8-x 第八章总结与测验
章节回顾
CPU在程序中执行的特定语句序列称为程序的执行路径execution path。直线型程序straight-line program每次运行都遵循相同路径。
控制流语句control flow statements（也称流程控制语句flow control statements）允许程序员改变常规执行路径。当控制流语句导致程序开始执行非顺序指令序列时，这种情况称为分支branch。
条件语句conditional statement用于指定关联语句是否应被执行。
if语句if statements根据条件真伪决定关联语句的执行；else语句else statements则在条件为假时执行。多个if和else语句可串联使用。
悬空elsedangling else指else语句与if语句的关联关系存在歧义的情况。悬空else语句将与同一代码块中最后一个未匹配的if语句配对。因此，只需确保if语句主体置于代码块内，即可轻松避免悬空else问题。
空语句null statement仅由分号构成，不执行任何操作。当语言要求存在语句但程序员无需其执行任何操作时使用。
switch语句switch statements为多项匹配选择提供了更简洁高效的方案。该语法仅适用于整数类型，通过case标签case labels标识待匹配的条件值。当未找到匹配的case标签时，系统将执行default标签default label下的语句。
当执行流程从某标签下的语句流向后续标签下的语句时，称为贯穿（穿透）fallthrough。可通过break语句（或return语句）阻止贯穿。可使用[[fallthrough]]属性标注有意设计的穿透行为。
goto语句goto statements允许程序向前或向后跳转至代码其他位置。通常应避免使用此类语句，因其易导致程序执行路径如意大利面般错综复杂，形成“意大利面代码spaghetti code”。
while循环while loops使程序在给定条件为真时持续执行。条件判断在循环执行前进行。
无限循环infinite loop是指条件始终为真的循环，除非使用其他控制流语句终止，否则将持续执行。
循环变量loop variable（又称计数器counter）是用于统计循环执行次数的整型变量，每次循环执行称为一次迭代iteration。
do while循环do while loops与while循环类似，但条件在循环执行后而非之前进行评估。
for循环for loops是最常用的循环结构，适用于需要固定次数迭代的场景。当循环迭代次数多一次或少一次时，会引发差一错误off-by-one error。
break语句break statements可使程序跳出switch、while、do while或for循环（包括尚未讲解的基于范围的for循环）。continue语句continue statements则能使程序立即进入下一次循环迭代。
终止halts操作可强制程序结束。正常终止normal termination指程序以预期方式退出（状态码将指示成功与否）。std::exit()会在main函数末尾自动调用，也可显式调用终止程序。它会执行部分清理工作，但不会清理局部变量或展开调用栈。
异常终止abnormal termination发生于程序遭遇意外错误而被迫关闭时。std::abort可用于实现异常终止。
算法algorithm是为解决特定问题或产生有用结果而设计的有限指令序列。若算法在调用间保留信息，则称为有状态的stateful。反之，无状态stateless算法不存储任何信息（调用时必须提供其运行所需的所有信息）。应用于算法时，术语“状态state”指有状态变量中持有的当前值。
若给定输入（即初始值）总能产生相同输出序列，则被视为算法的确定性deterministic。
伪随机数生成器（PRNG） pseudo-random number generator (PRNG)是一种生成序列的算法，其特性可模拟随机数序列。PRNG实例化时，可提供称为随机种子random seed（或简称种子seed）的初始值（或值集）来初始化其状态。当PRNG通过种子完成初始化时，我们称其已被种子化seeded。种子值的大小可能小于PRNG状态的大小。此时我们称PRNG处于种子不足underseeded状态。PRNG开始重复输出前的序列长度称为周期period。
随机数分布random number distribution将伪随机数生成器的输出转换为另一种数字分布。均匀分布uniform distribution是一种随机数分布，其输出在两个数值X和Y（含边界值）之间以等概率产生。
测验时间
警告：从此刻起测验难度将逐步提升，但你一定能行。让我们一起征服这些测验吧！
问题 #1
在第4.x课——第4章总结与测验中，我们编写了一个模拟球体从塔顶坠落的程序。由于当时尚未学习循环结构，该程序只能模拟5秒的下落过程。
请修改下方程序，使球体下落时间可自由设定直至触地。同时更新程序以应用所有已学最佳实践（命名空间、constexpr等）。
#include <iostream>
// Gets tower height from user and returns it
double getTowerHeight()
{
std::cout << "Enter the height of the tower in meters: ";
double towerHeight{};
std::cin >> towerHeight;
return towerHeight;
}
// Returns the current ball height after "seconds" seconds
double calculateBallHeight(double towerHeight, int seconds)
{
const double gravity { 9.8 };
// Using formula: s = (u * t) + (a * t^2) / 2
// here u (initial velocity) = 0, so (u * t) = 0
const double fallDistance { gravity * (seconds * seconds) / 2.0 };
const double ballHeight { towerHeight - fallDistance };
// If the ball would be under the ground, place it on the ground
if (ballHeight < 0.0)
return 0.0;
return ballHeight;
}
// Prints ball height above ground
void printBallHeight(double ballHeight, int seconds)
{
if (ballHeight > 0.0)
std::cout << "At " << seconds << " seconds, the ball is at height: " << ballHeight << " meters\n";
else
std::cout << "At " << seconds << " seconds, the ball is on the ground.\n";
}
// Calculates the current ball height and then prints it
// This is a helper function to make it easier to do this
void calculateAndPrintBallHeight(double towerHeight, int seconds)
{
const double ballHeight{ calculateBallHeight(towerHeight, seconds) };
printBallHeight(ballHeight, seconds);
}
int main()
{
const double towerHeight{ getTowerHeight() };
calculateAndPrintBallHeight(towerHeight, 0);
calculateAndPrintBallHeight(towerHeight, 1);
calculateAndPrintBallHeight(towerHeight, 2);
calculateAndPrintBallHeight(towerHeight, 3);
calculateAndPrintBallHeight(towerHeight, 4);
calculateAndPrintBallHeight(towerHeight, 5);
return 0;
}
显示方案
#include <iostream>
namespace Constants
{
constexpr double gravity { 9.8 };
}
// Gets tower height from user and returns it
double getTowerHeight()
{
std::cout << "Enter the height of the tower in meters: ";
double towerHeight{};
std::cin >> towerHeight;
return towerHeight;
}
// Returns the current ball height after "seconds" seconds
// note: this function could be constexpr, but we haven't covered constexpr functions yet
double calculateBallHeight(double towerHeight, int seconds)
{
// Using formula: s = (u * t) + (a * t^2) / 2
// here u (initial velocity) = 0, so (u * t) = 0
const double fallDistance { Constants::gravity * (seconds * seconds) / 2.0 };
const double ballHeight { towerHeight - fallDistance };
if (ballHeight < 0.0)
return 0.0;
return ballHeight;
}
// Prints ball height above ground
void printBallHeight(double ballHeight, int seconds)
{
if (ballHeight > 0.0)
std::cout << "At " << seconds << " seconds, the ball is at height: " << ballHeight << " meters\n";
else
std::cout << "At " << seconds << " seconds, the ball is on the ground.\n";
}
// Calculates the current ball height and then prints it
// This is a helper function to make it easier to do this
double calculateAndPrintBallHeight(double towerHeight, int seconds)
{
const double ballHeight{ calculateBallHeight(towerHeight, seconds) };
printBallHeight(ballHeight, seconds);
return ballHeight;
}
int main()
{
const double towerHeight{ getTowerHeight() };
int seconds { 0 };
while (calculateAndPrintBallHeight(towerHeight, seconds) > 0.0)
{
++seconds;
}
return 0;
}
问题 #2
质数是指大于1的自然数，它只能被1和它自身整除（无余数）。
请编写isPrime()函数并使用for循环完成以下程序。成功时，程序将输出“Success!”。
// Make sure that assert triggers even if we compile in release mode
#undef NDEBUG
#include <cassert> // for assert
#include <iostream>
bool isPrime(int x)
{
return false;
// write this function using a for loop
}
int main()
{
assert(!isPrime(0)); // terminate program if isPrime(0) is true
assert(!isPrime(1));
assert(isPrime(2)); // terminate program if isPrime(2) is false
assert(isPrime(3));
assert(!isPrime(4));
assert(isPrime(5));
assert(isPrime(7));
assert(!isPrime(9));
assert(isPrime(11));
assert(isPrime(13));
assert(!isPrime(15));
assert(!isPrime(16));
assert(isPrime(17));
assert(isPrime(19));
assert(isPrime(97));
assert(!isPrime(99));
assert(isPrime(13417));
std::cout << "Success!\n";
return 0;
}
相关内容
assert 是一个预处理器宏，当关联的参数评估为假时会终止程序。因此当我们编写 assert(!isPrime(0)) 时，其含义是“如果 isPrime(0) 为真，则终止程序”。我们在第 9.6 课——assert 和 static_assert 中将更详细地讲解 assert。
显示方案
// Make sure that assert triggers even if we compile in release mode
#undef NDEBUG
#include <cassert> // for assert
#include <iostream>
// Non-optimized version
bool isPrime(int x)
{
if (x <= 1) // if x is negative, 0, or 1 then the number is not prime
return false;
for (int test{ 2 }; test < x; ++test)
{
if (x % test == 0) // if x is evenly divisible
return false; // then this number isn't prime
}
return true; // if we didn't find any divisors, then x must be prime
}
int main()
{
assert(!isPrime(0));
assert(!isPrime(1));
assert(isPrime(2));
assert(isPrime(3));
assert(!isPrime(4));
assert(isPrime(5));
assert(isPrime(7));
assert(!isPrime(9));
assert(isPrime(11));
assert(isPrime(13));
assert(!isPrime(15));
assert(!isPrime(16));
assert(isPrime(17));
assert(isPrime(19));
assert(isPrime(97));
assert(!isPrime(99));
assert(isPrime(13417));
std::cout << "Success!\n";
return 0;
}
额外加分题：
上述解决方案中的 for 循环存在两个不足之处：
- 它会检查偶数因数。我们无需测试这些因数（2 除外）。
- 它会检查所有小于等于 x 的数是否为因数。非质数（合数）至少有一个小于或等于其平方根的因数，因此无需检查大于x平方根的因数。std::sqrt(x)（位于
头文件中）可返回x的平方根。
针对后者，有两种优化方案：在循环前预先计算std::sqrt(x)，再将循环变量与该值进行比较。或者，通过将比较式两边平方来完全优化掉 std::sqrt(x) 的计算（感谢读者 JJag 提出此建议）（如需更多帮助请参阅提示）。我们在测验解决方案中将采用后者。
显示提示
提示：对于两个变量 a ≥ 0 和 b ≥ 0，当比较式 a ≤ √b 的两边都平方后，该比较式仍然成立。这得到 a² ≤ √b²，等价于 a² ≤ b。
更新上述解决方案以实现这两种优化。
显示方案
#include <cassert>
#include <cmath> // for std::sqrt
#include <iostream>
// optimized version
bool isPrime(int x)
{
if (x <= 1) // if x is negative, 0, or 1 then the number is not prime
return false;
if (x == 2) // the number 2 is the only even prime
return true;
if (x % 2 == 0) // any other even number is not prime
return false;
// For any number 3 or greater, test odd values (this is why we add 2)
// between 3 and sqrt(x) to see if they are a divisor
// Also see https://stackoverflow.com/questions/5811151/why-do-we-check-up-to-the-square-root-of-a-number-to-determine-if-the-number-is
// Since test >= 0 and x >=0, we can optimize test < std::sqrt(x) to test * text < x
for (int test{ 3 }; test * test <= x; test += 2)
{
if (x % test == 0) // if x is evenly divisible
return false; // then this number isn't prime
}
return true; // if we didn't find any divisors, then x must be prime
}
int main()
{
assert(!isPrime(0));
assert(!isPrime(1));
assert(isPrime(2));
assert(isPrime(3));
assert(!isPrime(4));
assert(isPrime(5));
assert(isPrime(7));
assert(!isPrime(9));
assert(isPrime(11));
assert(isPrime(13));
assert(!isPrime(15));
assert(!isPrime(16));
assert(isPrime(17));
assert(isPrime(19));
assert(isPrime(97));
assert(!isPrime(99));
assert(isPrime(13417));
std::cout << "Success!\n";
return 0;
}
问题 #3
实现一个猜数字游戏。首先，程序应随机生成一个1到100之间的整数。用户有7次机会猜数字。
若用户未猜中正确数字，程序应告知其猜得过高还是过低。若用户猜中数字，程序应告知其获胜。若用尽尝试次数，程序应告知其失败并显示正确数字。游戏结束时应询问用户是否继续，若未输入'y'或'n'则再次询问。
本测验假设用户输入有效数字。
使用8.15节——全局随机数生成（Random.h）中的Random.h头文件。
输出效果应如下所示：
Let's play a game. I'm thinking of a number between 1 and 100. You have 7 tries to guess what it is.
Guess #1: 64
Your guess is too high.
Guess #2: 32
Your guess is too low.
Guess #3: 54
Your guess is too high.
Guess #4: 51
Correct! You win!
Would you like to play again (y/n)? y
Let's play a game. I'm thinking of a number between 1 and 100. You have 7 tries to guess what it is.
Guess #1: 64
Your guess is too high.
Guess #2: 32
Your guess is too low.
Guess #3: 54
Your guess is too high.
Guess #4: 51
Your guess is too high.
Guess #5: 36
Your guess is too low.
Guess #6: 45
Your guess is too low.
Guess #7: 48
Your guess is too low.
Sorry, you lose. The correct number was 49.
Would you like to play again (y/n)? q
Would you like to play again (y/n)? n
Thank you for playing.
额外加分题：将最小值、最大值和猜测次数设为可配置参数。
显示方案
#include <iostream>
#include "Random.h" // https://www.learncpp.com/cpp-tutorial/global-random-numbers-random-h/
// Returns true if the user won, false if they lost
// We don't use the return value in this program, but it doesn't add complexity to have it, and may be useful in a future update
// (e.g. if we wanted to move the won/lost messages out of the function, or conditionalize other behavior based on won/lost)
bool playHiLo(int guesses, int min, int max)
{
std::cout << "Let's play a game. I'm thinking of a number between " << min << " and " << max << ". You have " << guesses << " tries to guess what it is.\n";
const int number { Random::get(min, max) }; // this is the number the user needs to guess
// Loop through all of the guesses
for (int count{ 1 }; count <= guesses; ++count)
{
std::cout << "Guess #" << count << ": ";
int guess{};
std::cin >> guess;
if (guess > number)
std::cout << "Your guess is too high.\n";
else if (guess < number)
std::cout << "Your guess is too low.\n";
else // guess == number, so the user won
{
std::cout << "Correct! You win!\n";
return true;
}
}
// The user lost
std::cout << "Sorry, you lose. The correct number was " << number << '\n';
return false;
}
bool playAgain()
{
// Keep asking the user if they want to play again until they pick y or n.
while (true)
{
char ch{};
std::cout << "Would you like to play again (y/n)? ";
std::cin >> ch;
switch (ch)
{
case 'y': return true;
case 'n': return false;
}
}
}
int main()
{
constexpr int guesses { 7 }; // the user has this many guesses
constexpr int min { 1 };
constexpr int max { 100 };
do
{
playHiLo(guesses, min, max);
} while (playAgain());
std::cout << "Thank you for playing.\n";
return 0;
}
我们将在第9.x课——第9章总结与测验中为该解决方案添加错误处理功能。
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