added kadane algorithm function (#1079)

* added kadane algorithm function

* added changes

* third commit

* fixed some problems

* fixed warnings

* added documentation

* Update kadane_algorithm/kadane.cpp

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

* Update kadane_algorithm/kadane.cpp

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

* Update kadane_algorithm/kadane.cpp

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

* added details in the documentation

* Update kadane_algorithm/kadane.cpp

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

* Update kadane_algorithm/kadane.cpp

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

* added kadane2.cpp

* Update dynamic_programming/kadane2.cpp

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

* added some things

* fixed

* Update dynamic_programming/kadane2.cpp

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

* changes

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

* added code

* added changes suggested

* Update .vscode/settings.json

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

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

* Update dynamic_programming/kadane2.cpp

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

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

dynamic_programming/kadane2.cpp

@@ -0,0 +1,73 @@
+/**
+ * @file
+ * @brief Implementation of [Kadane
+ * Algorithm] (https://en.wikipedia.org/wiki/Kadane%27s_algorithm)
+ *
+ * @details
+ * Kadane algorithm is used to find the maximum sum subarray in an array and
+ * maximum sum subarray problem is the task of finding a contiguous subarray
+ * with the largest sum
+ *
+ * ### Algorithm
+ * The simple idea of the algorithm is to search for all positive
+ * contiguous segments of the array and keep track of maximum sum contiguous
+ * segment among all positive segments(curr_sum is used for this)
+ * Each time we get a positive sum we compare it with max_sum and update max_sum
+ * if it is greater than curr_sum
+ *
+ * @author [Ayush Singh](https://github.com/ayush523)
+ */
+#include <array>
+#include <climits>
+#include <iostream>
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming {
+/**
+ * @namespace kadane
+ * @brief Functions for [Kadane](https://en.wikipedia.org/wiki/Kadane%27s_algorithm) algorithm.
+ */
+namespace kadane {
+/**
+ * @brief maxSubArray function is used to calculate the maximum sum subarray
+ * and returns the value of maximum sum which is stored in the variable max_sum
+ * @tparam N number of array size
+ * @param n array where numbers are saved
+ * @returns the value of maximum subarray sum
+ */
+template <size_t N>
+int maxSubArray(const std::array<int, N> &n) {
+    int curr_sum =
+        0;  // declaring a variable named as curr_sum and initialized it to 0
+    int max_sum = INT_MIN;  // Initialized max_sum to INT_MIN
+    for (int i : n) {  // for loop to iterate over the elements of the array
+        curr_sum += n[i];
+        max_sum = std::max(max_sum, curr_sum);  // getting the maximum value
+        curr_sum = std::max(curr_sum, 0);  // updating the value of curr_sum
+    }
+    return max_sum;  // returning the value of max_sum
+}
+}  // namespace kadane
+}  // namespace dynamic_programming
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    const int N = 5;
+    std::array<int, N> n{};  // declaring array
+                             // taking values of elements from user
+    for (int i = 0; i < n.size(); i++) {
+        std::cout << "Enter value of n[" << i << "]"
+                  << "\n";
+        std::cin >> n[i];
+    }
+    int max_sum = dynamic_programming::kadane::maxSubArray<N>(
+        n);  // calling maxSubArray function
+    std::cout << "Maximum subarray sum is " << max_sum;  // Printing the answer
+
+    return 0;
+}