Merge branch 'master' into add/number_of_paths

DIRECTORY.md

@@ -340,6 +340,7 @@
   * [Sparse Table](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/range_queries/sparse_table.cpp)
 
 ## Search
+  * [Longest Increasing Subsequence Using Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/Longest_Increasing_Subsequence_using_binary_search.cpp)
   * [Binary Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/binary_search.cpp)
   * [Exponential Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/exponential_search.cpp)
   * [Fibonacci Search](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/search/fibonacci_search.cpp)

greedy_algorithms/binary_addition.cpp

@@ -0,0 +1,119 @@
+/**
+ * @file binary_addition.cpp
+ * @brief Adds two binary numbers and outputs resulting string
+ *
+ * @details The algorithm for adding two binary strings works by processing them
+ * from right to left, similar to manual addition. It starts by determining the
+ * longer string's length to ensure both strings are fully traversed. For each
+ * pair of corresponding bits and any carry from the previous addition, it
+ * calculates the sum. If the sum exceeds 1, a carry is generated for the next
+ * bit. The results for each bit are collected in a result string, which is
+ * reversed at the end to present the final binary sum correctly. Additionally,
+ * the function validates the input to ensure that only valid binary strings
+ * (containing only '0' and '1') are processed. If invalid input is detected,
+ * it returns an empty string.
+ * @author [Muhammad Junaid Khalid](https://github.com/mjk22071998)
+ */
+
+#include <algorithm>  /// for reverse function
+#include <cassert>    /// for tests
+#include <iostream>   /// for input and outputs
+#include <string>     /// for string class
+
+/**
+ * @namespace
+ * @brief Greedy Algorithms
+ */
+namespace greedy_algorithms {
+/**
+ * @brief A class to perform binary addition of two binary strings.
+ */
+class BinaryAddition {
+ public:
+    /**
+     * @brief Adds two binary strings and returns the result as a binary string.
+     * @param a The first binary string.
+     * @param b The second binary string.
+     * @return The sum of the two binary strings as a binary string, or an empty
+     * string if either input string contains non-binary characters.
+     */
+    std::string addBinary(const std::string& a, const std::string& b) {
+        if (!isValidBinaryString(a) || !isValidBinaryString(b)) {
+            return "";  // Return empty string if input contains non-binary
+                        // characters
+        }
+
+        std::string result;
+        int carry = 0;
+        int maxLength = std::max(a.size(), b.size());
+
+        // Traverse both strings from the end to the beginning
+        for (int i = 0; i < maxLength; ++i) {
+            // Get the current bits from both strings, if available
+            int bitA = (i < a.size()) ? (a[a.size() - 1 - i] - '0') : 0;
+            int bitB = (i < b.size()) ? (b[b.size() - 1 - i] - '0') : 0;
+
+            // Calculate the sum of bits and carry
+            int sum = bitA + bitB + carry;
+            carry = sum / 2;  // Determine the carry for the next bit
+            result.push_back((sum % 2) +
+                             '0');  // Append the sum's current bit to result
+        }
+        if (carry) {
+            result.push_back('1');
+        }
+        std::reverse(result.begin(), result.end());
+        return result;
+    }
+
+ private:
+    /**
+     * @brief Validates whether a string contains only binary characters (0 or 1).
+     * @param str The string to validate.
+     * @return true if the string is binary, false otherwise.
+     */
+    bool isValidBinaryString(const std::string& str) const {
+        return std::all_of(str.begin(), str.end(),
+                           [](char c) { return c == '0' || c == '1'; });
+    }
+};
+}  // namespace greedy_algorithms
+
+/**
+ * @brief run self test implementation.
+ * @returns void
+ */
+static void tests() {
+    greedy_algorithms::BinaryAddition binaryAddition;
+
+    // Valid binary string tests
+    assert(binaryAddition.addBinary("1010", "1101") == "10111");
+    assert(binaryAddition.addBinary("1111", "1111") == "11110");
+    assert(binaryAddition.addBinary("101", "11") == "1000");
+    assert(binaryAddition.addBinary("0", "0") == "0");
+    assert(binaryAddition.addBinary("1111", "1111") == "11110");
+    assert(binaryAddition.addBinary("0", "10101") == "10101");
+    assert(binaryAddition.addBinary("10101", "0") == "10101");
+    assert(binaryAddition.addBinary("101010101010101010101010101010",
+                                    "110110110110110110110110110110") ==
+           "1100001100001100001100001100000");
+    assert(binaryAddition.addBinary("1", "11111111") == "100000000");
+    assert(binaryAddition.addBinary("10101010", "01010101") == "11111111");
+
+    // Invalid binary string tests (should return empty string)
+    assert(binaryAddition.addBinary("10102", "1101") == "");
+    assert(binaryAddition.addBinary("ABC", "1101") == "");
+    assert(binaryAddition.addBinary("1010", "1102") == "");
+    assert(binaryAddition.addBinary("111", "1x1") == "");
+    assert(binaryAddition.addBinary("1x1", "111") == "");
+    assert(binaryAddition.addBinary("1234", "1101") == "");
+}
+
+/**
+ * @brief main function
+ * @returns 0 on successful exit
+ */
+int main() {
+    tests(); /// To execute tests
+    return 0;
+}

math/modular_inverse_fermat_little_theorem.cpp

@@ -30,8 +30,8 @@
  * a^{m-2} &≡&  a^{-1} \;\text{mod}\; m
  * \f}
  *
- * We will find the exponent using binary exponentiation. Such that the
- * algorithm works in \f$O(\log m)\f$ time.
+ * We will find the exponent using binary exponentiation such that the
+ * algorithm works in \f$O(\log n)\f$ time.
  *
  * Examples: -
  * * a = 3 and m = 7
@@ -43,56 +43,98 @@
  * (as \f$a\times a^{-1} = 1\f$)
  */
 
-#include <iostream>
-#include <vector>
+#include <cassert>  /// for assert
+#include <cstdint>  /// for std::int64_t
+#include <iostream> /// for IO implementations
 
-/** Recursive function to calculate exponent in \f$O(\log n)\f$ using binary
- * exponent.
+/**
+ * @namespace math
+ * @brief Maths algorithms.
+ */
+namespace math {
+/**
+ * @namespace modular_inverse_fermat
+ * @brief Calculate modular inverse using Fermat's Little Theorem.
+ */
+namespace modular_inverse_fermat {
+/**
+ * @brief Calculate exponent with modulo using binary exponentiation in \f$O(\log b)\f$ time.
+ * @param a The base
+ * @param b The exponent
+ * @param m The modulo
+ * @return The result of \f$a^{b} % m\f$
  */
-int64_t binExpo(int64_t a, int64_t b, int64_t m) {
-    a %= m;
-    int64_t res = 1;
-    while (b > 0) {
-        if (b % 2) {
-            res = res * a % m;
-        }
-        a = a * a % m;
-        // Dividing b by 2 is similar to right shift.
-        b >>= 1;
+std::int64_t binExpo(std::int64_t a, std::int64_t b, std::int64_t m) {
+  a %= m;
+  std::int64_t res = 1;
+  while (b > 0) {
+    if (b % 2 != 0) {
+      res = res * a % m;
     }
-    return res;
+    a = a * a % m;
+    // Dividing b by 2 is similar to right shift by 1 bit
+    b >>= 1;
+  }
+  return res;
 }
-
-/** Prime check in \f$O(\sqrt{m})\f$ time.
+/**
+ * @brief Check if an integer is a prime number in \f$O(\sqrt{m})\f$ time.
+ * @param m An intger to check for primality
+ * @return true if the number is prime
+ * @return false if the number is not prime
  */
-bool isPrime(int64_t m) {
-    if (m <= 1) {
-        return false;
-    } else {
-        for (int64_t i = 2; i * i <= m; i++) {
-            if (m % i == 0) {
-                return false;
-            }
-        }
+bool isPrime(std::int64_t m) {
+  if (m <= 1) {
+    return false;
+  } 
+  for (std::int64_t i = 2; i * i <= m; i++) {
+    if (m % i == 0) {
+      return false;
     }
-    return true;
+  }
+  return true;
+}
+/**
+ * @brief calculates the modular inverse.
+ * @param a Integer value for the base
+ * @param m Integer value for modulo
+ * @return The result that is the modular inverse of a modulo m
+ */
+std::int64_t modular_inverse(std::int64_t a, std::int64_t m) {
+  while (a < 0) {
+    a += m;
+  }
+
+  // Check for invalid cases
+  if (!isPrime(m) || a == 0) {
+    return -1; // Invalid input
+  }
+
+  return binExpo(a, m - 2, m);  // Fermat's Little Theorem
+}
+} // namespace modular_inverse_fermat
+} // namespace math
+
+/**
+ * @brief Self-test implementation
+ * @return void
+ */
+static void test() {
+  assert(math::modular_inverse_fermat::modular_inverse(0, 97) == -1);
+  assert(math::modular_inverse_fermat::modular_inverse(15, -2) == -1);
+  assert(math::modular_inverse_fermat::modular_inverse(3, 10) == -1);
+  assert(math::modular_inverse_fermat::modular_inverse(3, 7) == 5);
+  assert(math::modular_inverse_fermat::modular_inverse(1, 101) == 1);
+  assert(math::modular_inverse_fermat::modular_inverse(-1337, 285179) == 165519);
+  assert(math::modular_inverse_fermat::modular_inverse(123456789, 998244353) == 25170271);
+  assert(math::modular_inverse_fermat::modular_inverse(-9876543210, 1000000007) == 784794281);
 }
 
 /**
- * Main function
+ * @brief Main function
+ * @return 0 on exit
  */
 int main() {
-    int64_t a, m;
-    // Take input of  a and m.
-    std::cout << "Computing ((a^(-1))%(m)) using Fermat's Little Theorem";
-    std::cout << std::endl << std::endl;
-    std::cout << "Give input 'a' and 'm' space separated : ";
-    std::cin >> a >> m;
-    if (isPrime(m)) {
-        std::cout << "The modular inverse of a with mod m is (a^(m-2)) : ";
-        std::cout << binExpo(a, m - 2, m) << std::endl;
-    } else {
-        std::cout << "m must be a prime number.";
-        std::cout << std::endl;
-    }
+  test();  // run self-test implementation
+  return 0;
 }