Merge pull request kelvins#195 from thomas-martin-uf/tower_of_hanoi_cpp

adding towers of hanoi recursive cpp solution. updated readme to incl…

Author: kelvins

README.md

@@ -1290,8 +1290,8 @@ Com o objetivo de alcançar uma abrangência maior e encorajar mais pessoas a co
                 </a>
             </td>
             <td> <!-- C++ -->
-                <a href="./CONTRIBUTING.md">
-                    <img align="center" height="25" src="https://cdn.jsdelivr.net/gh/devicons/devicon/icons/github/github-original.svg" />
+                <a href="./src/cpp/TowerOfHanoi.cpp">
+                    <img align="center" height="25" src="https://cdn.jsdelivr.net/gh/devicons/devicon/icons/cplusplus/cplusplus-original.svg" />
                 </a>
             </td>
             <td> <!-- Java -->

src/cpp/TowerOfHanoi.cpp

@@ -0,0 +1,70 @@
+/*
+    Recursive Towers of Hanoi Solution
+    Thomas Martin - 2023
+    https://github.com/thomas-martin-uf
+
+    Problem Description: (from wikipedia)
+    The Tower of Hanoi is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters,
+    which can slide onto any rod.
+
+    The puzzle begins with the disks stacked on one rod in order of decreasing size, the smallest at the top,
+    thus approximating a conical shape.
+
+    The objective of the puzzle is to move the entire stack to the last rod, obeying the following rules:
+
+    Only one disk may be moved at a time.
+
+    Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
+
+    No disk may be placed on top of a disk that is smaller than it.
+
+    With 3 disks, the puzzle can be solved in 7 moves.
+
+    The minimal number of moves required to solve a Tower of Hanoi puzzle is 2^n − 1, where n is the number of disks.
+
+*/
+
+#include <iostream>
+using std::cout;
+
+size_t solve_tower(int n, char first, char second, char third)
+{
+
+    // recursive base case
+    if (n == 1)
+    {
+        cout << "Move disk 1 from " << first << " to " << third << "\n";
+        return 1;
+    }
+
+    // move n-1 disks from first to other using second as a placeholder
+    size_t num_moves = solve_tower(n - 1, first, third, second);
+
+    // move the nth disk from first to second
+    cout << "Move disk " << n << " from " << first << " to " << third << "\n";
+
+    // move the n-1 disks from third to second using first as an placeholder
+    num_moves += solve_tower(n - 1, second, first, third);
+
+    // return the total moves plus 1
+    return num_moves + 1;
+}
+
+int main()
+{
+
+    // names of rods
+    char a = 'A';
+    char b = 'B';
+    char c = 'C';
+
+    // number of disks to move in puzzle
+    size_t num_disk = 3;
+
+    // find the total number of moves needed to solve
+    size_t num_moves = solve_tower(num_disk, a, b, c);
+
+    // output result
+    cout << "Total moves needed to solve: " << num_moves;
+    return 0;
+}