feat: remove kadane and replace it with kadane2

Author: realstealthninja

dynamic_programming/kadane.cpp

@@ -1,29 +1,74 @@
+/**
+ * @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>
-
-int maxSubArraySum(int a[], int size) {
-    int max_so_far = INT_MIN, max_ending_here = 0;
-
-    for (int i = 0; i < size; i++) {
-        max_ending_here = max_ending_here + a[i];
-        if (max_so_far < max_ending_here)
-            max_so_far = max_ending_here;
-
-        if (max_ending_here < 0)
-            max_ending_here = 0;
+/**
+ * @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_so_far;
+    return max_sum;  // returning the value of max_sum
 }
+}  // namespace kadane
+}  // namespace dynamic_programming
 
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
 int main() {
-    int n, i;
-    std::cout << "Enter the number of elements \n";
-    std::cin >> n;
-    int a[n];  // NOLINT
-    for (i = 0; i < n; i++) {
-        std::cin >> a[i];
+    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 = maxSubArraySum(a, n);
-    std::cout << "Maximum contiguous sum is " << max_sum;
+    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;
 }