦头烂额，辛苦各位了

Answer 1

基于Monster 组和AIGC的调写：若有帮助，还望采纳~~：

• 你要的MATLAB代码如下：

1. 回文数生成器

function [palindromeCount, nonPalindromeCount] = palindromeGenerator(limit)
    palindromeCount = 0;
    nonPalindromeCount = 0;
    for i = 1:limit
        if isPalindromeGenerator(i, 6)
            palindromeCount = palindromeCount + 1;
        else
            nonPalindromeCount = nonPalindromeCount + 1;
        end
    end
end

function isPalindrome = isPalindromeGenerator(num, steps)
    for i = 1:steps
        num = num + str2num(flip(num2str(num)));
        if isPalindrome(num)
            isPalindrome = true;
            return;
        end
    end
    isPalindrome = false;
end

function result = isPalindrome(num)
    str = num2str(num);
    result = strcmp(str, flip(str));
end

2. 完美数查找

function perfectNumbers = findPerfectNumbers(limit)
    perfectNumbers = [];
    for n = 1:limit
        if isPerfect(n)
            perfectNumbers(end + 1) = n;
        end
    end
end

function result = isPerfect(number)
    sumOfDivisors = sum(divisors(number)) - number;
    result = sumOfDivisors == number;
end

function divs = divisors(n)
    divs = [1];
    for i = 2:sqrt(n)
        if mod(n, i) == 0
            divs(end+1) = i;
            if i ~= n / i
                divs(end+1) = n / i;
            end
        end
    end
end

3. 亲和数对查找

function amicablePairs = findAmicablePairs(limit)
    amicablePairs = [];
    for a = 1:limit
        b = sum(divisors(a)) - a;
        if a < b && sum(divisors(b)) - b == a
            amicablePairs(end+1, :) = [a, b];
        end
    end
end

function divs = divisors(n)
    divs = [1];
    for i = 2:sqrt(n)
        if mod(n, i) == 0
            divs(end+1) = i;
            if i ~= n / i
                divs(end+1) = n / i;
            end
        end
    end
end

4. 哥德巴赫猜想验证

function [prime1, prime2] = goldbachConjecture(evenNumber)
    for i = 2:evenNumber-2
        if isPrime(i) && isPrime(evenNumber-i)
            prime1 = i;
            prime2 = evenNumber - i;
            return;
        end
    end
end

function result = isPrime(n)
    if n <= 1
        result = false;
    elseif n <= 3
        result = true;
    else
        result = all(mod(n, 2:floor(sqrt(n))) ~= 0);
    end
end

5. 成绩统计

function stats = calculateGradeStats(grades)
    n = length(grades);
    total = sum(grades);
    avg = mean(grades);
    countBelow60 = sum(grades < 60);
    count60to70 = sum(grades >= 60 & grades < 70);
    count70to80 = sum(grades >= 70 & grades < 80);
    count80to90 = sum(grades >= 80 & grades < 90);
    countAbove90 = sum(grades >= 90);
    
    stats = struct('TotalStudents', n, 'TotalScore', total, 'AverageScore', avg, ...
                   'CountBelow60', countBelow60, 'Count60to70', count60to70, ...
                   'Count70to80', count70to80, 'Count80to90', count80to90, ...
                   'CountAbove90', countAbove90);
end

6. 猜数游戏

function guessNumberGame()
    randomNumber = randi([1, 100]);
    attempts = 7;
    for i = 1:attempts
        guess = input('Guess a number between 1 and 100: ');
        if guess == randomNumber
            disp('You win!');
            return;
        elseif guess > randomNumber
            disp('High');
        else
            disp('Low');
        end
    end
    disp(['Game over. The number was ', num2str(randomNumber

)]);
end

7. 星座查找

function zodiac = findZodiac(month, day)
    zodiacDates = [120, 219, 321, 420, 521, 621, 723, 823, 923, 1023, 1122, 1222, 1231; ...
                   218, 320, 420, 520, 620, 722, 822, 922, 1022, 1121, 1221, 1231, 119];
    zodiacs = {'水瓶座', '双鱼座', '白羊座', '金牛座', '双子座', '巨蟹座', '狮子座', '处女座', ...
               '天秤座', '天蝎座', '射手座', '摩羯座', '水瓶座'};
    dateNum = month * 100 + day;
    for i = 1:length(zodiacDates)-1
        if dateNum >= zodiacDates(1, i) && dateNum <= zodiacDates(2, i)
            zodiac = zodiacs{i};
            return;
        end
    end
end

8. 函数图形绘制

% (1) z=(xy)/(x²+y²), x²+y²≠0
[x, y] = meshgrid(-2:0.1:2, -2:0.1:2);
z = (x .* y) ./ (x.^2 + y.^2);
z(x.^2 + y.^2 == 0) = 0;
mesh(x, y, z);

% (2) z=(1+x+y)²
z = (1 + x + y).^2;
mesh(x, y, z);

% (3) z=√(x²+y²)
z = sqrt(x.^2 + y.^2);
mesh(x, y, z);

% (4) y=z²+1 绕z轴旋转
z = linspace(-2, 2, 100);
r = sqrt(z.^2 + 1);
[X, Y, Z] = cylinder(r);
surf(X, Y, Z * 4 - 2);

9. 绘制函数 z=(sin(x²+y²))/(√(x²+y²)

[x, y] = meshgrid(-8:0.2:8, -8:0.2:8);
z = (sin(x.^2 + y.^2)) ./ sqrt(x.^2 + y.^2);
mesh(x, y, z);  % 使用 mesh
meshc(x, y, z); % 使用 meshc
meshz(x, y, z); % 使用 meshz

10. 空间区域图形绘制

% (1) 2z=x²+y², z=1
[x, y] = meshgrid(-2:0.1:2, -2:0.1:2);
z = (x.^2 + y.^2) / 2;
z1 = ones(size(z));
surf(x, y, z);
hold on;
surf(x, y, z1);
hold off;

% 其他部分的代码可以类似编写，根据具体的数学表达式调整。

11. 球面绘制

% 球面 x²+y²+z²=4
[x, y, z] = sphere;
surf(2*x, 2*y, 2*z);

% 球面 x²+y²+(z-2)²=4
surf(2*x, 2*y, 2*(z+1));