03-1. Two-point method to find a polynomial-type single

The principle of the dichotomy method is: if the continuous function f (x) in the interval [a, b] two endpoints of the value of the difference, that is F (a) f (b) <0, then it has at least 1 root R in this interval, that is, f (r) = 0.

The steps of the dichotomy are:

• Check the interval length, if it is less than the given threshold, stop, the output interval midpoint (a+b)/2;
• If f (a) f (b) <0, the value of the midpoint is computed F ((A+B)/2);
• If f ((A+B)/2) is exactly 0, then (a+b)/2 is the root of the requirement;
• If f ((A+B)/2) is the same as F (a), then the root is in the interval [(A+B)/2, b], making a= (A+B)/2, repeating the cycle;
• If f ((A+B)/2) is the same as F (b), then the root is in the interval [A, (A+B)/2], making b= (A+B)/2, repeating the cycle;

  This topic requires a program to calculate the root of a given 3-order polynomial f (x) =a3x3+a2x2+a1x+a0 within a given interval [a, b].

  Input Format:

  Enter the 4 coefficients A3, A2, A1, A0 of the polynomial in the order given in the 1th row, giving the interval endpoints a and B sequentially in line 2nd. The topic guarantees that the polynomial has a unique single root within a given interval.

  output Format:

  The root of the polynomial within the interval is output in a row, which is exactly 2 digits after the decimal point.

  Input Sample:

  3-1-3 1-0.5 0.5

  Sample output:

#include <iostream> #include <cstdio> #include <cmath>using namespace Std;const double threshold=0.01 ; The threshold double a3,a2,a1,a0;double f (double x) {    return  x * (x * (A3 * x + A2) + A1) + a0;} int main () {    double a,b,mid;    CIN >> A3 >> A2 >> A1 >> A0;    Cin >> a >> b;    while (B-a>=threshold)    {        mid= (a+b)/2;        if (f (mid) ==0) break            ;        else if (f (mid) *f (a) >0)            A=mid;        else if (f (mid) *f (b) >0)            b=mid;    }    Mid= (A+B)/2;    printf ("%.2lf\n", mid);    return 0;}

03-1. Two-point method to find a polynomial-type single