Question

我有一个c ++算法来计算整数的平方根。除了一个缺陷外，该程序可以正常运行。它无法计算低于1的数字的平方根。例如，它无法计算.5或.9或.0000001等的平方根，但在所有其他情况下按计划工作。我有X设置所以它不允许负输入，但我仍然不明白为什么它不会返回任何小于1的值。

include <iostream>
#include <cmath>
#include <cassert>

using namespace std;

double squareroot(double x)

{ /* computes the square root of x */

  /* make sure x is not negative .. no math crimes allowed! */
    assert(x >= 0);
    if (x == 0) return 0;

    /* the sqrt must be between xhi and xlo */
    double xhi = x;
    double xlo = 0;
    double guess = x / 2;

    /* We stop when guess*guess-x is very small */

    while (abs(guess*guess - x) > 0.000001)
    {
        if (guess*guess > x)  xhi = guess;
        else xlo = guess;
        guess = (xhi + xlo) / 2;
    }

    return guess;
}

/* Test Stub */


int main()
{
    double testvalue;
    cout << "\n Enter a TestValue= ";
    cin >> testvalue;
    cout << endl;
    double testresult = squareroot(testvalue);
    cout << "\n Square Root= " << testresult << "\n";
}

感谢您的帮助！我能够通过使用以下方法解决问题：

if (x<1) {
    xhi = 1;
    xlo = x;
    guess = (x + 1) / 2;
}

Answer 1

0.5的平方根是~0.7。如果检查失败，您的逻辑就是猜测一个较小的数字。您需要做的是添加一个额外的检测层，以查看该数字是否为＆lt; 1，然后修改流程以增加下一个猜测，而不是减少它。

Answer 2

如果x <1，则需要更改初始边界，因为平方根不位于0和x之间，而是位于x和1之间

double xhi, xlo, guess;
if (x > 1){
    xhi = x;
    xlo = 0;
    guess = x / 2;
}
else{
    xhi = 1;
    xlo = x;
    guess = (x + 1) / 2;
}

Answer 3

添加一些调试输出。这将有助于您理解为什么程序在x < 1.0时永远不会收敛到解决方案。

while (abs(guess*guess - x) > 0.000001)
{
    if (guess*guess > x)
    {
       cout << "Changing xhi\n";
       xhi = guess;
    }
    else
    {
       cout << "Changing xlo\n";
       xlo = guess;
    }

    guess = (xhi + xlo) / 2;
    cout << "guess: " << guess << endl;
}

如果您关注the Newton-Raphson method，程序将更快收敛。此外，无论x是否大于或小于1，它都能正常工作。

double squareroot(double x)
{
   /* make sure x is not negative .. no math crimes allowed! */
   assert(x >= 0);
   if (x == 0) return 0;

   double guess = x / 2;
   while (abs(guess*guess - x) > 0.000001)
   {
      double dx = 0.5*(guess*guess -x)/guess;
      guess -= dx;
      cout << "guess: " << guess << endl;
   }

   return guess;
}

C ++ Square Root Function Bug

3 个答案: