feat: add maximum circular subarray sum (#2242)

* Create maximum_circular_subarray.cpp

* Delete maximum_circular_subarray.cpp

* Create maximum_circular_subarray.cpp

* Update maximum_circular_subarray.cpp

Used the template provided.

* updating DIRECTORY.md

* Update maximum_circular_subarray.cpp

* Update maximum_circular_subarray.cpp

* Update maximum_circular_subarray.cpp

* Update maximum_circular_subarray.cpp

* Update maximum_circular_subarray.cpp

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update maximum_circular_subarray.cpp

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update dynamic_programming/maximum_circular_subarray.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update maximum_circular_subarray.cpp

Fixed the comments according to @krishnacx

* chore: apply suggestions from code review

---------

Co-authored-by: Suman Mondal <94859440+sumanarlert@users.noreply.github.com>
Co-authored-by: github-actions[bot] <github-actions@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>

DIRECTORY.md

@@ -108,6 +108,7 @@
   * [Longest Increasing Subsequence (Nlogn)](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_increasing_subsequence_(nlogn).cpp)
   * [Longest Palindromic Subsequence](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/longest_palindromic_subsequence.cpp)
   * [Matrix Chain Multiplication](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/matrix_chain_multiplication.cpp)
+  * [Maximum Circular Subarray](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/maximum_circular_subarray.cpp)
   * [Minimum Edit Distance](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/minimum_edit_distance.cpp)
   * [Palindrome Partitioning](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/palindrome_partitioning.cpp)
   * [Partition Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/HEAD/dynamic_programming/partition_problem.cpp)

dynamic_programming/maximum_circular_subarray.cpp

@@ -0,0 +1,90 @@
+/**
+* @file
+* @brief C++ program for maximum contiguous circular sum problem using [Kadane's Algorithm](https://en.wikipedia.org/wiki/Maximum_subarray_problem)
+* @details
+* The idea is to modify Kadane’s algorithm to find a minimum contiguous subarray sum and the maximum contiguous subarray sum,
+* then check for the maximum value between the max_value and the value left after subtracting min_value from the total sum.
+* For more information, check [Geeks For Geeks](https://www.geeksforgeeks.org/maximum-contiguous-circular-sum/) explanation page.
+*/
+
+#include <cassert>     /// for assert
+#include <iostream>   /// for IO operations
+#include <vector>     /// for std::vector
+
+
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming {
+/**
+ * @brief returns the maximum contiguous circular sum of an array
+ * 
+ * @param arr is the array/vector
+ * @return int which is the maximum sum
+ */
+int maxCircularSum(std::vector<int>& arr)
+{
+    // Edge Case
+    if (arr.size() == 1)
+        return arr[0];
+  
+    // Sum variable which stores total sum of the array.
+    int sum = 0;
+    for (int i = 0; i < arr.size(); i++) {
+        sum += arr[i];
+    }
+  
+    // Every variable stores first value of the array.
+    int current_max = arr[0], max_so_far = arr[0], current_min = arr[0], min_so_far = arr[0];
+  
+    // Concept of Kadane's Algorithm
+    for (int i = 1; i < arr.size(); i++) {
+        // Kadane's Algorithm to find Maximum subarray sum.
+        current_max = std::max(current_max + arr[i], arr[i]);
+        max_so_far = std::max(max_so_far, current_max);
+  
+        // Kadane's Algorithm to find Minimum subarray sum.
+        current_min = std::min(current_min + arr[i], arr[i]);
+        min_so_far = std::min(min_so_far, current_min);
+    }
+  
+    if (min_so_far == sum)
+        return max_so_far;
+  
+    // Return the maximum value
+    return std::max(max_so_far, sum - min_so_far);
+}
+}  // namespace dynamic_programming
+
+/**
+ * @brief Self-test implementation
+ * @returns void
+ */
+static void test() {
+    // Description of the test
+    // Input: arr[] = {8, -8, 9, -9, 10, -11, 12}
+    // Output: 22 
+    // Explanation: Subarray 12, 8, -8, 9, -9, 10 gives the maximum sum, that is 22.
+
+    int n = 7; // size of the array
+    std::vector<int> arr = {8, -8, 9, -9, 10, -11, 12}; 
+    assert(dynamic_programming::maxCircularSum(arr) == 22); // this ensures that the algorithm works as expected
+
+    arr = {8, -8, 10, -9, 10, -11, 12};
+    assert(dynamic_programming::maxCircularSum(arr) == 23);
+
+    std::cout << "All tests have successfully passed!\n";
+}
+
+
+/**
+ * @brief Main function
+ * @param argc commandline argument count (ignored)
+ * @param argv commandline array of arguments (ignored)
+ * @returns 0 on exit
+ */
+int main(int argc, char *argv[]) {
+     test();  // run self-test implementations
+     return 0;
+}