Add boundary traversal of binary tree (#5639)

Author: xuyang471

src/main/java/com/thealgorithms/datastructures/trees/BoundaryTraversal.java

@@ -0,0 +1,168 @@
+package com.thealgorithms.datastructures.trees;
+
+import java.util.ArrayList;
+import java.util.Deque;
+import java.util.LinkedList;
+import java.util.List;
+
+/**
+ * BoundaryTraversal
+ * <p>
+ * Start with the Root:
+ * Add the root node to the boundary list.
+ * Traverse the Left Boundary (Excluding Leaf Nodes):
+ * Move down the left side of the tree, adding each non-leaf node to the boundary list.
+ * If a node has a left child, go left; otherwise, go right.
+ * Visit All Leaf Nodes:
+ * Traverse the tree and add all leaf nodes to the boundary list, from left to right.
+ * Traverse the Right Boundary (Excluding Leaf Nodes) in Reverse Order:
+ * Move up the right side of the tree, adding each non-leaf node to a temporary list.
+ * If a node has a right child, go right; otherwise, go left.
+ * Reverse the temporary list and add it to the boundary list.
+ * Combine and Output:
+ * The final boundary list contains the root, left boundary, leaf nodes, and reversed right boundary in that order.
+ */
+public final class BoundaryTraversal {
+    private BoundaryTraversal() {
+    }
+
+    // Main function for boundary traversal, returns a list of boundary nodes in order
+    public static List<Integer> boundaryTraversal(BinaryTree.Node root) {
+        List<Integer> result = new ArrayList<>();
+        if (root == null) {
+            return result;
+        }
+
+        // Add root node if it's not a leaf node
+        if (!isLeaf(root)) {
+            result.add(root.data);
+        }
+
+        // Add left boundary
+        addLeftBoundary(root, result);
+
+        // Add leaf nodes
+        addLeaves(root, result);
+
+        // Add right boundary
+        addRightBoundary(root, result);
+
+        return result;
+    }
+
+    // Adds the left boundary, including nodes that have no left child but have a right child
+    private static void addLeftBoundary(BinaryTree.Node node, List<Integer> result) {
+        BinaryTree.Node cur = node.left;
+
+        // If there is no left child but there is a right child, treat the right child as part of the left boundary
+        if (cur == null && node.right != null) {
+            cur = node.right;
+        }
+
+        while (cur != null) {
+            if (!isLeaf(cur)) {
+                result.add(cur.data); // Add non-leaf nodes to result
+            }
+            if (cur.left != null) {
+                cur = cur.left; // Move to the left child
+            } else if (cur.right != null) {
+                cur = cur.right; // If left child is null, move to the right child
+            } else {
+                break; // Stop if there are no children
+            }
+        }
+    }
+
+    // Adds leaf nodes (nodes without children)
+    private static void addLeaves(BinaryTree.Node node, List<Integer> result) {
+        if (node == null) {
+            return;
+        }
+        if (isLeaf(node)) {
+            result.add(node.data); // Add leaf node
+        } else {
+            addLeaves(node.left, result); // Recur for left subtree
+            addLeaves(node.right, result); // Recur for right subtree
+        }
+    }
+
+    // Adds the right boundary, excluding leaf nodes
+    private static void addRightBoundary(BinaryTree.Node node, List<Integer> result) {
+        BinaryTree.Node cur = node.right;
+        List<Integer> temp = new ArrayList<>();
+
+        // If no right boundary is present and there is no left subtree, skip
+        if (cur != null && node.left == null) {
+            return;
+        }
+        while (cur != null) {
+            if (!isLeaf(cur)) {
+                temp.add(cur.data); // Store non-leaf nodes temporarily
+            }
+            if (cur.right != null) {
+                cur = cur.right; // Move to the right child
+            } else if (cur.left != null) {
+                cur = cur.left; // If right child is null, move to the left child
+            } else {
+                break; // Stop if there are no children
+            }
+        }
+
+        // Add the right boundary nodes in reverse order
+        for (int i = temp.size() - 1; i >= 0; i--) {
+            result.add(temp.get(i));
+        }
+    }
+
+    // Checks if a node is a leaf node
+    private static boolean isLeaf(BinaryTree.Node node) {
+        return node.left == null && node.right == null;
+    }
+
+    // Iterative boundary traversal
+    public static List<Integer> iterativeBoundaryTraversal(BinaryTree.Node root) {
+        List<Integer> result = new ArrayList<>();
+        if (root == null) {
+            return result;
+        }
+
+        // Add root node if it's not a leaf node
+        if (!isLeaf(root)) {
+            result.add(root.data);
+        }
+
+        // Handle the left boundary
+        BinaryTree.Node cur = root.left;
+        if (cur == null && root.right != null) {
+            cur = root.right;
+        }
+        while (cur != null) {
+            if (!isLeaf(cur)) {
+                result.add(cur.data); // Add non-leaf nodes to result
+            }
+            cur = (cur.left != null) ? cur.left : cur.right; // Prioritize left child, move to right if left is null
+        }
+
+        // Add leaf nodes
+        addLeaves(root, result);
+
+        // Handle the right boundary using a stack (reverse order)
+        cur = root.right;
+        Deque<Integer> stack = new LinkedList<>();
+        if (cur != null && root.left == null) {
+            return result;
+        }
+        while (cur != null) {
+            if (!isLeaf(cur)) {
+                stack.push(cur.data); // Temporarily store right boundary nodes in a stack
+            }
+            cur = (cur.right != null) ? cur.right : cur.left; // Prioritize right child, move to left if right is null
+        }
+
+        // Add the right boundary nodes from the stack to maintain the correct order
+        while (!stack.isEmpty()) {
+            result.add(stack.pop());
+        }
+        return result;
+    }
+}

src/test/java/com/thealgorithms/datastructures/trees/BoundaryTraversalTest.java

@@ -0,0 +1,108 @@
+package com.thealgorithms.datastructures.trees;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.util.Collections;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+/**
+ *
+ */
+public class BoundaryTraversalTest {
+
+    @Test
+    public void testNullRoot() {
+        assertEquals(Collections.emptyList(), BoundaryTraversal.boundaryTraversal(null));
+        assertEquals(Collections.emptyList(), BoundaryTraversal.iterativeBoundaryTraversal(null));
+    }
+
+    @Test
+    public void testSingleNodeTree() {
+        final BinaryTree.Node root = new BinaryTree.Node(1);
+
+        List<Integer> expected = List.of(1);
+
+        assertEquals(expected, BoundaryTraversal.boundaryTraversal(root));
+        assertEquals(expected, BoundaryTraversal.iterativeBoundaryTraversal(root));
+    }
+
+    /*
+        1
+       / \
+      2   3
+     / \ / \
+    4  5 6  7
+
+    */
+    @Test
+    public void testCompleteBinaryTree() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[] {1, 2, 3, 4, 5, 6, 7});
+
+        List<Integer> expected = List.of(1, 2, 4, 5, 6, 7, 3);
+
+        assertEquals(expected, BoundaryTraversal.boundaryTraversal(root));
+        assertEquals(expected, BoundaryTraversal.iterativeBoundaryTraversal(root));
+    }
+
+    /*
+        1
+       / \
+      2   7
+     /     \
+    3       8
+     \     /
+      4   9
+         / \
+        5   6
+           / \
+         10  11
+    */
+    @Test
+    public void testBoundaryTraversal() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[] {1, 2, 7, 3, null, null, 8, null, 4, 9, null, 5, 6, 10, 11});
+
+        List<Integer> expected = List.of(1, 2, 3, 4, 5, 6, 10, 11, 9, 8, 7);
+
+        assertEquals(expected, BoundaryTraversal.boundaryTraversal(root));
+        assertEquals(expected, BoundaryTraversal.iterativeBoundaryTraversal(root));
+    }
+
+    /*
+          1
+         /
+        2
+       /
+      3
+     /
+    4
+    */
+    @Test
+    public void testLeftSkewedTree() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[] {1, 2, null, 3, null, 4, null});
+
+        List<Integer> expected = List.of(1, 2, 3, 4);
+
+        assertEquals(expected, BoundaryTraversal.boundaryTraversal(root));
+        assertEquals(expected, BoundaryTraversal.iterativeBoundaryTraversal(root));
+    }
+
+    /*
+              5
+               \
+                6
+                 \
+                  7
+                   \
+                    8
+    */
+    @Test
+    public void testRightSkewedTree() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[] {5, null, 6, null, 7, null, 8});
+
+        List<Integer> expected = List.of(5, 6, 7, 8);
+
+        assertEquals(expected, BoundaryTraversal.boundaryTraversal(root));
+        assertEquals(expected, BoundaryTraversal.iterativeBoundaryTraversal(root));
+    }
+}