dynamical programming and recurrent descent

I have a task and solution. How can I solve it with the help of dynamical programming or recurrent descent?

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#include <iostream>
#include <string>
#include <vector>
#include <cmath>

using namespace std;

void minPoly(const string &str, double x) {
   vector<double> coefficients;
   if (x <= 1.0) {
      for (int i = 0; i < str.size(); i++) {
         int a = str[i] - '0';
         cout << a << " ";
         coefficients.push_back(a);
      }
   }
   else {
      double L = 0, R = stod(str), tenf = pow(10.0, str.size() - 1.0), xn = 1.0;
      for (int i = 0; i < str.size(); i++) {
         int a = str[i] - '0';
         cout << a;

         L = 10.0*L+a;
         R -= tenf*a*xn;

         if (( tenf - 1.0 )*L > R/xn(x-1.0)) {
            coefficients.push_back(L);
            L = 0.0;
            R *= x;
            xn *= x;
            cout << " ";
         }
         tenf /= 10.0;
      }
      coefficients.push_back(L);
   }
   cout << '\n';

   double poly = 0.0, xn = 1.0;
   for (double c : coefficients) {
      poly += c*xn;
      xn *= x;
   }
   cout << poly << '\n';
}

int main() {
   string str;
   double x;
   cout << "Enter string: ";   cin >> str;
   cout << "Enter x: ";        cin >> x;
   minPoly(str, x);
}


Enter string: 1234
Enter x: 1
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