differentials

main.cpp (4976B)

---

 #include <iostream>
 #include <iterator>
 #include <map>
 #include <math.h>
 #include <sstream>
 #include <vector>
 
 #define SEQUENCE_SIZE 7
 #define POWER 7 // also the maximum space a number in the sequence takes
 
 using namespace std;
 
 /* the functions doing actual calculations */
 void populate(const string& deffinition);
 /* --------------------------------------- */
 
 void pseq(const string& str);
 void psubseq(const string& str);
 void interactive();
 
 map<string, vector<int>> sequences;
 
 int main(int argc, char** argv)
 {
     if (argv[1] && argv[1] == (string) "post")
         populate("post");
     else
         populate("prior");
 
     interactive();
 
     return 0;
 }
 
 void pseq(const string& str)
 {
     vector<int> sequence = sequences[str];
     for (int i = 0; i < sequence.size(); ++i) {
         cout << sequence[i] << " ";
     }
     cout << endl;
 }
 
 void psubseq(const string& str)
 {
     // splitting the input str by spaces
     istringstream iss(str);
     vector<string> results((istream_iterator<string>(iss)),
         istream_iterator<string>());
 
     /* if (results.size() == 1) { */
     /*     vector<int> sequence = sequences[str]; */
     /*     for (int i = 0; i < sequence.size(); ++i) { */
     /*         cout << sequence[i] << " "; */
     /*     } */
     /*     cout << endl; */
     /* } else { */
     vector<int> sequence = sequences[results[0]];
     for (int i = 0; i < sequence.size(); ++i) {
         cout << sequence[i] + stoi(results[1]) << " ";
     }
     cout << endl;
     /* } */
 }
 
 void interactive()
 {
     string str;
     while (true) {
         getline(cin, str, '\n');
         if (str.find(" ") != string::npos)
             psubseq(str);
         else
             pseq(str);
     }
 }
 
 void populate(const string& deffinition)
 {
     for (int power = 1; power <= POWER; ++power) {
         // getting sequence name e.g. d1x1
         string seq_name = "x";
         seq_name.append(to_string(power));
         string diff_name = "d";
         diff_name.append(to_string(1));
         string res_name = diff_name.append(seq_name);
         ;
         cout << res_name << " = ";
 
         // calculates the sequence
         vector<int> n;
         int num;
         for (int place = -SEQUENCE_SIZE; place <= SEQUENCE_SIZE; ++place) {
             // raises the num in the sequence to the correct power
             num = pow(place, power);
             if (place == 0)
                 num = 0;
             /* num += 1; */
             n.push_back(num);
             for (int l = 0; l <= POWER - to_string(num).length(); ++l)
                 cout << " ";
             cout << num;
         }
         cout << endl;
         // stores the sequence in the map
         sequences.insert(pair<string, vector<int>>(res_name, n));
 
         // calculates the differentials of the sequences
         for (int diff = 2; true; ++diff) {
             // gets the sequence name e.g. d2n3 (aka ddn^3)
             string diff_name = "d";
             diff_name.append(to_string(diff));
             string res_name = diff_name.append(seq_name);
 
             // finds the sequence it's supposed to differentiate
             vector<int> s;
             if (diff == 2) {
                 s = n;
             } else {
                 string prev_diff_name = "d";
                 prev_diff_name.append(to_string(diff - 1));
                 prev_diff_name.append(seq_name);
                 s = sequences[prev_diff_name];
             }
 
             // differentiates
             cout << diff_name << " = ";
 
             if (deffinition == "prior")
                 for (int l = 0; l < (diff)-1; ++l) {
                     for (int i = 0; i < POWER; ++i)
                         cout << " ";
                     cout << " ";
                 }
 
             vector<int> m;
             int n;
             for (int i = 0; i < s.size() - 1; ++i) {
                 n = s[i + 1] - s[i];
                 m.push_back(n);
                 for (int l = 0; l <= POWER - to_string(n).length(); ++l)
                     cout << " ";
                 cout << n;
             }
 
             // stores the differential in the map
             sequences.insert(pair<string, vector<int>>(res_name, m));
 
             cout << endl;
 
             int l = m.front();
             for (int i = 0; i < m.size(); ++i) {
                 if (m[i] != m.front())
                     goto cont;
             }
             break;
         cont:
             continue;
         }
         if (power != POWER)
             cout << endl;
     }
 }
 
 void integrate()
 {
     // calculates the sequence
     vector<int> n;
     int num;
     for (int place = -SEQUENCE_SIZE; place <= SEQUENCE_SIZE; ++place) {
         // raises the num in the sequence to the correct power
         /* num = pow(place, power); */
         num = place;
         if (place == 0)
             num = 0;
         /* num += 1; */
         n.push_back(num);
         for (int l = 0; l <= POWER - to_string(num).length(); ++l)
             cout << " ";
         cout << num;
     }
     cout << endl;
 }