bfs

src/algorithms/graphs/breadthFirstSearch.java

@@ -0,0 +1,133 @@
+package src.algorithms.graphs;
+
+import java.util.*;
+
+import src.algorithms.graphs.util.BinaryTreeNode;
+import src.algorithms.graphs.util.GraphNode;
+
+/**
+ * Implementation of BFS
+ *
+ * Breadth-First search is a graph traversal algorithm that utilizes a queue (FIFO) data structure
+ * It is useful in finding a shortest-hops solution in graphs
+ * This method is also used to obtain level order traversals of trees.
+ *
+ * In general, BFS works as such:
+ *  - Start with a queue that contains the root node
+ *  - While the queue is not empty:
+ *      - Pop a vertex from the queue
+ *      - Push all neighbours to the queue if they have not been visited yet
+ *      - Update any variables as needed
+ *
+ * Time: O(V + E), where V is the number of vertices/nodes, and E is the number of edges in the graph
+ * Explanation: Each vertex is popped in O(1) time from the stack exactly once, hence O(V)
+ *              For each edge, we must check in O(1) time if we have visited the adjacent vertex to know
+ *              whether to push it into the queue, hence O(E).
+ *              Note that if the graph is a forest, BFS will likely terminate earlier, as fewer vertices are traversed
+ *
+ * Space: O(V): We utilize a Hashset to store the vertices we have visited already. In the worst case we have a
+ *              connected graph where all vertices are traversed, and our Hashset stores all O(V) vertices.
+ *              Further, we use a queue to hold the vertices to be traversed. In the worst case, the root will have all
+ *              other vertices as neighbours, and our queue will contain O(V) vertices.
+ *
+ * ** Note: The above description assumes an adjacency list in order to consider neighbours in an efficient manner
+ *          If an adjacency matrix were used, it would cost O(V) to find neighbours for a single vertex, making our
+ *          average case time complexity O(V^2) for a connected graph
+ *
+ * The implementation demonstrates the use of BFS in finding the level-order (Root, Left, Right) traversal of a binary tree
+ * The tree is represented using a custom BinaryTreeNode class
+ *
+ */
+public class breadthFirstSearch {
+
+    // Prints level order traversal from left to right
+    public static List<Integer> levelOrder(BinaryTreeNode root) {
+        if (root == null) { return new ArrayList<>(); }
+        List<Integer> traversal = new ArrayList<>();
+        Queue<BinaryTreeNode> queue = new LinkedList<>();
+        queue.add(root);
+
+        while (!queue.isEmpty()) {
+            BinaryTreeNode curr = queue.remove();
+            traversal.add((Integer) curr.getVal());
+            if (curr.getLeft() != null) { queue.add(curr.getLeft()); }
+            if (curr.getRight() != null) { queue.add(curr.getRight()); }
+        }
+
+        return traversal;
+    }
+
+    // Finds the number of friend hops needed to go from person A to person B
+    // Uses GraphNode<String>, where a node holds a String of the persons name, and an edge represents a friendship
+    public static int friendHops(GraphNode<String> personA, GraphNode<String> personB) {
+        // Hashset to store the people we have seen already
+        HashSet<GraphNode> checked = new HashSet<>();
+        // Hashmap to remember how many hops were needed to get to a specific friend *
+        HashMap<GraphNode, Integer> map = new HashMap<>();
+
+        Queue<GraphNode> queue = new LinkedList<>();
+        queue.add(personA);
+        // the number of hops to the person themselves is 0, so we map: personA -> 0
+        map.put(personA, 0);
+        int hops = 0;
+
+        while (!queue.isEmpty()) {
+            // poll the queue to get the next person to consider
+            GraphNode<String> currPerson = queue.remove();
+            // add the person to the checked hashset so we don't consider them again
+            checked.add(currPerson);
+            // grab the number of hops from the hashmap and add 1
+            hops = map.get(currPerson) + 1;
+
+            List<GraphNode> neighbours = currPerson.neighbours();
+            for (GraphNode neighbour : neighbours) {
+                if (neighbour == personB) { return hops; }
+                if (!checked.contains(neighbour)) {
+                    queue.add(neighbour);
+                    map.put(neighbour, hops);
+                }
+            }
+        }
+        // Returns -1 if person not found
+        return -1;
+
+        // * Note that we can actually use just the hashmap instead of both the hashmap and the hashset!
+        //   This is because the hashmap supports the map.containsKey() function.
+    }
+
+    public static int friendHopsVisualize(GraphNode<String> personA, GraphNode<String> personB) {
+        // Hashset to store the people we have seen already
+        HashSet<GraphNode> checked = new HashSet<>();
+        // Hashmap to remember how many hops were needed to get to a specific friend *
+        HashMap<GraphNode, Integer> map = new HashMap<>();
+
+        Queue<GraphNode> queue = new LinkedList<>();
+        queue.add(personA);
+        // the number of hops to the person themselves is 0, so we map: personA -> 0
+        map.put(personA, 0);
+        int hops = 0;
+
+        while (!queue.isEmpty()) {
+            System.out.println("Current queue: " + String.valueOf(queue) + ", current hops: " + hops);
+            // poll the queue to get the next person to consider
+            GraphNode<String> currPerson = queue.remove();
+            // add the person to the checked hashset so we don't consider them again
+            checked.add(currPerson);
+            // grab the number of hops from the hashmap and add 1
+            hops = map.get(currPerson) + 1;
+
+            System.out.println("Looking at friends of: " + currPerson.toString());
+            List<GraphNode> neighbours = currPerson.neighbours();
+            for (GraphNode neighbour : neighbours) {
+                if (neighbour == personB) { return hops; }
+                if (!checked.contains(neighbour)) {
+                    queue.add(neighbour);
+                    map.put(neighbour, hops);
+                }
+            }
+            System.out.println("Current queue: " + String.valueOf(queue) + ", current hops: " + hops);
+        }
+        // Returns -1 if person not found
+        return -1;
+    }
+}

src/algorithms/graphs/depthFirstSearch.java

@@ -1,12 +1,12 @@
 package src.algorithms.graphs;
 
 import java.util.*;
-import src.algorithms.graphs.util.TreeNode;
+import src.algorithms.graphs.util.BinaryTreeNode;
 
 /**
  * Implementation of DFS
  *
- * Depth-First search is a graph traversal algorithm that utilizes a stack (FIFO) data structure
+ * Depth-First search is a graph traversal algorithm that utilizes a stack (LIFO) data structure
  * It is useful in finding a shortest-path solution (IN TREES), or a single solution in graphs
  * This method is also used to obtain order-traversals of trees.
  *
@@ -22,28 +22,32 @@
  *              For each edge, we must check in O(1) time if we have visited the adjacent vertex to know
  *              whether to push it into the stack, hence O(E).
  *              Note that if the graph is a forest, DFS will likely terminate earlier, as fewer vertices are traversed
+ *
  * Space: O(V): We utilize a Hashset to store the vertices we have visited already. In the worst case we have a
- *              connected graph where all vertices are traversed, and our Hashset stores O(V) vertices.
+ *              connected graph where all vertices are traversed, and our Hashset stores all O(V) vertices.
  *              Further, we use a stack to hold the vertices to be traversed. In the worst case, the root will have all
  *              other vertices as neighbours, and our stack will contain O(V) vertices.
+ *
  * ** Note: The above description assumes an adjacency list in order to consider neighbours in an efficient manner
  *          If an adjacency matrix were used, it would cost O(V) to find neighbours for a single vertex, making our
  *          average case time complexity O(V^2) for a connected graph
  *
  * The implementation demonstrates the use of DFS in finding the pre-order (Root, Left, Right) traversal of a binary tree
- * The tree is represented using a custom TreeNode class
+ * The tree is represented using a custom BinaryTreeNode class
+ *
+ * TODO: Add new examples, and algo for all orderings
  */
 
 public class depthFirstSearch {
 
-    public static List<Integer> preOrder(TreeNode root) {
+    public static List<Integer> preOrder(BinaryTreeNode root) {
         if (root == null) { return new ArrayList<>(); }
         List<Integer> traversal = new ArrayList<>();
-        Stack<TreeNode> stack = new Stack<>();
+        Stack<BinaryTreeNode> stack = new Stack<>();
         stack.push(root);
 
         while (!stack.empty()) {
-            TreeNode curr = stack.pop();
+            BinaryTreeNode curr = stack.pop();
             traversal.add(curr.getVal());
             if (curr.getRight() != null) { stack.push(curr.getRight()); }
             if (curr.getLeft() != null) { stack.push(curr.getLeft()); }
@@ -53,15 +57,15 @@ public static List<Integer> preOrder(TreeNode root) {
     }
 
     // call this for visualization of process
-    public static List<Integer> preOrderVisualize(TreeNode root) {
+    public static List<Integer> preOrderVisualize(BinaryTreeNode root) {
         if (root == null) { return new ArrayList<>(); }
         List<Integer> traversal = new ArrayList<>();
-        Stack<TreeNode> stack = new Stack<>();
+        Stack<BinaryTreeNode> stack = new Stack<>();
         stack.push(root);
 
         while (!stack.empty()) {
             System.out.println("Current stack: " + stack.toString() + ", Current traversal: " + traversal.toString());
-            TreeNode curr = stack.pop();
+            BinaryTreeNode curr = stack.pop();
             System.out.println("Popped Node: " + Integer.toString(curr.getVal()));
             traversal.add(curr.getVal());
             System.out.println("Current stack: " + stack.toString() + ", Current traversal: " + traversal.toString());

src/algorithms/graphs/util/BinaryTreeNode.java

@@ -0,0 +1,39 @@
+package src.algorithms.graphs.util;
+
+public class BinaryTreeNode {
+    int val;
+    BinaryTreeNode left = null;
+    BinaryTreeNode right = null;
+
+    public BinaryTreeNode(int val) {
+        this.val = val;
+    }
+
+    public BinaryTreeNode(int val, BinaryTreeNode left, BinaryTreeNode right) {
+        this.val = val;
+        this.left = left;
+        this.right = right;
+    }
+
+    public int getVal() { return this.val; }
+    public BinaryTreeNode getLeft() { return this.left; }
+    public BinaryTreeNode getRight() { return this.right; }
+
+    public void setLeft(BinaryTreeNode left) { this.left = left; }
+    public void setRight(BinaryTreeNode right) { this.right = right; }
+
+    @Override
+    public boolean equals(Object other) {
+        if (other == this) { return true; }
+        if (!(other instanceof BinaryTreeNode)) { return false; }
+        BinaryTreeNode node = (BinaryTreeNode) other;
+        return this.val == node.val;
+    }
+
+    @Override
+    public int hashCode() { return this.val; }
+
+    @Override
+    public String toString() { return String.valueOf(this.val); }
+
+}

src/algorithms/graphs/util/GraphNode.java

@@ -0,0 +1,44 @@
+package src.algorithms.graphs.util;
+
+import java.util.*;
+
+public class GraphNode <T> {
+    public T val;
+    public List<GraphNode> neighbour;
+
+    public GraphNode(T val) {
+        this.val = val;
+        neighbour = new ArrayList<>();
+    }
+
+    public GraphNode(T val, List<GraphNode> neighbours) {
+        this.val = val;
+        this.neighbour = neighbours;
+    }
+
+    public static <T> void connect(GraphNode<T> a, GraphNode<T> b) {
+        a.neighbour.add(b);
+        b.neighbour.add(a);
+    }
+
+
+    public List<GraphNode> neighbours() { return this.neighbour; }
+
+    public T getVal() { return this.val; }
+
+    @Override
+    public String toString() { return String.valueOf(this.val); }
+
+    @Override
+    public boolean equals(Object other) {
+        if (other == this) { return true; }
+        if (!(other instanceof GraphNode)) { return false; }
+        GraphNode node = (GraphNode) other;
+        return this.val == node.val;
+    }
+
+    @Override
+    public int hashCode() {
+        return val.hashCode();
+    }
+}