Merge branch 'TheAlgorithms:master' into master

DIRECTORY.md

@@ -11,9 +11,11 @@
   * [Subarray Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subarray_sum.cpp)
   * [Subset Sum](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/subset_sum.cpp)
   * [Sudoku Solve](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/sudoku_solve.cpp)
+  * [Wildcard Matching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/backtracking/wildcard_matching.cpp)
 
 ## Bit Manipulation
   * [Count Of Set Bits](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_set_bits.cpp)
+  * [Count Of Trailing Ciphers In Factorial N](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp)
   * [Hamming Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/bit_manipulation/hamming_distance.cpp)
 
 ## Ciphers
@@ -64,6 +66,9 @@
   * [Trie Tree](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_tree.cpp)
   * [Trie Using Hashmap](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/data_structures/trie_using_hashmap.cpp)
 
+## Divide And Conquer
+  * [Karatsuba Algorithm For Fast Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp)
+
 ## Dynamic Programming
   * [0 1 Knapsack](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/0_1_knapsack.cpp)
   * [Abbreviation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/dynamic_programming/abbreviation.cpp)
@@ -180,6 +185,7 @@
   * [Modular Division](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_division.cpp)
   * [Modular Exponentiation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_exponentiation.cpp)
   * [Modular Inverse Fermat Little Theorem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/modular_inverse_fermat_little_theorem.cpp)
+  * [N Bonacci](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_bonacci.cpp)
   * [N Choose R](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/n_choose_r.cpp)
   * [Ncr Modulo P](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/ncr_modulo_p.cpp)
   * [Number Of Positive Divisors](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/number_of_positive_divisors.cpp)

backtracking/wildcard_matching.cpp

@@ -0,0 +1,155 @@
+/**
+ * @file
+ * @brief Implementation of the [Wildcard
+ * Matching](https://www.geeksforgeeks.org/wildcard-pattern-matching/) problem.
+ * @details
+ * Given a matching string and a pattern, implement wildcard pattern
+ * matching with support for `?` and `*`. `?` matches any single character.
+ * `*` matches any sequence of characters (including the empty sequence).
+ * The matching should cover the entire matching string (not partial). The task
+ * is to determine if the pattern matches with the matching string
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+#include <vector>    /// for std::vector
+
+/**
+ * @namespace backtracking
+ * @brief Backtracking algorithms
+ */
+namespace backtracking {
+/**
+ * @namespace wildcard_matching
+ * @brief Functions for the [Wildcard
+ * Matching](https://www.geeksforgeeks.org/wildcard-pattern-matching/) problem.
+ */
+namespace wildcard_matching {
+/**
+ * @brief The main function implements if pattern can be matched with given
+ * string
+ * @param s is the given matching string
+ * @param p is the given pattern
+ * @param pos1 is the starting index
+ * @param pos2 is the last index
+ * @returns 1 if pattern matches with matching string otherwise 0
+ */
+std::vector<std::vector<int64_t>> dpTable(1000, std::vector<int64_t>(1000, -1));
+bool wildcard_matching(std::string s, std::string p, uint32_t pos1,
+                       uint32_t pos2) {
+    uint32_t n = s.length();
+    uint32_t m = p.length();
+    // matching is successfull if both strings are done
+    if (pos1 == n && pos2 == m) {
+        return true;
+    }
+
+    // matching is unsuccessfull if pattern is not finished but matching string
+    // is
+    if (pos1 != n && pos2 == m) {
+        return false;
+    }
+
+    // all the remaining characters of patterns must be * inorder to match with
+    // finished string
+    if (pos1 == n && pos2 != m) {
+        while (pos2 < m && p[pos2] == '*') {
+            pos2++;
+        }
+
+        return pos2 == m;
+    }
+
+    // if already calculted for these positions
+    if (dpTable[pos1][pos2] != -1) {
+        return dpTable[pos1][pos2];
+    }
+
+    // if the characters are same just go ahead in both the string
+    if (s[pos1] == p[pos2]) {
+        return dpTable[pos1][pos2] =
+                   wildcard_matching(s, p, pos1 + 1, pos2 + 1);
+    }
+
+    else {
+        // can only single character
+        if (p[pos2] == '?') {
+            return dpTable[pos1][pos2] =
+                       wildcard_matching(s, p, pos1 + 1, pos2 + 1);
+        }
+        // have choice either to match one or more charcters
+        else if (p[pos2] == '*') {
+            return dpTable[pos1][pos2] =
+                       wildcard_matching(s, p, pos1, pos2 + 1) ||
+                       wildcard_matching(s, p, pos1 + 1, pos2);
+        }
+        // not possible to match
+        else {
+            return dpTable[pos1][pos2] = 0;
+        }
+    }
+}
+
+}  // namespace wildcard_matching
+}  // namespace backtracking
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st test
+    std::cout << "1st test ";
+    std::string matching1 = "baaabab";
+    std::string pattern1 = "*****ba*****ab";
+    assert(backtracking::wildcard_matching::wildcard_matching(matching1,
+                                                              pattern1, 0, 0) ==
+           1);  // here the pattern matches with given string
+    std::cout << "passed" << std::endl;
+
+    // 2nd test
+    std::cout << "2nd test ";
+    std::string matching2 = "baaabab";
+    std::string pattern2 = "ba*****ab";
+    assert(backtracking::wildcard_matching::wildcard_matching(matching2,
+                                                              pattern2, 0, 0) ==
+           1);  // here the pattern matches with given string
+    std::cout << "passed" << std::endl;
+
+    // 3rd test
+    std::cout << "3rd test ";
+    std::string matching3 = "baaabab";
+    std::string pattern3 = "ba*ab";
+    assert(backtracking::wildcard_matching::wildcard_matching(matching3,
+                                                              pattern3, 0, 0) ==
+           1);  // here the pattern matches with given string
+    std::cout << "passed" << std::endl;
+
+    // 4th test
+    std::cout << "4th test ";
+    std::string matching4 = "baaabab";
+    std::string pattern4 = "a*ab";
+    assert(backtracking::wildcard_matching::wildcard_matching(matching4,
+                                                              pattern4, 0, 0) ==
+           1);  // here the pattern matches with given string
+    std::cout << "passed" << std::endl;
+
+    // 5th test
+    std::cout << "5th test ";
+    std::string matching5 = "baaabab";
+    std::string pattern5 = "aa?ab";
+    assert(backtracking::wildcard_matching::wildcard_matching(matching5,
+                                                              pattern5, 0, 0) ==
+           1);  // here the pattern matches with given string
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}

bit_manipulation/count_of_trailing_ciphers_in_factorial_n.cpp

@@ -0,0 +1,98 @@
+/**
+ * @file
+ * @brief [Count the number of
+ * ciphers](https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus) in `n!` implementation
+ * @details
+ * Given an integer number as input. The goal is to find the number of trailing
+ zeroes in the factorial calculated for
+ * that number. A factorial of a number N is a product of all numbers in the
+ range [1, N].
+
+ * We know that we get a trailing zero only if the number is multiple of 10 or
+ has a factor pair (2,5). In all factorials of
+ * any number greater than 5, we have many 2s more than 5s in the prime
+ factorization of that number. Dividing a
+ * number by powers of 5 will give us the count of 5s in its factors. So, the
+ number of 5s will tell us the number of trailing zeroes.
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#include <cassert>   /// for assert
+#include <iostream>  /// for IO operations
+
+/**
+ * @namespace bit_manipulation
+ * @brief Bit manipulation algorithms
+ */
+namespace bit_manipulation {
+/**
+ * @namespace count_of_trailing_ciphers_in_factorial_n
+ * @brief Functions for the [Count the number of
+ * ciphers](https://www.tutorialspoint.com/count-trailing-zeros-in-factorial-of-a-number-in-cplusplus)
+ * in `n!` implementation
+ */
+namespace count_of_trailing_ciphers_in_factorial_n {
+/**
+ * @brief Function to count the number of the trailing ciphers
+ * @param n number for which `n!` ciphers are returned
+ * @return count, Number of ciphers in `n!`.
+ */
+uint64_t numberOfCiphersInFactorialN(uint64_t n) {
+    // count is to store the number of 5's in factorial(n)
+    uint64_t count = 0;
+
+    // Keep dividing n by powers of
+    // 5 and update count
+    for (uint64_t i = 5; n / i >= 1; i *= 5) {
+        count += static_cast<uint64_t>(n) / i;
+    }
+
+    return count;
+}
+}  // namespace count_of_trailing_ciphers_in_factorial_n
+}  // namespace bit_manipulation
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st test
+    std::cout << "1st test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(395) == 97);
+    std::cout << "passed" << std::endl;
+
+    // 2nd test
+    std::cout << "2nd test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(977) == 242);
+    std::cout << "passed" << std::endl;
+
+    // 3rd test
+    std::cout << "3rd test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(871) == 215);
+    std::cout << "passed" << std::endl;
+
+    // 4th test
+    std::cout << "4th test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(239) == 57);
+    std::cout << "passed" << std::endl;
+
+    // 5th test
+    std::cout << "5th test ";
+    assert(bit_manipulation::count_of_trailing_ciphers_in_factorial_n::
+               numberOfCiphersInFactorialN(0) == 0);
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}

divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp

@@ -0,0 +1,167 @@
+/**
+ * @file
+ * @brief Implementation of the [Karatsuba algorithm for fast
+ * multiplication](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
+ * @details
+ * Given two strings in binary notation we want to multiply them and return the
+ * value Simple approach is to multiply bits one by one which will give the time
+ * complexity of around O(n^2). To make it more efficient we will be using
+ * Karatsuba' algorithm to find the product which will solve the problem
+ * O(nlogn) of time.
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#include <cassert>   /// for assert
+#include <cstring>   /// for string
+#include <iostream>  /// for IO operations
+#include <vector>    /// for std::vector
+
+/**
+ * @namespace divide_and_conquer
+ * @brief Divide and Conquer algorithms
+ */
+namespace divide_and_conquer {
+/**
+ * @namespace karatsuba_algorithm
+ * @brief Functions for the [Karatsuba algorithm for fast
+ * multiplication](https://en.wikipedia.org/wiki/Karatsuba_algorithm)
+ */
+namespace karatsuba_algorithm {
+/**
+ * @brief Helper function for the main function, that implements Karatsuba's
+ * algorithm for fast multiplication
+ * @param first the input string 1
+ * @param second the input string 2
+ * @returns the concatenated string
+ */
+std::string addStrings(std::string first, std::string second) {
+    std::string result;  // To store the resulting sum bits
+
+    int64_t len1 = first.size();
+    int64_t len2 = second.size();
+    int64_t length = std::max(len1, len2);
+    std::string zero = "0";
+    if (len1 < len2)  // make the string lengths equal
+    {
+        for (int64_t i = 0; i < len2 - len1; i++) {
+            zero += first;
+            first = zero;
+        }
+    } else if (len1 > len2) {
+        zero = "0";
+        for (int64_t i = 0; i < len1 - len2; i++) {
+            zero += second;
+            second = zero;
+        }
+    }
+    int64_t carry = 0;
+    for (int64_t i = length - 1; i >= 0; i--) {
+        int64_t firstBit = first.at(i) - '0';
+        int64_t secondBit = second.at(i) - '0';
+
+        int64_t sum = (firstBit ^ secondBit ^ carry) + '0';  // sum of 3 bits
+        std::string temp;
+        temp = std::to_string(sum);
+        temp += result;
+        result = temp;
+
+        carry = (firstBit & secondBit) | (secondBit & carry) |
+                (firstBit & carry);  // sum of 3 bits
+    }
+
+    if (carry) {
+        result = '1' + result;  // adding 1 incase of overflow
+    }
+    return result;
+}
+/**
+ * @brief The main function implements Karatsuba's algorithm for fast
+ * multiplication
+ * @param str1 the input string 1
+ * @param str2 the input string 2
+ * @returns the multiplicative number value
+ */
+int64_t karatsuba_algorithm(std::string str1, std::string str2) {
+    int64_t len1 = str1.size();
+    int64_t len2 = str2.size();
+    int64_t n = std::max(len1, len2);
+    std::string zero = "0";
+    if (len1 < len2) {
+        for (int64_t i = 0; i < len2 - len1; i++) {
+            zero += str1;
+            str1 = zero;
+        }
+    } else if (len1 > len2) {
+        zero = "0";
+        for (int64_t i = 0; i < len1 - len2; i++) {
+            zero += str2;
+            str2 = zero;
+        }
+    }
+    if (n == 0) {
+        return 0;
+    }
+    if (n == 1) {
+        return (str1[0] - '0') * (str2[0] - '0');
+    }
+    int64_t fh = n / 2;     // first half of string
+    int64_t sh = (n - fh);  // second half of string
+
+    std::string Xl = str1.substr(0, fh);   // first half of first string
+    std::string Xr = str1.substr(fh, sh);  // second half of first string
+
+    std::string Yl = str2.substr(0, fh);   // first half of second string
+    std::string Yr = str2.substr(fh, sh);  // second half of second string
+
+    // Calculating the three products of inputs of size n/2 recursively
+    int64_t product1 = karatsuba_algorithm(Xl, Yl);
+    int64_t product2 = karatsuba_algorithm(Xr, Yr);
+    int64_t product3 = karatsuba_algorithm(
+        divide_and_conquer::karatsuba_algorithm::addStrings(Xl, Xr),
+        divide_and_conquer::karatsuba_algorithm::addStrings(Yl, Yr));
+
+    return product1 * (1 << (2 * sh)) +
+           (product3 - product1 - product2) * (1 << sh) +
+           product2;  // combining the three products to get the final result.
+}
+}  // namespace karatsuba_algorithm
+}  // namespace divide_and_conquer
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // 1st test
+    std::string s11 = "1";
+    std::string s12 = "1010";
+    std::cout << "1st test... ";
+    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(
+               s11, s12) == 10);  // here the multiplication is 10
+    std::cout << "passed" << std::endl;
+
+    // 2nd test
+    std::string s21 = "11";
+    std::string s22 = "1010";
+    std::cout << "2nd test... ";
+    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(
+               s21, s22) == 30);  // here the multiplication is 30
+    std::cout << "passed" << std::endl;
+
+    // 3rd test
+    std::string s31 = "110";
+    std::string s32 = "1010";
+    std::cout << "3rd test... ";
+    assert(divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm(
+               s31, s32) == 60);  // here the multiplication is 60
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}

math/check_prime.cpp

@@ -22,11 +22,11 @@ template <typename T>
 bool is_prime(T num) {
     bool result = true;
     if (num <= 1) {
-        return 0;
+        return false;
     } else if (num == 2) {
-        return 1;
+        return true;
     } else if ((num & 1) == 0) {
-        return 0;
+        return false;
     }
     if (num >= 3) {
         for (T i = 3; (i * i) <= (num); i = (i + 2)) {
@@ -47,7 +47,7 @@ int main() {
     assert(is_prime(50) == false);
     assert(is_prime(115249) == true);
 
-    int num;
+    int num = 0;
     std::cout << "Enter the number to check if it is prime or not" << std::endl;
     std::cin >> num;
     bool result = is_prime(num);

math/n_bonacci.cpp

@@ -0,0 +1,123 @@
+/**
+ * @file
+ * @brief Implementation of the
+ * [N-bonacci](http://oeis.org/wiki/N-bonacci_numbers) series
+ *
+ * @details
+ * In general, in N-bonacci sequence,
+ * we generate sum of preceding N numbers from the next term.
+ *
+ * For example, a 3-bonacci sequence is the following:
+ * 0, 0, 1, 1, 2, 4, 7, 13, 24, 44, 81
+ * In this code we take N and M as input where M is the number of terms
+ * to be printed of the N-bonacci series
+ *
+ * @author [Swastika Gupta](https://github.com/Swastyy)
+ */
+
+#include <algorithm>  /// for std::is_equal, std::swap
+#include <cassert>    /// for assert
+#include <iostream>   /// for IO operations
+#include <vector>     /// for std::vector
+
+/**
+ * @namespace math
+ * @brief Mathematical algorithms
+ */
+namespace math {
+/**
+ * @namespace n_bonacci
+ * @brief Functions for the [N-bonacci](http://oeis.org/wiki/N-bonacci_numbers)
+ * implementation
+ */
+namespace n_bonacci {
+/**
+ * @brief Finds the N-Bonacci series for the `n` parameter value and `m`
+ * parameter terms
+ * @param n is in the N-Bonacci series
+ * @param m is the number of terms in the N-Bonacci sequence
+ * @returns the n-bonacci sequence as vector array
+ */
+std::vector<uint64_t> N_bonacci(const uint64_t &n, const uint64_t &m) {
+    std::vector<uint64_t> a(m, 0);  // we create an empty array of size m
+
+    a[n - 1] = 1;  /// we initialise the (n-1)th term as 1 which is the sum of
+                   /// preceding N zeros
+    a[n] = 1;  /// similarily the sum of preceding N zeros and the (N+1)th 1 is
+               /// also 1
+    for (uint64_t i = n + 1; i < m; i++) {
+        // this is an optimized solution that works in O(M) time and takes O(M)
+        // extra space here we use the concept of the sliding window the current
+        // term can be computed using the given formula
+        a[i] = 2 * a[i - 1] - a[i - 1 - n];
+    }
+    return a;
+}
+}  // namespace n_bonacci
+}  // namespace math
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+    // n = 1 m = 1 return [1, 1]
+    std::cout << "1st test";
+    std::vector<uint64_t> arr1 = math::n_bonacci::N_bonacci(
+        1, 1);  // first input is the param n and second one is the param m for
+                // N-bonacci func
+    std::vector<uint64_t> output_array1 = {
+        1, 1};  // It is the expected output series of length m
+    assert(std::equal(std::begin(arr1), std::end(arr1),
+                      std::begin(output_array1)));
+    std::cout << "passed" << std::endl;
+
+    // n = 5 m = 15 return [0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 31, 61, 120, 236,
+    // 464]
+    std::cout << "2nd test";
+    std::vector<uint64_t> arr2 = math::n_bonacci::N_bonacci(
+        5, 15);  // first input is the param n and second one is the param m for
+                 // N-bonacci func
+    std::vector<uint64_t> output_array2 = {
+        0, 0,  0,  0,  1,   1,   2,  4,
+        8, 16, 31, 61, 120, 236, 464};  // It is the expected output series of
+                                        // length m
+    assert(std::equal(std::begin(arr2), std::end(arr2),
+                      std::begin(output_array2)));
+    std::cout << "passed" << std::endl;
+
+    // n = 6 m = 17 return [0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 63, 125, 248,
+    // 492, 976]
+    std::cout << "3rd test";
+    std::vector<uint64_t> arr3 = math::n_bonacci::N_bonacci(
+        6, 17);  // first input is the param n and second one is the param m for
+                 // N-bonacci func
+    std::vector<uint64_t> output_array3 = {
+        0, 0,  0,  0,  0,   1,   1,   2,  4,
+        8, 16, 32, 63, 125, 248, 492, 976};  // It is the expected output series
+                                             // of length m
+    assert(std::equal(std::begin(arr3), std::end(arr3),
+                      std::begin(output_array3)));
+    std::cout << "passed" << std::endl;
+
+    // n = 56 m = 15 return [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+    std::cout << "4th test";
+    std::vector<uint64_t> arr4 = math::n_bonacci::N_bonacci(
+        56, 15);  // first input is the param n and second one is the param m
+                  // for N-bonacci func
+    std::vector<uint64_t> output_array4 = {
+        0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 0, 0, 0, 0, 0};  // It is the expected output series of length m
+    assert(std::equal(std::begin(arr4), std::end(arr4),
+                      std::begin(output_array4)));
+    std::cout << "passed" << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    test();  // run self-test implementations
+    return 0;
+}