recursion_basics solutions added

11_recursion/practice/recursion_basic/tasks_01-02.cpp

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+#include <iostream>
+
+const int MAX = 12;
+
+/*************** Task 1 ***************/
+unsigned int factorial(unsigned int number) {
+	//limit
+	if (number > MAX)
+		return 0;
+	if (number == 0 || number == 1) 
+		return 1;
+	return number * factorial(number - 1);
+}
+
+/*************** Task 2 ***************/
+// main logic
+bool is_prime_rec(unsigned int number, unsigned int stop, unsigned int i) {
+
+	if (number == 1 || number == 2)
+		return true;
+	if (number % i == 0) 
+		return false;
+	if (i == stop) 
+		return true;
+
+	return is_prime_rec(number, stop, i + 1);
+}
+
+// "wrapper function" is a function which wraps another function (in our example the recursive one). 
+// It's essentially another function which calls the actual function.
+bool is_prime(unsigned int number) {
+
+	return is_prime_rec(number, sqrt(number), 2);
+}
+
+int main() {
+	unsigned int number;
+
+	// task_01
+	std::cin >> number;
+	std::cout << factorial(number) << std::endl;
+
+	// task_02
+	std::cin >> number;
+	if (is_prime(number))
+		std::cout << "Is prime \n";
+	else
+		std::cout << "Not prime \n";
+
+	return 0;
+}

11_recursion/practice/recursion_basic/tasks_03-04.cpp

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+#include <iostream>
+
+/*************** Task 3 ***************/
+// print the binary representation of a number
+// "actual function"
+void print_bits_rec(unsigned int number, unsigned int position) {
+
+	unsigned int mask = 1 << (position - 1);
+	std::cout << ((number&mask) ? "1" : "0");
+
+	if (position == 1)
+		return;
+	else
+		return print_bits_rec(number, position - 1);
+}
+
+// example of a "wrapper function"
+// "wrapper function" is a function which wraps another function (in our example the recursive one). 
+// It's essentially another function which calls the actual function.
+void print_bits(unsigned int number) {
+
+	unsigned int position = sizeof(unsigned int) * 8; 
+	return print_bits_rec(number, position);
+}
+
+/*************** Task 4 ***************/
+// print the number of zeros and ones in the binary representation of a number
+// main logic
+void count_bits_rec(unsigned int number, unsigned int position, int &zeroes, int &ones) {
+
+	unsigned int mask = 1 << (position - 1);
+	((number&mask) ? ones++ : zeroes++);
+
+	if (position == 1)
+		return;
+
+	else
+		return count_bits_rec(number, position - 1, zeroes, ones);
+}
+
+void count_bits(unsigned int number) {
+
+	int zeroes = 0;
+	int ones = 0;
+	unsigned int position = sizeof(unsigned int) * 8;
+	count_bits_rec(number, position,zeroes,ones);
+	std::cout << "In number: " << number << " we have " << zeroes << " zeroes and " << ones << " ones! \n";
+ }
+
+int main() {
+
+	unsigned int number;
+	std::cin >> number;
+	// task_03
+	print_bits(number);
+
+	std::cout << std::endl;
+
+	// task_04
+	count_bits(number);
+	std::cout << std::endl;
+
+	return 0;
+}

11_recursion/practice/recursion_basic/tasks_05-06.cpp

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+#include <iostream>
+
+// PAY ATTENTION how swapping two code lines changes the whole program
+/*************** Task 5 ***************/
+void print_forward(unsigned int number) {
+	if (number <= 0)
+		return;
+	print_forward(number / 10);
+	std::cout << (number % 10) << " ";
+}
+
+/*************** Task 6 ***************/
+void print_backward(unsigned int number) {
+
+	if (number <= 0)
+		return;
+
+	std::cout << (number % 10) << " ";
+	print_backward(number / 10);
+}
+
+int main() {
+
+	unsigned int number;
+	std::cin >> number;
+
+	// task_05
+	std::cout << "Forward: "; 
+	print_forward(number);
+	std::cout << std::endl;
+
+	// task_06
+	std::cout << "Backward: ";
+	print_backward(number);
+	std::cout << std::endl;
+
+	return 0;
+}

11_recursion/practice/recursion_basic/tasks_07-08.cpp

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+#include<iostream>
+
+/*************** Task 7 ***************/
+// the actual recursive function
+void print_line_rec(unsigned int k,unsigned int it, unsigned long long result) {
+
+	std::cout << result << ' ';
+
+	if (it < k)
+		print_line_rec(k, it + 1, result * 10);
+
+	std::cout << result << ' ';
+
+
+}
+
+// the wrapper
+void printLine(unsigned int k) {
+
+	print_line_rec(k, 1, 10);
+}
+
+
+/*************** Task 8 ***************/
+// just by following the recursive definition of the algorithm
+int gcd(int a, int b) {
+
+	return (b == 0) ? a : gcd(b, a % b);
+}
+
+
+int main() {
+
+	// task_07 output
+	std::cout << "Enter a positive number k >= 1, k = ";
+	unsigned int k;
+
+	std::cin >> k;
+
+	if (k < 1)
+		std::cout << "cheater!\n";
+	else {
+		std::cout << "The line looks like : \n";
+		printLine(k);
+	}
+
+	// task_08 output
+	std::cout << "\n\nEnter two numbers :\n";
+
+	int a, b;
+
+	std::cin >> a >> b;
+
+	std::cout << "gcd(" << a << ", " << b << ") = "
+		<< gcd(a, b) << '\n';
+
+
+	return 0;
+}