commit c12547b518de514696693d496d557a57fdbf00b3
Author: Petar Yotsev <petar@yotsev.xyz>
Date: Wed, 5 May 2021 14:37:02 +0100
Initial commit
Diffstat:
| A | Makefile | | | 16 | ++++++++++++++++ |
| A | README.md | | | 31 | +++++++++++++++++++++++++++++++ |
| A | main.cpp | | | 183 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
3 files changed, 230 insertions(+), 0 deletions(-)
diff --git a/Makefile b/Makefile
@@ -0,0 +1,16 @@
+CC = g++
+CC_FLAGS = -g -O2
+
+EXEC = prog
+SOURCES = $(wildcard *.cpp)
+OBJECTS = $(SOURCES:.cpp=.o)
+
+$(EXEC): $(OBJECTS)
+ $(CC) $(OBJECTS) -o $(EXEC) $(CC_FLAGS)
+ rm -f $(OBJECTS)
+
+%.o: %.cpp
+ $(CC) -c $(CC_FLAGS) $< -o $@
+
+clean:
+ rm -f $(EXEC) $(OBJECTS)
diff --git a/README.md b/README.md
@@ -0,0 +1,31 @@
+## Dependencies
+
+* Boost libraries and headers, namely multiprecision
+
+This dependency is not really required anymore and it will soon be
+removed but for now you need it to compile the program.
+
+## Compilation
+
+ $ make
+
+## Usage
+
+ $ ./prog
+ $ ./prog post
+ $ ./prog prior
+
+After the program is done printing, you are dropped into interactive
+mode where you can enter the name of a sequence to print it again or do
+simple addition/subtraction on it and print the result. The syntax of
+the three are respectively:
+
+ d2n4
+ d2n4 3
+ d2n4 -5
+
+To exit interactive mode press Ctrl-C
+
+If you want to change the maximum power or the number of numbers in a
+sequence, go to `main.cpp`, change the value of `POWER` and
+`SEQUENCE_SIZE`` respectively and recompile.
diff --git a/main.cpp b/main.cpp
@@ -0,0 +1,183 @@
+#include <boost/multiprecision/cpp_int.hpp>
+#include <iostream>
+#include <map>
+#include <math.h>
+#include <vector>
+
+#define SEQUENCE_SIZE 7
+#define POWER 7 // also the maximum space a number in the sequence takes
+
+using namespace std;
+using namespace boost::multiprecision;
+
+/* 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;
+}
