Merge commit upstream/master into merge_upstream

Signed-off-by: Krishna Vedala <[email protected]>

Author: kvedala

DIRECTORY.md

@@ -100,6 +100,7 @@
 
 ## Math
   * [Binary Exponent](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/binary_exponent.cpp)
+  * [Check Prime](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/check_prime.cpp)
   * [Double Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/double_factorial.cpp)
   * [Eulers Totient Function](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/eulers_totient_function.cpp)
   * [Extended Euclid Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/extended_euclid_algorithm.cpp)

math/check_prime.cpp

@@ -0,0 +1,58 @@
+/**
+ * Copyright 2020 @author omkarlanghe
+ *
+ * @file 
+ * A simple program to check if the given number if prime or not.
+ * 
+ * @brief
+ * Reduced all possibilities of a number which cannot be prime.
+ * Eg: No even number, except 2 can be a prime number, hence we will increment our loop with i+2 jumping on all odd numbers only.
+ * If number is <= 1 or if it is even except 2, break the loop and return false telling number is not prime.
+ */
+#include <iostream>
+#include <cassert>
+ /**
+ * Function to check if the given number is prime or not.
+ * @param num number to be checked.
+ * @return if number is prime, it returns @ true, else it returns @ false.
+ */
+template<typename T>
+bool is_prime(T num) {
+    bool result = true;
+    if (num <= 1) {
+        return 0;
+    } else if (num == 2) {
+        return 1;
+    } else if ((num & 1) == 0) {
+        return 0;
+    }
+    if (num >= 3) {
+        for (T i = 3 ; (i*i) < (num) ; i = (i + 2)) {
+            if ((num % i) == 0) {
+                result = false;
+                break;
+            }
+        }
+    }
+    return (result);
+}
+
+/**
+ * Main function
+ */
+int main() {
+    int num;
+    std::cout << "Enter the number to check if it is prime or not" <<
+    std::endl;
+    std::cin >> num;
+    bool result = is_prime(num);
+    if (result) {
+        std::cout << num << " is a prime number" <<
+        std::endl;
+    } else {
+        std::cout << num << " is not a prime number" <<
+        std::endl;
+    }
+    assert(is_prime(50) == false);
+    assert(is_prime(115249) == true);
+}

math/least_common_multiple.cpp

@@ -0,0 +1,70 @@
+/**
+ * Copyright 2020 @author tjgurwara99
+ * @file
+ *
+ * A basic implementation of LCM function
+ */
+
+#include <cassert>
+#include <iostream>
+
+/**
+ * Function for finding greatest common divisor of two numbers.
+ * @params two integers x and y whose gcd we want to find.
+ * @return greatest common divisor of x and y.
+ */
+unsigned int gcd(unsigned int x, unsigned int y) {
+    if (x == 0) {
+        return y;
+    }
+    if (y == 0) {
+        return x;
+    }
+    if (x == y) {
+        return x;
+    }
+    if (x > y) {
+        // The following is valid because we have checked whether y == 0
+
+        int temp = x / y;
+        return gcd(y, x - temp * y);
+    }
+    // Again the following is valid because we have checked whether x == 0
+
+    int temp = y / x;
+    return gcd(x, y - temp * x);
+}
+
+/**
+ * Function for finding the least common multiple of two numbers.
+ * @params integer x and y whose lcm we want to find.
+ * @return lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y)
+ */
+unsigned int lcm(unsigned int x, unsigned int y) { return x * y / gcd(x, y); }
+
+/**
+ * Function for testing the lcm() functions with some assert statements.
+ */
+void tests() {
+    // First test on lcm(5,10) == 10
+    assert(((void)"LCM of 5 and 10 is 10 but lcm function gives a different "
+                  "result.\n",
+            lcm(5, 10) == 10));
+    std::cout << "First assertion passes: LCM of 5 and 10 is " << lcm(5, 10)
+              << std::endl;
+
+    // Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)
+    assert(((void)"LCM of 2 and 3 is 6 but lcm function gives a different "
+                  "result.\n",
+            lcm(2, 3) == 6));
+    std::cout << "Second assertion passes: LCM of 2 and 3 is " << lcm(2, 3)
+              << std::endl;
+}
+
+/**
+ * Main function
+ */
+int main() {
+    tests();
+    return 0;
+}