Added Number_Theory_Algorithms under include directory

dsalglib/dsalglib.h

@@ -17,4 +17,7 @@
 #include "include/heap.h"
 #include "include/graph.h"
 
+#include "include/Number_Theory_Algorithms/fundamental_functions.h"
+#include "include/Number_Theory_Algorithms/prime_numbers.h"
+
 #endif //DSALGLIB_DSALGLIB_H

dsalglib/include/Number_Theory_Algorithms/fundamental_functions.h

@@ -0,0 +1,63 @@
+/*
+ * Created by yadvendra20 on 3/12/2020
+*/
+
+#ifndef DSALGLIB_NUMTHEORY_FF_H
+#define DSALGLIB_NUMTHEORY_FF_H
+
+#include "../alginc.h"
+
+namespace dsa {
+
+	/*
+	 * The binary exponentiation method computes 
+	 * powers directed by the exponent bits, one 
+	 * at a time. Bits of value 0 require a squaring; 
+	 * bits of value 1 require a squaring and a multiplication.
+	 * 
+	 * More about binary exponentiantion: https://cp-algorithms.com/algebra/binary-exp.html
+	*/
+
+	long long binaryExponentiation(long long base, long long exponent) {
+		if(base == 0LL)
+			return 0LL;
+		long long result = 1LL;
+		while(exponent > 0) {
+			if(exponent%2LL == 1LL)
+				result *= base;
+			base *= base;
+			exponent /= 2LL;
+		}
+		return result;
+	}
+
+	/*
+	 * Modular binary exponentiation
+	*/
+	long long modularBinaryExponentiation(long long base, long long exponent, long long mod) {
+		if(base == 0LL)
+			return 0LL;
+		long long result = 1LL;
+		while(exponent > 0) {
+			if(exponent%2LL == 1LL)
+				result = (result * base)%mod;
+			base = (base * base)%mod;
+			exponent /= 2LL;
+		}
+		return result;
+	}
+
+	/*
+	 * GCD Computation
+	*/
+
+	long long gcd(long long first_num, long long second_num) {
+		while(second_num > 0) {
+			first_num %= second_num;
+			swapit(first_num, second_num);
+		}
+		return first_num;
+	}
+}
+
+#endif // DSALGLIB_NUMTHEORY_FF_H

dsalglib/include/Number_Theory_Algorithms/prime_numbers.h

@@ -0,0 +1,53 @@
+/*
+ * Created by yadvendra20 on 3/12/2020
+*/
+
+#ifndef DSALGLIB_NUMTHEORY_PRIMES_H
+#define DSALGLIB_NUMTHEORY_PRIMES_H
+
+#include "../array.h"
+
+namespace dsa {
+
+	// returns true if the number is prime otherwise returns false
+
+	/*
+	 * The complexity of the isNumPrime function is O(square_root(number))
+	*/
+
+	bool isNumPrime(int number) {
+		if(number <= 1)
+			return false;
+		for(int i = 2; i * i <= number; i++) {
+			if(number % i == 0)
+				return false;
+		}
+		return true;
+	}
+
+	// Sieve of eratosthenes
+
+	/*
+	 * The sieve function returns a boolean array is_prime of 'number' size
+	 * where is_prime[num] = true (if num is a prime number) otherwise false
+	 * 
+	 * More about sieve of eratosthenes: https://cp-algorithms.com/algebra/sieve-of-eratosthenes.html
+	*/
+
+	array<bool> sieve(long long int number) {
+
+		array<bool> is_prime(number + 1, true);
+		is_prime[0] = false;
+		is_prime[1] = false;
+
+		for(int i = 2; i * i <= number; i++) {
+			if(is_prime[i]) {
+				for(int j = i * i; j <= number; j += i)
+					is_prime[j] = false;
+			}
+		}
+		return is_prime;
+	}
+}
+
+#endif // DSALGLIB_NUMTHEORY_PRIMES_H

dsalglib/include/array.h

@@ -26,9 +26,13 @@ namespace dsa
                     count = size;
                     capacity=size+spare;
                     objs = new type[capacity];
+                    if(!objs)
+                    	throw "Memory allocation failed";
+                    else {
                     long long int i;
-                    for(i=0;i<count;i++)
-                        objs[i]=param;
+		                for(i=0;i<count;i++)
+		                    objs[i]=param;
+                    }
                 }
 
 
@@ -38,6 +42,11 @@ namespace dsa
 
                     type *old = objs;
                     objs = new type[newsize];
+
+                    if(!objs) {
+                    	throw "Memory allocation failed";
+                    	return;
+                    }
 
                     long long int temp;
                     for(temp=0;temp<count;temp++)
@@ -125,6 +134,8 @@ namespace dsa
                     count = 0;
                     capacity = spare;
                     objs = new type[capacity];
+                    if(!objs)
+                    	throw "Memory allocation failed";
                 }
         };
 }

dsalglib/tests.h

@@ -249,4 +249,29 @@ void trie_test(){
     cout << t.search("third") << "\n";
 }
 
+void num_theory_functions_test() {
+	cout << binaryExponentiation(4, 3) << "\n";
+	cout << binaryExponentiation(0, 4) << "\n";
+	cout << binaryExponentiation(5, 0) << "\n";
+
+	const long long mod = 1e9 + 7;
+	long long a = 2, b = 1e9;
+	cout << modularBinaryExponentiation(a, b, mod) << "\n";
+}
+
+void num_theory_primes_test() {
+	cout << isNumPrime(7) << "\n";
+	cout << isNumPrime(1) << "\n";
+	cout << isNumPrime(1299653) << "\n";
+
+	try {
+		array<bool> is_prime = sieve(100);
+		for(int i = 0; i < 100; i++)
+			if(is_prime[i])
+				cout << i << " ";
+	} catch(const char* exception) {
+		cout << exception << "\n";
+	}
+}
+
 #endif //DSALGLIB_TESTS_H