Need to do compare without functions by using 3 variables on - c++

Question

Need to do compare without functions. I gotta do compare by using function just once and use no more 3 variables. Task that I got: need to tabulate (A to B, with h step) and show local minimum by “*”
——————————
#include <iostream>
#include "clocale"
#include "cmath"
#include <iomanip>
using namespace std;
// ------------------------- f(x) = x*sin(3*x) - 1 -------------------
double f(double x){
return x*sin(3*x) - 1;
}
// -------------------------------------------------------------------------------
int main()
{
setlocale(LC_ALL, "russian");
double A,B;
double h;
// ------------------ ---------------------
cout << "A = ";
cin >> A;
cout << "B = ";
cin >> B;
cout << "h = ";
cin >> h;
// ------------------------------------------------------
cout.setf(ios_base::fixed);
cout.precision(4);
for (double k=A; k<=B; k+=h){
if (f(k - h) >= f(k) && f(k + h) >= f(k)){
cout << "*";
}
else{
cout << " ";
}
cout << "x = " << k << " y = " << f(k) << "\n";
}
system("pause");
return 0;
}

Answer 1

I hope I guess right what you want to do. For each f(x) you want to compare that value to f(x-h) and f(x+h) to see if f(x) is a local minimum. You seem to have something, but you are recalculating f(x-h), f(x) and f(x+h) every time you use the value, when in fact on each iteration you only need to compute a single new value.
Just remember previous values. Note that the first point you can compare previous and next value is A+h, hence we start with
auto current = f(A+h);
auto previous = f(A);
auto next = f(A+2*h);
if (do the comparison of current vs previous and next) print something
// now the loop
for (double x = A+2*h; x < B; x+=h){
previous = current;
current = next; // in the first iteration this is f(A+2*h)
next = f(x+h);
if (do the comparison of current vs previous and next) print something
}
Note that now in each iteration only the next value is calculated, while current and previous are already known from the iteration before.

Answer 2

since you are trying to find local minima then you should try following code. this is exactly as you wanted but more robust.
#include <iostream>
#include "clocale"
#include "cmath"
#include <iomanip>
using namespace std;
// ------------------------- f(x) = x*sin(3*x) - 1 -------------------
double f(double x){
return x*sin(3*x) - 1;
}
// -------------------------------------------------------------------------------
bool is_minima(double a, double b, double c){
if(a > b && c > b){
return true;
else
return false;
}
int main()
{
setlocale(LC_ALL, "russian");
double A,B;
double h;
// ------------------ ---------------------
cout << "A = ";
cin >> A;
cout << "B = ";
cin >> B;
cout << "h = ";
cin >> h;
// ------------------------------------------------------
cout.setf(ios_base::fixed);
cout.precision(4);
for (double k=A; k<=B; k+=h){
if (is_minima(f(k-h),f(k),f(k+h))){
cout << "*";
}
else{
cout << " ";
}
cout << "x = " << k << " y = " << f(k) << "\n";
}
system("pause");
return 0;
}