Solved all unsolved exercises from Seminar 4

5 files changed, 165 insertions, 0 deletions

diff --git a/Sem. 04/Solutions/exercise02.cpp b/Sem. 04/Solutions/exercise02.cpp
new file mode 100644
index 0000000..700962e
--- /dev/null
+++ b/Sem. 04/Solutions/exercise02.cpp
@@ -0,0 +1,18 @@
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+double distanceBetweenPoints(int x1, int y1, int x2, int y2)
+{
+	int sideA = abs(x1 - x2), sideB = abs(y1 - y2);
+	return sqrt(sideA * sideA + sideB * sideB); // Pythagorean theorem
+}
+
+int main()
+{
+	int x1, y1, x2, y2;
+	cin >> x1 >> y1 >> x2 >> y2;
+
+	cout << distanceBetweenPoints(x1, y1, x2, y2) << endl;
+}
diff --git a/Sem. 04/Solutions/exercise03.cpp b/Sem. 04/Solutions/exercise03.cpp
new file mode 100644
index 0000000..c238d44
--- /dev/null
+++ b/Sem. 04/Solutions/exercise03.cpp
@@ -0,0 +1,26 @@
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+// Taken from exercise02.cpp
+double distanceBetweenPoints(int x1, int y1, int x2, int y2)
+{
+	int sideA = abs(x1 - x2), sideB = abs(y1 - y2);
+	return sqrt(sideA * sideA + sideB * sideB); // Pythagorean theorem
+}
+
+double trianglePerimeterFromPoints(int x1, int y1, int x2, int y2, int x3, int y3)
+{
+	return distanceBetweenPoints(x1, y1, x2, y2) +
+		   distanceBetweenPoints(x1, y1, x3, y3) +
+		   distanceBetweenPoints(x2, y2, x3, y3);
+}
+
+int main()
+{
+	int x1, y1, x2, y2, x3, y3;
+	cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3;
+
+	cout << trianglePerimeterFromPoints(x1, y1, x2, y2, x3, y3) << endl;
+}
diff --git a/Sem. 04/Solutions/exercise04.cpp b/Sem. 04/Solutions/exercise04.cpp
new file mode 100644
index 0000000..56909ba
--- /dev/null
+++ b/Sem. 04/Solutions/exercise04.cpp
@@ -0,0 +1,50 @@
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+bool isPrime(int n)
+{
+	double rootOfN = sqrt(n);
+	for (int i = 2; i <= rootOfN; i++)
+	{
+		if (n % i == 0)
+			return false;
+	}
+	return true;
+}
+
+int countOfUniqueSimpleDivisors(int n)
+{
+	int divisorsCount = 0;
+	for (int i = 2; i <= n && n != 1; i++)
+	{
+		if (n % i == 0 && isPrime(i))
+		{
+			n /= i;
+			divisorsCount++;
+
+			if (n == 1)
+				return divisorsCount;
+		}
+	}
+	return -1; // Some divisors repeat themselves, so we can't have a proper count
+}
+
+void kCountOfSimpleDivisorsBetween(int a, int b, int k)
+{
+	for (int i = a; i <= b; i++)
+	{
+		if (countOfUniqueSimpleDivisors(i) == k)
+			cout << i << " ";
+	}
+	cout << endl;
+}
+
+int main()
+{
+	int a, b, k;
+	cin >> a >> b >> k;
+
+	kCountOfSimpleDivisorsBetween(a, b, k);
+}
diff --git a/Sem. 04/Solutions/exercise05.cpp b/Sem. 04/Solutions/exercise05.cpp
new file mode 100644
index 0000000..cfe60e4
--- /dev/null
+++ b/Sem. 04/Solutions/exercise05.cpp
@@ -0,0 +1,33 @@
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+// Taken from exercise04.cpp
+bool isPrime(int n)
+{
+	double rootOfN = sqrt(n);
+	for (int i = 2; i <= rootOfN; i++)
+	{
+		if (n % i == 0)
+			return false;
+	}
+	return true;
+}
+
+void printPrimeNumberPairs(int n)
+{
+	for (int i = 2; i <= n / 2; i++)
+	{
+		if (isPrime(i) && isPrime(n - i))
+			cout << i << ", " << n - i << endl;
+	}
+}
+
+int main()
+{
+	int n;
+	cin >> n;
+
+	printPrimeNumberPairs(n);
+}
diff --git a/Sem. 04/Solutions/exercise06.cpp b/Sem. 04/Solutions/exercise06.cpp
new file mode 100644
index 0000000..3ced4c3
--- /dev/null
+++ b/Sem. 04/Solutions/exercise06.cpp
@@ -0,0 +1,38 @@
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+bool isPowerOfSomething(int n)
+{
+	double rootOfN = sqrt(n);
+	for (int i = 2; i <= rootOfN; i++)
+	{
+		if (n % i == 0)
+		{
+			while (n % i == 0)
+				n /= i;
+
+			return n == 1;
+		}
+	}
+	return false; // Obligatory default case
+}
+
+void powerNumbersBetween(int a, int b)
+{
+	for (int i = a; i <= b; i++)
+	{
+		if (isPowerOfSomething(i))
+			cout << i << " ";
+	}
+	cout << endl;
+}
+
+int main()
+{
+	int a, b;
+	cin >> a >> b;
+
+	powerNumbersBetween(a, b);
+}