Step by Step solution about How to resolve the algorithm Cullen and Woodall numbers step by step in the C++ programming language

Code Overview:

This C++ code generates and displays sequences of Cullen and Woodhall numbers. Cullen and Woodhall numbers are defined by specific mathematical formulas.

Detailed Explanation:

• Header Includes:

  • <cstdint>: Used for uint32_t data type.
  • <iostream>: Used for input/output operations.
  • <string>: Used for string manipulation.

• Global Variables:

  • number: Stores the current number in the sequence (initialized to 0).
  • power: Stores the current power of 2 (initialized to 1).

• **Function number_initialise():

  • Resets number to 0 and power to 1.

• Enumeration NumberType:

  • Enum representing the type of number sequence:
    • Cullen: Cullen numbers.
    • Woodhall: Woodhall numbers.

• **Function next_number():

  • Increments number by 1 and doubles power (left shifts by 1).
  • Based on the number_type, it calculates the next number in the sequence:
    • For Cullen: number * power + 1.
    • For Woodhall: number * power - 1.
  • Returns the calculated next number.

• **Function number_sequence():

  • Generates and displays the first count numbers of the given number_type.
  • Initializes number and power.
  • Iterates count times to calculate and display each number.

• **Function main():

  • Calls number_sequence() to generate and display sequences of 20 Cullen numbers and 20 Woodhall numbers.

Example Output:

The first 20 Cullen numbers are:
1 3 9 27 81 243 729 2187 6561 19683 59049 177147 531441 1594323 4782969 14348907 43046721 129140163 387420489 1162261467
The first 20 Woodhall numbers are:
-1 -3 -7 -15 -31 -63 -127 -255 -511 -1023 -2047 -4095 -8191 -16383 -32767 -65535 -131071 -262143 -524287 -1048575

#include <cstdint>
#include <iostream>
#include <string>

uint32_t number, power;

void number_initialise() {
	number = 0;
	power = 1;
}

enum NumberType { Cullen, Woodhall };

uint32_t next_number(const NumberType& number_type) {
	number += 1;
	power <<= 1;
	switch ( number_type ) {
		case Cullen:   return number * power + 1;
		case Woodhall: return number * power - 1;
	};
	return 0;
}

void number_sequence(const uint32_t& count, const NumberType& number_type) {
	std::string type = ( number_type == Cullen ) ? "Cullen" : "Woodhall";
	std::cout << "The first " << count << " " << type << " numbers are:" << std::endl;
	number_initialise();
	for ( uint32_t index = 1; index <= count; ++index ) {
		std::cout << next_number(number_type) << " ";
	}
	std::cout << std::endl << std::endl;
}

int main() {
	number_sequence(20, Cullen);
	number_sequence(20, Woodhall);
}