adding level order animation

lectures/20_trees_III/README.md

@@ -62,8 +62,6 @@ We can also implement operator++ for the ds_set iterator without using the paren
 - Write an algorithm to print the nodes in the tree one tier at a time, that is, in a breadth-first manner.
 
   ```cpp
-  BFS code discussed in class
-
   void breadth_first_traverse(Node* root)
   {
     int level=0;
@@ -93,6 +91,10 @@ We can also implement operator++ for the ds_set iterator without using the paren
 - What is the best/average/worst-case running time of this algorithm? What is the best/average/worst-case
 memory usage of this algorithm? Give a specific example tree that illustrates each case.
 
+- Run [this bfs_main.cpp program](bfs_main.cpp) to test the above function.
+
+- Play this [animation](https://jidongxiao.github.io/CSCI1200-DataStructures/animations/trees/level_order/index.html) to understand how this works.
+
 ## 20.5 Height and Height Calculation Algorithm
 
 - The height of a node in a tree is the length of the longest path down the tree from that node to a leaf node. The height of a tree with only one node (the root node) is 1. The height of an empty tree (a tree with no nodes) is 0.
@@ -189,7 +191,7 @@ Draw picture of each case!
 
   - Then we recursively apply erase to remove that node — which is guaranteed to have at most one child.
 
-play this [animation](https://jidongxiao.github.io/CSCI1200-DataStructures/animations/trees/delete_node/index.html) to understand how this works.
+Play this [animation](https://jidongxiao.github.io/CSCI1200-DataStructures/animations/trees/delete_node/index.html) to understand how this works.
 
 Exercise: Write a recursive version of erase.
  

lectures/20_trees_III/bfs_main.cpp

@@ -0,0 +1,72 @@
+#include <iostream>
+#include <vector>
+
+class Node {
+public:
+    int value;
+    Node* left;
+    Node* right;
+
+    // constructor to create a new node
+    Node(int val) : value(val), left(NULL), right(NULL) {}
+};
+
+// The breadth-first traversal function you provided
+void breadth_first_traverse(Node* root) {
+    int level = 0;
+    std::vector<Node*> current_level;
+    std::vector<Node*> next_level;
+
+    if (root == NULL) {
+        return;
+    }
+
+    current_level.push_back(root);
+
+    while (current_level.size() != 0) {
+        std::cout << "level " << level << ":";
+        for (unsigned i = 0; i < current_level.size(); i++) {
+            if (current_level[i]->left != NULL) {
+                next_level.push_back(current_level[i]->left);
+            }
+            if (current_level[i]->right != NULL) {
+                next_level.push_back(current_level[i]->right);
+            }
+            std::cout << " " << current_level[i]->value;
+        }
+        current_level = next_level;
+        level++;
+        next_level.clear();
+        std::cout << std::endl;
+    }
+}
+
+int main() {
+    // creating a simple binary tree
+    //     1
+    //   /   \
+    //  2     3
+    // / \   / \
+    //4   5 6   7
+    Node* root = new Node(1);
+    root->left = new Node(2);
+    root->right = new Node(3);
+    root->left->left = new Node(4);
+    root->left->right = new Node(5);
+    root->right->left = new Node(6);
+    root->right->right = new Node(7);
+
+    // calling the breadth-first traversal function
+    breadth_first_traverse(root);
+
+    // cleaning up dynamically allocated memory
+    delete root->left->left;
+    delete root->left->right;
+    delete root->right->left;
+    delete root->right->right;
+    delete root->left;
+    delete root->right;
+    delete root;
+
+    return 0;
+}