[fix]: dynamic_programming/cut_rod.cpp does not compile (#1085)

* Create largestBST_in_binary_tree.cpp

* formatting filenames b15bd1ea

* updating DIRECTORY.md

* Update DIRECTORY.md

* updating DIRECTORY.md

* fixed compilation error in cut_rod.cpp code

* fixed clang-tidy warnings

* Delete largestbst_in_binary_tree.cpp

* removed compilation errors

* Update cut_rod.cpp

* added requested changes in the code

* added testing

* Update DIRECTORY.md

* Delete largestbst_in_binary_tree.cpp

* added namespaces

* added kadane2 algorithm

* 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/cut_rod.cpp

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

* Update dynamic_programming/cut_rod.cpp

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

* Update dynamic_programming/cut_rod.cpp

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

* added right funtion name in comments

* Update dynamic_programming/cut_rod.cpp

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

* Update dynamic_programming/cut_rod.cpp

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

* added documentation for template parameter

* checking for github actions

* clang-format and clang-tidy fixes for db70ae2f

Co-authored-by: anishmo99 <ani10sh@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: Anish Mookherjee <59157112+anishmo99@users.noreply.github.com>
Co-authored-by: David Leal <halfpacho@gmail.com>

dynamic_programming/cut_rod.cpp

@@ -1,25 +1,104 @@
-/*Given a rod of length n inches and an array of prices that
-contains prices of all pieces of size smaller than n. Determine
-the maximum value obtainable by cutting up the rod and selling
-the pieces.*/
+/**
+ * @file
+ * @brief Implementation of cutting a rod problem
+ *
+ * @details
+ * Given a rod of length n inches and an array of prices that
+ * contains prices of all pieces of size<=n. Determine
+ * the maximum profit obtainable by cutting up the rod and selling
+ * the pieces.
+ *
+ * ### Algorithm
+ * The idea is to break the given rod into every smaller piece as possible
+ * and then check profit for each piece, by calculating maximum profit for
+ * smaller pieces we will build the solution for larger pieces in bottom-up
+ * manner.
+ *
+ * @author [Anmol](https://github.com/Anmol3299)
+ * @author [Pardeep](https://github.com/Pardeep009)
+ */
 
+#include <array>
+#include <cassert>
+#include <climits>
 #include <iostream>
-using namespace std;
-int cutrod(int p[], int n) {
-    int r[n + 1];
-    r[0] = 0;
-    for (int j = 0; j < n; j++) {
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming {
+/**
+ * @namespace cut_rod
+ * @brief Implementation of cutting a rod problem
+ */
+namespace cut_rod {
+/**
+ * @brief Cuts the rod in different pieces and
+ * stores the maximum profit for each piece of the rod.
+ * @tparam T size of the price array
+ * @param n size of the rod in inches
+ * @param price an array of prices that contains prices of all pieces of size<=n
+ * @return maximum profit obtainable for @param n inch rod.
+ */
+template <size_t T>
+int maxProfitByCuttingRod(const std::array<int, T> &price, const int n) {
+    int *profit =
+        new int[n + 1];  // profit[i] will hold maximum profit for i inch rod
+
+    profit[0] = 0;  // if length of rod is zero, then no profit
+
+    // outer loop will select size of rod, starting from 1 inch to n inch rod.
+    // inner loop will evaluate the maximum profit we can get for i inch rod by
+    // making every possible cut on it and will store it in profit[i].
+    for (size_t i = 1; i <= n; i++) {
         int q = INT_MIN;
-        for (int i = 0; i <= j; i++) {
-            q = max(q, p[i] + r[j - i]);
+        for (size_t j = 1; j <= i; j++) {
+            q = std::max(q, price[j - 1] + profit[i - j]);
         }
-        r[j + 1] = q;
+        profit[i] = q;
     }
-    return r[n];
+    int ans = profit[n];
+    delete[] profit;
+    return ans;  // returning maximum profit
 }
+}  // namespace cut_rod
+}  // namespace dynamic_programming
+
+/**
+ * @brief Function to test above algorithm
+ * @returns void
+ */
+static void test() {
+    // Test 1
+    const int n1 = 8;                                           // size of rod
+    std::array<int, n1> price1 = {1, 5, 8, 9, 10, 17, 17, 20};  // price array
+    const int max_profit1 =
+        dynamic_programming::cut_rod::maxProfitByCuttingRod(price1, n1);
+    const int expected_max_profit1 = 22;
+    assert(max_profit1 == expected_max_profit1);
+    std::cout << "Maximum profit with " << n1 << " inch road is " << max_profit1
+              << std::endl;
+
+    // Test 2
+    const int n2 = 30;  // size of rod
+    std::array<int, n2> price2 = {
+        1,  5,  8,  9,  10, 17, 17, 20, 24, 30,  // price array
+        31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
+        41, 42, 43, 44, 45, 46, 47, 48, 49, 50};
+    const int max_profit2 =
+        dynamic_programming::cut_rod::maxProfitByCuttingRod(price2, n2);
+    const int expected_max_profit2 = 90;
+    assert(max_profit2 == expected_max_profit2);
+    std::cout << "Maximum profit with " << n2 << " inch road is " << max_profit2
+              << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
 int main() {
-    int price[] = {1,  5,  8,  9,  10, 17, 17, 20, 24, 30, 31, 32, 33, 34, 35,
-                   36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50};
-    cout << cutrod(price, 30);
+    // Testing
+    test();
     return 0;
 }

dynamic_programming/kadane2.cpp

@@ -27,7 +27,8 @@
 namespace dynamic_programming {
 /**
  * @namespace kadane
- * @brief Functions for [Kadane](https://en.wikipedia.org/wiki/Kadane%27s_algorithm) algorithm.
+ * @brief Functions for
+ * [Kadane](https://en.wikipedia.org/wiki/Kadane%27s_algorithm) algorithm.
  */
 namespace kadane {
 /**