// load automata for scanning valid identifiers
void Scanner::load_id_machine() {
// create the id scan automata
auto id_machine = FSMachinePtr(
new FiniteMachineContainer(get_token_info(TokType::MP_ID).first,
true));
// detects ids without two underscores
id_machine->add_state("0", true, false);
id_machine->add_state("1", false, true);
id_machine->add_state("2", false, true);
id_machine->add_state("3", false, false);
id_machine->add_state("4", false, false);
// add transitions
id_machine->add_alphabet("0", "1");
id_machine->add_alphabet("1", "1");
id_machine->add_digits("1", "1");
id_machine->add_transition("1", '_', "4");
id_machine->add_alphabet("4", "1");
id_machine->add_digits("4", "1");
// other part
id_machine->add_transition("0", '_', "3");
id_machine->add_alphabet("3", "2");
id_machine->add_digits("3", "2");
id_machine->add_alphabet("2", "2");
id_machine->add_digits("2", "2");
id_machine->add_transition("2", '_', "3");
// set priority
id_machine->set_priority(2);
// add to finite machines
this->fsmachines->push_back(FSMachinePtr(id_machine));
}
void Scanner::load_strand_machines(unsigned int within) {
// comments and strings, take that!
// add nested strings and comments feature using within variable
auto comment_machine = FSMachinePtr(
new FiniteMachineContainer(get_token_info(TokType::MP_COMMENT).first, true));
// add states
comment_machine->add_state("0", true, false);
comment_machine->add_state("1", false, false);
comment_machine->add_state("2", false, true);
// for state 1
comment_machine->add_alphabet("1", "1");
comment_machine->add_symbols("1", "1");
comment_machine->add_digits("1", "1");
comment_machine->add_transition("1", ' ', "1");
comment_machine->add_transition("1", '\n', "1");
comment_machine->add_transition("1", '\t', "1");
comment_machine->add_transition("1", '\v', "1");
comment_machine->add_transition("1", '\r', "1");
comment_machine->add_transition("1", '\f', "1");
comment_machine->remove_transition("1", '{');
comment_machine->remove_transition("1", '}');
comment_machine->add_transition("0", '{', "1");
comment_machine->add_transition("1", '}', "2");
// new machine
auto string_machine = FSMachinePtr(
new FiniteMachineContainer(get_token_info(TokType::MP_STRING_LITERAL).first, true));
// add states
string_machine->add_state("0", true, false);
string_machine->add_state("1", false, false);
string_machine->add_state("2", false, true);
// add transitions
string_machine->add_transition("0", '\'', "1");
string_machine->add_alphabet("1", "1");
string_machine->add_symbols("1", "1");
string_machine->add_digits("1", "1");
string_machine->add_transition("1", ' ', "1");
string_machine->remove_transition("1", '\'');
string_machine->remove_transition("1", '\'');
string_machine->add_transition("1", '\'', "2");
// set machine priority
comment_machine->set_priority(1);
string_machine->set_priority(1);
// add the machines to our FSMachines list
this->fsmachines->push_back(comment_machine);
this->fsmachines->push_back(string_machine);
}
int main(){
std::set<unsigned long> products;
unsigned long result = 0;
//number of digits total must be 9
//each part of the identity has at least 1 and at most 7 digits
//multiplicand has at most 7 digits
for(unsigned long multiplicand = 1; multiplicand < 10000000; ++multiplicand){
int multiplicand_digits = get_num_digits(multiplicand);
//digits of multiplier depends on digits of multiplicand and product (which is not known yet)
for(unsigned long multiplier = 1; multiplier < static_cast<unsigned long>(pow(10,8-multiplicand_digits)); ++multiplier){
int multiplier_digits = get_num_digits(multiplier);
int num_digits = multiplicand_digits + multiplier_digits +
(int) (log10(multiplicand) + log10(multiplier) + 1);
if( num_digits < 9 ){
continue;
}
if( num_digits > 9 ){
break;
}
unsigned long product = multiplicand * multiplier;
std::array<bool, 10> digit_table;
digit_table.fill(false);
//add digits to digit table. if a digit was already added, continue to next loop
if(!add_digits(multiplicand, digit_table)){
continue;
}
if(!add_digits(multiplier, digit_table)){
continue;
}
if(!add_digits(product, digit_table)){
continue;
}
//at this point, there are 9 digits in the identity and each one was added
//also there was no zero added, so there must be all digits in the sum
if(products.find(product) == products.end()){
result += product;
products.insert(product);
}
}
}
std::cout << result << std::endl;
return 0;
}
void Scanner::load_num_machines() {
// create floating point automata for scanning numeric literals
auto float_machine = FSMachinePtr(
new FiniteMachineContainer(get_token_info(TokType::MP_FLOAT_LITERAL).first, true));
// add states to this DFA, first and final
float_machine->add_state("0", true, false);
float_machine->add_state("1", false, false);
float_machine->add_state("2", false, true);
float_machine->add_state("3", false, false);
float_machine->add_state("4", false, false);
float_machine->add_state("5", false, true);
float_machine->add_digits("0", "1");
float_machine->add_digits("1", "1");
float_machine->add_transition("1", '.', "2");
float_machine->add_digits("2", "2");
float_machine->add_transition("2", 'e', "3");
float_machine->add_transition("2", 'E', "3");
float_machine->add_transition("3", '+', "4");
float_machine->add_transition("3", '-', "4");
float_machine->add_digits("3", "5");
float_machine->add_digits("4", "5");
float_machine->add_digits("5", "5");
// create integer automata
auto integer_machine = FSMachinePtr(
new FiniteMachineContainer(get_token_info(TokType::MP_INT_LITERAL).first, true));
// add states to this DFA
integer_machine->add_state("0", true, false);
integer_machine->add_state("1", false, true);
integer_machine->add_digits("0", "1");
integer_machine->add_digits("1", "1");
// reset both
float_machine->reset();
integer_machine->reset();
// set machine priorities
float_machine->set_priority(1);
integer_machine->set_priority(1);
// add both to the finite machines list
this->fsmachines->push_back(FSMachinePtr(float_machine));
this->fsmachines->push_back(FSMachinePtr(integer_machine));
}
int add_digits(int x)
{
static int sum = 0;
if (x == 0)
{
return 0;
}
sum = x%10 + add_digits(x / 10);
return sum;
}
void BigInt::add_vector(std::vector<int> &a, std::vector<int> &b) {
assert(a.size() == b.size());
int remainder = 0;
for (int i = 0; i < a.size(); ++i) {
a[i] = add_digits(a[i], b[i], remainder);
}
if (remainder != 0)
a.push_back(remainder);
}
int main()
{
// This function accepts a number and calculates the sum of its digits
int n, result;
printf("Enter a number\n");
scanf_s("%d", &n);
result = add_digits(n);
printf("The sum of %d is %d\n", n, result);
return 0;
}
