我正在尝试编写一个程序，该程序通过随机数生成器基于蒙特卡洛方法估算Pi。我正在尝试估计精度为1,2,3,4,5和6位数字的Pi，并将程序打印到屏幕上以使其在Pi的0.1位数之内需要多少点，然后在Pi的.01位数以内一直到Pi的.000001位数。我允许用户输入他们想运行的试验次数，因此它将打印“ Trial 1，2，3，4”等，上面列出了我所有的信息。我被困在最后一点，那就是让它在计算过程中循环返回（它不会打印出比试验1更多的内容）。尽管我没有收到消息程序已终止的消息，所以我无法确定是while循环失败还是嵌套的for循环。请帮忙！ ：）
我尝试在for循环之间切换，并尝试其他不同的if语句。这是我最接近的操作方式，只是允许用户进行多次试用。
#include "pch.h"
#include <iostream> //need this by default for cin
#include <math.h> //includes math functions
#include <cmath> //includes basic math
#include <cfloat> //includes floating point numbers
#include <iomanip> //includes setprecision for decimal places
#include <cstdlib> //needed for rand and srand functions
#include <ctime> //needed for time function used to seed generator
using namespace std;
int main()
{
cout << "The purpose of this program is to estimate pi using the monte
carlo method and a random number generator" << endl << endl;
unsigned seed = time(0);
srand(seed);
float radius;
int trialcount = 0;
int trials;
float accuracy;
const float pi = 3.14159265;
float randpi = 0;
int squarecount = 0;
int circlecount = 0;
float x;
float y;
int n;
cout << "The value of PI can be found as the ratio of areas of a circle of radius r located within a square of side 2r" << endl;
cout << "This program runs a MonteCarlo Simulation that generates numbers located randomly within a square" << endl;
cout << "The count of values within the square and the count of numbers within the circle approximate their areas" << endl;
cout << "An input value of radius determines the size of the circle and square" << endl;
cout << "The user specifies how many trials or test runs are desired" << endl << endl;
cout << "The true value of PI to 8 decimal places is 3.14159265" << endl << endl;
cout << "Input a value for radius: ";
cin >> radius;
cout << endl;
cout << "How many trials would you like? ";
cin >> trials;
cout << endl << endl;
cout << "Square count gives the Total number of random samples (they are within the square)" << endl;
cout << "Circle count gives the number of random samples that also fall within the circle" << endl << endl;
while (trialcount != trials)
{
accuracy = .1;
cout << "Trial " << trialcount + 1 << endl;
cout << "Accuracy \t\t" << "Square Count \t\t" << "Circle Count \t\t" << "Pi" << endl << endl;
for (int j = 0; randpi >= pi - accuracy || randpi <= pi + accuracy; j++)
{
cout << setprecision(6) << fixed << accuracy << " \t\t" << squarecount << " \t\t" << circlecount << " \t\t" << randpi << endl << endl;
accuracy = accuracy / 10;
for (int i = 0; randpi >= pi + accuracy || randpi <= pi - accuracy; i++)
{
x = (float)(rand());
x = (x / 32767) * radius;
y = (float)(rand());
y = (y / 32767) * radius;
squarecount++;
if ((x * x) + (y * y) <= (radius * radius))
{
circlecount++;
}
randpi = float(4 * circlecount) / squarecount;
}
}
trialcount++;
}
}
答案 0 :(得分：1)
我看到的问题：
第一个for循环没有任何意义。如果要确保使用0.1、0.01、0.001等精度，则只需要一个简单的for循环。应该执行以下操作：
for ( int j = 0; j < 6; ++j )
{
...
}
x和y的值计算不正确。您要确保其值小于或等于radius。但是，当您使用时：
x = (float)(rand());
x = (x / 32767) * radius;
y = (float)(rand());
y = (y / 32767) * radius;
不能保证它们小于或等于radius。他们将比radius多得多。您需要使用
x = (float)(rand() % 32768);
x = (x / 32767) * radius;
y = (float)(rand() % 32768);
y = (y / 32767) * radius;
您需要在内部randpi循环的每次迭代中重置squarecount，circlecount和for的值。否则，您的计算将受到上一次迭代的计算的影响。
外部for循环必须始于：
for (int j = 0; j < 6; j++)
{
accuracy /= 10;
randpi = 0;
squarecount = 0;
circlecount = 0;
内部for循环必须限制为只能运行一定次数。如果由于某种原因未达到精度，则要确保不会溢出i。例如：
int stopAt = (INT_MAX >> 8);
for (int i = 0; (randpi >= pi + accuracy || randpi <= pi - accuracy) && i < stopAt; i++)
对于使用32位int（今天在实践中最常见）的计算机，循环运行的次数不得超过0x7FFFFF（十进制8388607）次
这是代码中的核心问题。您的计算有时不会收敛，也无法确保在循环一定次数的迭代后退出。
程序中不需要radius作为变量。您可以将x和y计算为：
x = (float)(rand() % 32768);
x = (x / 32767);
y = (float)(rand() % 32768);
y = (y / 32767);
并更改逻辑以检查这是否是圆内的一个点
if ((x * x) + (y * y) <= 1.0 )
还应该尝试仅在需要它们的作用域中定义变量。这样可以确保您最终不会使用上一次迭代中的陈旧值。
以下经修改的程序对我有用。
#include <iostream> //need this by default for cin
#include <math.h> //includes math functions
#include <cmath> //includes basic math
#include <cfloat> //includes floating point numbers
#include <iomanip> //includes setprecision for decimal places
#include <cstdlib> //needed for rand and srand functions
#include <ctime> //needed for time function used to seed generator
#include <climits>
using namespace std;
int main()
{
cout << "The purpose of this program is to estimate pi using the monte "
"carlo method and a random number generator" << endl << endl;
unsigned seed = time(0);
srand(seed);
int trialcount = 0;
int trials;
float accuracy;
const float pi = 3.14159265;
cout << "The value of PI can be found as the ratio of areas of a circle of radius r located within a square of side 2r" << endl;
cout << "This program runs a MonteCarlo Simulation that generates numbers located randomly within a square" << endl;
cout << "The count of values within the square and the count of numbers within the circle approximate their areas" << endl;
cout << "An input value of radius determines the size of the circle and square" << endl;
cout << "The user specifies how many trials or test runs are desired" << endl << endl;
cout << "The true value of PI to 8 decimal places is 3.14159265" << endl << endl;
cout << endl;
cout << "How many trials would you like? ";
cin >> trials;
cout << endl << endl;
cout << "Square count gives the Total number of random samples (they are within the square)" << endl;
cout << "Circle count gives the number of random samples that also fall within the circle" << endl << endl;
while (trialcount != trials)
{
accuracy = 0.1;
cout << "Trial " << trialcount + 1 << endl;
cout << "Accuracy \t\t" << "Square Count \t\t" << "Circle Count \t\t" << "Pi" << endl << endl;
for (int j = 0; j < 6; j++)
{
accuracy /= 10;
float randpi = 0;
int squarecount = 0;
int circlecount = 0;
int stopAt = (INT_MAX >> 8);
for (int i = 0; (randpi >= pi + accuracy || randpi <= pi - accuracy) && i < stopAt; i++)
{
float x = ((float)(rand() % 32768) / 32767);
float y = ((float)(rand() % 32768) / 32767);
squarecount++;
if ((x * x) + (y * y) <= 1.0 )
{
circlecount++;
}
randpi = float(4 * circlecount) / squarecount;
}
cout << setprecision(8) << fixed << accuracy << " \t\t" << squarecount << " \t\t" << circlecount << " \t\t" << randpi << endl << endl;
}
trialcount++;
}
}
查看它在https://ideone.com/laF27X上的运行情况。