c++ - 如何找到以 3.14159 开头的第一个 pi

Question

为了确定第一次获得以 3.14159 开头的 pi 需要多少项，我编写了以下程序来计算项为 (pi = 4 - 4/3 + 4/5 - 4/7 + ...) .

我的问题是结果我达到了 146063 个术语，但是当我检查时，有很多 pi 在此之前以类似的方式开始。

//piEstimation.cpp
//estima mathematical pi and detrmin when 
//to get a value beganing with 3.14159

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

int main(){
    //initialize vars
    double denominator{1.0};
    double pi{0};
    string piString;
    double desiredPi;    
    int terms;
    int firstDesiredTerm;

    //format output floating point numbers to show 10 digits after 
    // decimal poin
    cout << setprecision (10) <<fixed;

    for (terms = 1;  ; terms++){
        if(0 == terms % 2){ //if term is even
            pi -= 4/denominator;
        }
        else{ //if term is odd
            pi += 4/denominator;
        }

        // draw table
        cout << terms << "\t" << pi << endl;

        //determin first time the pi begains with 3.14159
        piString = to_string(pi).substr(0,7);
        if(piString == "3.14159"){
             firstDesiredTerm = terms;
             desiredPi = pi;
             break;
        }
        denominator += 2;
    }//end for

    cout << "The first time that pi value begans with 3.14159 "
        << "the number of terms are " << firstDesiredTerm << " and pi value is  "<< desiredPi <<endl;
}//end main

Answer 1

号码x如果 x >= 3.14159 && x < 3.1416，则以 3.14159 开头.不需要使用字符串和比较字符。 to_string必须使用某种圆形操作。如果没有字符串，算法会在 136121 步后找到结果

#include <iostream>
#include <iomanip>

int main(){
    //initialize vars
    double denominator{1.0};
    double pi{0};
    double desiredPi;    
    int terms;
    int firstDesiredTerm;

    //format output floating point numbers to show 10 digits after 
    // decimal poin
    std::cout << std::setprecision (20) << std::fixed;

    for (terms = 1;  ; terms++){
        if(0 == terms % 2){ //if term is even
            pi -= 4/denominator;
        }
        else{ //if term is odd
            pi += 4/denominator;
        }

        // draw table
        std::cout << terms << "\t" << pi << std::endl;

        if(pi >= 3.14159 && pi < 3.1416){
             firstDesiredTerm = terms;
             desiredPi = pi;
             break;
        }
        denominator += 2;
    }//end for

    std::cout << "The first time that pi value begans with 3.14159 "
        << "the number of terms are " << firstDesiredTerm 
        << " and pi value is  "<< desiredPi << std::endl;
}

输出:

The first time that pi value begans with 3.14159 the number of terms are 136121 and pi value is  3.14159999999478589672

在这里你可以看到如何 to_string舍入结果:

#include <iostream>
#include <iomanip>
#include <string>

int main(){
    std::cout << std::setprecision (20) << std::fixed;
    std::cout << std::to_string(3.14159999999478589672) << '\n';
}

输出:

3.141600

您可以阅读 cppreference

std::string to_string( double value ); Converts a floating point value to a string with the same content as what std::sprintf(buf, "%f", value) would produce for sufficiently large buf.

您可以阅读 cppreference

f F Precision specifies the exact number of digits to appear after the decimal point character. The default precision is 6

这意味着 std::to_string 6 位后四舍五入。