作业_实验报告.cpp

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// 作业_实验报告.cpp : 编写程序求无理数e,用牛顿迭代法求解方程.
/*
#include "stdafx.h"
#include <math.h>
#include <stdio.h>

//定义原函数
double F(double a, double b, double c, double x)
{
	return a*x*x + b*x + c;
}

//导数函数
double f(double a, double b, double x)
{
	return 2*a*x + b;
}

//迭代函数
double newtonIteration(double x0, double a, double b, double c, double(*F)(double, double, double, double), double(*f)(double, double, double))
{
	double x = x0 - (* F)(a, b, c, x0)/(* f)(a , b , x0);
	return x;
}

//迭代过程函数
void course(double x0, double a, double b, double c, double e, int n)
{
	double x1;
	int k;
	
    printf("迭代过程为：\n");

	for(k = 1; k <= n; k++)
	{
		if(f(a, b, x0) == 0)
		{
			printf("此函数的导函数值为0,不能用牛顿迭代法求解!\n");
			break;
		}
		else
		{
		    x1 = newtonIteration(x0, a, b, c, (*F), (*f));
		    printf("x%d=%lf\n", k, x1);

		    if(fabs(x1 - x0) < e)
			{
			   printf("共迭代了%d次,方程的根x=%lf\n", k, x1);
			   break;
			}
		    else if((k == n)&&(fabs(x1 - x0) > e))
			{
				printf("已达到最大迭代次数,但没有求出方程的根,\n请调整后再试!\n");
				break;
			}
			else
				x0 = x1;
		}
	}
}


int main(int argc, char* argv[])
{
	double A, B, C, x0, e;
	int n;

	printf("                   用牛顿迭代法求一元二次方程Ax^2+Bx+C=0的根\n\n");
	printf("请输入二次项系数A: ");
	scanf("%lf", &A);
	printf("请输入一次项系数: ");
	scanf("%lf", &B);
	printf("请输入常数项: ");
	scanf("%lf", &C);

	if (B*B - 4*A*C < 0)
	{
		printf("错误:此方程没有实数根!\n");
		return 0;
	}

	printf("输入迭代初值: ");
	scanf("%lf", &x0);
	printf("请输入所求实根的精度：e =");
	scanf("%lf", &e);
    printf("请输入您所要求计算时的最大迭代次数n：n=");
	scanf("%d", &n);
	printf("\n");
	course(x0, A, B, C, e, n);
	return 0;
}
*/
#include "stdafx.h"
#include <iostream.h>
#include <math.h>
#include <iomanip.h>

//n的阶乘,用来检验和对比
double factorial0(int counter)
{
	double factorial = 1;
	for(int i = 1; i <= counter; i++)
	{
		factorial *= i;
	}
	return factorial;
}

//求1/n!
double factorial(int counter)
{
	double factorial = 1;
	for(int i = 1; i <= counter; i++)
	{
		factorial *= i;
	}
	return 1/factorial;
}

//求1/1!到1/n!的和
double sumOfFatcorial(int counter)
{
	double sum = 0;
	for(int i = 0; i <= counter; i++)
	{
		sum += factorial(i);
	}
	return sum;
}


int main(int argc, char* argv[])
{
	double e;
	int n;
	cout << "------------------------------用泰勒公式求无理数e------------------------------" << endl;
	cout << "请输入精度(即公式的项数n): " << endl;
	cin >> n;

	for(int i = 1; i <= n; i++)
	{
		e = sumOfFatcorial(i);
		cout << i << "! = " << factorial0(i) << endl;
		cout << "1/" << i << "! = " << factorial(i) << endl;
		cout << "e = " << setprecision(15) << e << endl << endl;
	}
	cout << "------------------------------------------------------------------------------" << endl;
	cout << "e的准确值: e = 2.718281828459045376" << endl;
	return 0;
}