Add check if tree is symmetric or not (fixes #3471) (#3472)

Co-authored-by: Amit Kumar <akumar@indeed.com>
Co-authored-by: Andrii Siriak <siryaka@gmail.com>

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

@@ -0,0 +1,53 @@
+package com.thealgorithms.datastructures.trees;
+
+import com.thealgorithms.datastructures.trees.BinaryTree.Node;
+
+/**
+ * Check if a binary tree is symmetric or not.
+ * A binary tree is a symmetric tree if the left and right subtree of root are mirror image.
+ * Below is a symmetric tree
+ *                               1
+ *                   /                         \
+ *                2                           2
+ *         /                \             /             \
+ *      3                    4         4                3
+ *
+ * Below is not symmetric because values is different in last level
+ *                               1
+ *                   /                         \
+ *                 2                           2
+ *         /                \             /             \
+ *      3                    5         4                3
+ * <p>
+ * Approach:
+ * Recursively check for left and right subtree of root
+ * 1. left subtrees root's values should be equal right subtree's root value
+ * 2. recursively check with left subtrees' left child VS right subtree's right child AND
+ * left subtree's right child VS right subtree left child
+ * Complexity
+ * 1. Time: O(n)
+ * 2. Space: O(lg(n)) for height of tree
+ *
+ * @author kumanoit on 10/10/22 IST 12:52 AM
+ */
+public class CheckTreeIsSymmetric {
+
+    public static boolean isSymmetric(Node root) {
+        if (root == null) {
+            return true;
+        }
+        return isSymmetric(root.left, root.right);
+    }
+
+    private static boolean isSymmetric(Node leftSubtreeRoot, Node rightSubtreRoot) {
+        if (leftSubtreeRoot == null && rightSubtreRoot == null) {
+            return true;
+        }
+
+        if (leftSubtreeRoot == null || rightSubtreRoot == null || leftSubtreeRoot.data != rightSubtreRoot.data) {
+            return false;
+        }
+
+        return isSymmetric(leftSubtreeRoot.right, rightSubtreRoot.left) && isSymmetric(leftSubtreeRoot.left, rightSubtreRoot.right);
+    }
+}

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

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+package com.thealgorithms.datastructures.trees;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+/**
+ * @author kumanoit on 10/10/22 IST 1:02 AM
+ */
+public class CheckTreeIsSymmetricTest {
+
+    @Test
+    public void testRootNull() {
+        assertTrue(CheckTreeIsSymmetric.isSymmetric(null));
+    }
+
+    @Test
+    public void testSingleNodeTree() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[]{100});
+        assertTrue(CheckTreeIsSymmetric.isSymmetric(root));
+    }
+
+    @Test
+    public void testSymmetricTree() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[]{1,2,2,3,4,4,3});
+        assertTrue(CheckTreeIsSymmetric.isSymmetric(root));
+    }
+
+    @Test
+    public void testNonSymmetricTree() {
+        final BinaryTree.Node root = TreeTestUtils.createTree(new Integer[]{1,2,2,3,5,4,3});
+        assertFalse(CheckTreeIsSymmetric.isSymmetric(root));
+    }
+
+}