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A leaf is an endpoint node because it has no children."},{"text":"The top node of a tree is the parent; a node with no children is a leaf.","correct":false,"explanation":"A parent is any node that has one or more children, so it need not be at the top. The top node is the root, while a childless node is a leaf."},{"text":"The top node of a tree is the root; a node with no children is a branch.","correct":false,"explanation":"A branch connects or contains parts of a tree rather than naming a childless node. The top node is the root, and a node with no children is a leaf."},{"text":"The top node of a tree is the leaf; a node with no children is a root.","correct":false,"explanation":"This reverses the two definitions. The root is the top node of the tree, whereas a leaf is a node at an endpoint with no children."}]},{"id":"619b098f-c67f-4f99-b8f6-fa8109bb2a62","cardType":"cloze","points":null,"front":"A [ ] is a node with all nodes below it; it is still a [ ].","back":"A subtree is a node with all nodes below it; it is still a tree.","mcqOptions":[{"text":"A subtree is a node with all nodes below it; it is still a tree.","correct":true,"explanation":"A node together with all its descendants forms a subtree. It retains the hierarchical structure and defining properties of a tree."},{"text":"A branch is a node with all nodes below it; it is still a tree.","correct":false,"explanation":"A branch commonly describes a connection or part of a tree, not formally a node and all its descendants. That complete structure is called a subtree and is itself a tree."},{"text":"A subtree is a node with all nodes below it; it is still a leaf.","correct":false,"explanation":"A leaf has no children, whereas a subtree may include many descendants. A node together with everything below it is a subtree, and that structure remains a tree."},{"text":"A path is a node with all nodes below it; it is still a tree.","correct":false,"explanation":"A path is a sequence of connected nodes and does not necessarily include every descendant. A node and all nodes below it form a subtree, which is itself a tree."}]},{"id":"ab5b69cf-6449-4536-9517-87cf0d12777c","cardType":"cloze","points":null,"front":"In a binary tree, each node has at most [ ] children, usually called [ ] children.","back":"In a binary tree, each node has at most two children, usually called left and right children.","mcqOptions":[{"text":"In a binary tree, each node has at most two children, usually called left and right children.","correct":true,"explanation":"Binary means each node can have no more than two children. Their positions are conventionally distinguished as the left child and the right child."},{"text":"In a binary tree, each node has at most one children, usually called left and right children.","correct":false,"explanation":"Restricting every node to one child would produce a chain-like structure rather than the general binary-tree model. Binary nodes may have up to two children, called left and right."},{"text":"In a binary tree, each node has at most two children, usually called parent and child children.","correct":false,"explanation":"Parent and child describe the relationship between adjacent levels, not the two child positions of one node. Those positions are called left and right."},{"text":"In a binary tree, each node has at most three children, usually called left, middle and right children.","correct":false,"explanation":"This describes a ternary arrangement, where up to three children are permitted. A binary tree allows at most two children, conventionally called left and right."}]},{"id":"bf45bf1f-8c50-45bc-b936-b0a8a7cd8603","cardType":"cloze","points":null,"front":"In a binary search tree, the left subtree has [ ] values and the right subtree has [ ] values.","back":"In a binary search tree, the left subtree has smaller values and the right subtree has larger values.","mcqOptions":[{"text":"In a binary search tree, the left subtree has smaller values and the right subtree has larger values.","correct":true,"explanation":"The binary search tree ordering rule places values smaller than a node in its left subtree and values larger than it in its right subtree."},{"text":"In a binary search tree, the left subtree has larger values and the right subtree has smaller values.","correct":false,"explanation":"This reverses the standard binary search tree ordering rule. Smaller values belong in the left subtree, while larger values belong in the right subtree."},{"text":"In a binary search tree, the left subtree has smaller values and the right subtree has smaller values.","correct":false,"explanation":"Placing smaller values on both sides would prevent searches from choosing a direction reliably. Smaller values go left, and larger values go right."},{"text":"In a binary search tree, the left subtree has larger values and the right subtree has larger values.","correct":false,"explanation":"Placing larger values on both sides breaks the ordering needed for efficient searching. The left subtree contains smaller values and the right subtree contains larger values."}]},{"id":"2d45ed0c-ef2a-4865-ab7b-d211eef07f90","cardType":"basic","points":1,"front":"When checking a tree traversal trace, how many times should each node appear?","back":"Exactly once.","mcqOptions":[{"text":"Exactly once.","correct":true,"explanation":"A complete traversal visits and records every node once. A missing node or repeated node indicates that the traversal trace has not followed the algorithm correctly."},{"text":"Exactly twice.","correct":false,"explanation":"Tracing entry and return steps can make a node seem visited twice, but the output records it only at the traversal’s specified point. Each node should appear exactly once."},{"text":"At least once.","correct":false,"explanation":"Appearing at least once permits duplicate entries, which are not valid in a standard traversal output. Every node must be included exactly once."},{"text":"Only if it has children.","correct":false,"explanation":"Leaf nodes must be included even though they have no children. A complete tree traversal records every node exactly once, regardless of whether it has descendants."}]},{"id":"2be3c8f3-e46a-4e69-81e5-6d25e47f26af","cardType":"basic","points":1,"front":"For a non-empty node, what is the pre-order traversal order?","back":"Root, Left, Right.","mcqOptions":[{"text":"Root, Left, Right.","correct":true,"explanation":"Pre-order processes the root before recursively traversing its subtrees. It then visits the left subtree followed by the right subtree."},{"text":"Left, Root, Right.","correct":false,"explanation":"Visiting the root between the two subtrees is in-order traversal. Pre-order visits the root first, followed by the left subtree and then the right subtree."},{"text":"Left, Right, Root.","correct":false,"explanation":"Visiting the root after both subtrees is post-order traversal. Pre-order instead processes the root first, followed by the left and right subtrees."},{"text":"Root, Right, Left.","correct":false,"explanation":"The root is correctly placed first, but the subtree order has been reversed. Standard pre-order traversal is root, then left, then right."}]},{"id":"9e126202-b1cd-47e6-89c3-328bace8a825","cardType":"basic","points":1,"front":"For a non-empty node, what is the in-order traversal order?","back":"Left, Root, Right.","mcqOptions":[{"text":"Left, Root, Right.","correct":true,"explanation":"In-order recursively traverses the left subtree, processes the root, and then traverses the right subtree. In a binary search tree, this produces values in sorted order."},{"text":"Root, Left, Right.","correct":false,"explanation":"Processing the root before both subtrees is pre-order traversal. In-order visits the left subtree first, then the root, and finally the right subtree."},{"text":"Left, Right, Root.","correct":false,"explanation":"Processing the root after both subtrees is post-order traversal. In-order places the root between the left and right subtree traversals."},{"text":"Right, Root, Left.","correct":false,"explanation":"This is a reverse in-order traversal and would produce descending values in a binary search tree. Standard in-order traversal is left, root, then right."}]},{"id":"82566c02-2565-40c0-8c95-fb14240ac431","cardType":"basic","points":1,"front":"For a non-empty node, what is the post-order traversal order?","back":"Left, Right, Root.","mcqOptions":[{"text":"Left, Right, Root.","correct":true,"explanation":"Post-order recursively traverses both subtrees before processing their root. The left subtree is visited first, followed by the right subtree and then the root."},{"text":"Root, Left, Right.","correct":false,"explanation":"Processing the root before either subtree is pre-order traversal. Post-order visits the left and right subtrees first and processes the root last."},{"text":"Left, Root, Right.","correct":false,"explanation":"Processing the root between its subtrees is in-order traversal. Post-order delays the root until after both the left and right subtrees have been visited."},{"text":"Right, Left, Root.","correct":false,"explanation":"The root is correctly placed last, but the subtree order is reversed. Standard post-order traversal visits the left subtree, then the right subtree, then the root."}]},{"id":"baa4e921-a585-4531-b69e-2ed13ca3e837","cardType":"basic","points":1,"front":"What is the only difference between pre-order, in-order and post-order?","back":"The position of the root visit.","mcqOptions":[{"text":"The position of the root visit.","correct":true,"explanation":"All three traversals visit the left and right subtrees in the same relative order. Their defining difference is whether the root is visited before, between or after them."},{"text":"The position of the left subtree visit.","correct":false,"explanation":"The left subtree is visited before the right subtree in all three standard depth-first traversals. The changing feature is the position of the root visit."},{"text":"The direction of the subtree visits.","correct":false,"explanation":"These traversals normally process the left subtree before the right subtree, so their direction does not change. Only the root’s position changes."},{"text":"The number of times each node is visited.","correct":false,"explanation":"Each node is processed once in each standard traversal. Pre-order, in-order and post-order differ only in when the root is visited relative to its subtrees."}]},{"id":"e9ee1af8-0244-487b-a786-07ce82885f6e","cardType":"basic","points":1,"front":"What is the recursive base case for tree traversal?","back":"An empty subtree: do nothing.","mcqOptions":[{"text":"An empty subtree: do nothing.","correct":true,"explanation":"When the current subtree is empty, there is no node to process and no further recursive call to make, so the procedure returns immediately."},{"text":"A leaf node: output nothing.","correct":false,"explanation":"A leaf is still a real node and must be visited according to the traversal order. The base case is an empty subtree, which requires no action."},{"text":"A full subtree: return immediately.","correct":false,"explanation":"A full subtree contains nodes that must all be traversed. Recursion stops only when it reaches an empty subtree beyond a missing child."},{"text":"An unbalanced subtree: do nothing.","correct":false,"explanation":"An unbalanced subtree is still traversed normally because balance does not determine the stopping condition. The recursive base case is an empty subtree."}]},{"id":"84b4443c-2bc3-433f-8757-ec7334be39b1","cardType":"basic","points":1,"front":"In an A-Level traversal trace, what should normally happen to a missing child?","back":"Skip it - do not output null unless told to.","mcqOptions":[{"text":"Skip it - do not output null unless told to.","correct":true,"explanation":"A missing child represents an empty subtree, so the traversal performs no visit there. A-Level traces normally list only actual nodes unless null markers are explicitly requested."},{"text":"Output null - record every absent child.","correct":false,"explanation":"Null markers may be used in specialised tree representations, but they are not normally included in traversal output. A missing child should simply be skipped unless instructed otherwise."},{"text":"Visit its parent again - then continue the traversal.","correct":false,"explanation":"Returning from an empty child does not cause the parent to be output again. The missing child is skipped, and traversal continues from the existing call."},{"text":"Stop the traversal - do not process remaining nodes.","correct":false,"explanation":"A missing child ends only that recursive branch, not the entire traversal. It should be skipped before the algorithm continues with any remaining subtree."}]},{"id":"ebcb69cf-a783-4e9e-ba28-496607605ffa","cardType":"basic","points":2,"front":"Why is pre-order suitable for copying a tree?","back":"The parent is created before its children are copied and attached.","mcqOptions":[{"text":"The parent is created before its children are copied and attached.","correct":true,"explanation":"Pre-order visits each parent before either child. This allows the new parent node to exist before recursive copies of its children are attached to it."},{"text":"The children are created before their parent is copied and attached.","correct":false,"explanation":"Creating children first describes the useful property of post-order, not pre-order. Pre-order creates the parent before copying and attaching its children."},{"text":"The left subtree is copied before its parent is created and attached.","correct":false,"explanation":"Pre-order visits the parent before entering the left subtree. That ordering ensures the parent already exists when the copied left child is attached."},{"text":"The parent is created after its children are copied and attached.","correct":false,"explanation":"This reverses the defining pre-order relationship and resembles post-order processing. For copying with pre-order, the parent is created before its children."}]},{"id":"6b688b5a-d233-48da-a787-dc3c645fda8c","cardType":"basic","points":1,"front":"For root A, left subtree B(D,E) and right subtree C(F,G), what is the pre-order output?","back":"A B D E C F G","mcqOptions":[{"text":"A B D E C F G","correct":true,"explanation":"Pre-order follows root, left subtree, then right subtree. It therefore visits A, then B with D and E, followed by C with F and G."},{"text":"D B E A F C G","correct":false,"explanation":"This sequence uses left, root, right at each node, so it is the in-order output. Pre-order gives A B D E C F G."},{"text":"D E B F G C A","correct":false,"explanation":"This sequence visits both subtrees before each root, making it post-order. Pre-order visits each root first, producing A B D E C F G."},{"text":"A B C D E F G","correct":false,"explanation":"This is level-order because it processes nodes one depth at a time. Pre-order explores B’s entire subtree before C, giving A B D E C F G."}]},{"id":"c13c8a5b-ad13-4aa3-9007-6966bb9650f0","cardType":"basic","points":2,"front":"Why does in-order traversal output a binary search tree in ascending order?","back":"

Left subtree values are smaller.
Right subtree values are larger.

","mcqOptions":[{"text":"

Left subtree values are smaller.
Right subtree values are larger.

","correct":true,"explanation":"In-order visits the left subtree, root and right subtree. The BST ordering rule therefore places smaller values before the root and larger values after it."},{"text":"

Left subtree values are larger.
Right subtree values are smaller.

","correct":false,"explanation":"This reverses the BST ordering rule and would make in-order produce descending rather than ascending values. In a standard BST, left values are smaller and right values are larger."},{"text":"

Left subtree values are equal.
Right subtree values are equal.

","correct":false,"explanation":"A BST does not generally place values equal to the root throughout both subtrees. Ascending in-order output relies on smaller left values and larger right values."},{"text":"

Left subtree values are unordered.
Right subtree values are unordered.

","correct":false,"explanation":"If the subtrees were unordered, in-order traversal could not guarantee ascending output. The BST rule requires smaller values on the left and larger values on the right."}]},{"id":"f0af9e64-64b9-4560-a0be-bbe31e037da9","cardType":"basic","points":2,"front":"Does in-order traversal sort any arbitrary binary tree?","back":"No - it only works if the tree already obeys the BST ordering rule.","mcqOptions":[{"text":"No - it only works if the tree already obeys the BST ordering rule.","correct":true,"explanation":"In-order merely chooses the visit sequence left, root, right; it does not rearrange values. The result is sorted only when the tree already satisfies BST ordering."},{"text":"Yes - it always rearranges nodes into ascending order.","correct":false,"explanation":"Traversal reads nodes without moving or rearranging them. In-order produces ascending values only when the existing tree obeys the BST ordering rule."},{"text":"No - it only works if the tree is already a complete binary tree.","correct":false,"explanation":"Completeness concerns whether tree levels are filled, not how values are ordered. Ascending in-order output requires the BST ordering rule, even if the tree is incomplete."},{"text":"No - it only works if the tree is already a balanced binary tree.","correct":false,"explanation":"Balance affects tree height and performance, not whether in-order output is sorted. The necessary condition is BST ordering, and an unbalanced BST still works."}]},{"id":"182e9c9e-0b5a-43d8-ad8c-d887a1fadc83","cardType":"basic","points":1,"front":"For BST root 8, left child 3 with children 1 and 6, and right child 10 with right child 14, what is the in-order output?","back":"1 3 6 8 10 14","mcqOptions":[{"text":"1 3 6 8 10 14","correct":true,"explanation":"In-order visits left subtree, root, then right subtree. This visits 1, 3 and 6 before 8, followed by 10 and 14."},{"text":"8 3 1 6 10 14","correct":false,"explanation":"This places each root before its descendants, so it is pre-order. In-order visits left, root, right and produces 1 3 6 8 10 14."},{"text":"1 6 3 14 10 8","correct":false,"explanation":"This places each root after its descendants, so it is post-order. In-order places each root between its subtrees, producing 1 3 6 8 10 14."},{"text":"8 3 10 1 6 14","correct":false,"explanation":"This is level-order because it processes nodes by depth. In-order fully traverses the left subtree before 8, giving 1 3 6 8 10 14."}]},{"id":"cf5a3e5b-b4a4-4801-aead-b1dd31bf52d0","cardType":"basic","points":2,"front":"Why is post-order suitable for emptying a tree?","back":"Children are deleted before their parent.","mcqOptions":[{"text":"Children are deleted before their parent.","correct":true,"explanation":"Post-order processes every subtree before its root, so deleting a node cannot remove the links needed to reach and delete its descendants."},{"text":"Parents are deleted before their children.","correct":false,"explanation":"Deleting a parent first can destroy access to its descendants, which is the pre-order approach. Post-order safely deletes children before deleting their parent."},{"text":"Nodes are deleted one level at a time.","correct":false,"explanation":"Level-order deletion processes nodes by depth and may delete parents while their children remain. Post-order instead finishes and deletes each node’s children first."},{"text":"Right children are deleted before left children.","correct":false,"explanation":"The order between siblings does not make deletion safe. Post-order is suitable because every child is deleted before its parent, regardless of left-right order."}]},{"id":"6072c45d-5e14-4b62-85ac-60161097c7d4","cardType":"basic","points":1,"front":"Which traversal produces postfix/RPN from an expression tree?","back":"Post-order.","mcqOptions":[{"text":"Post-order.","correct":true,"explanation":"Post-order visits the left operand, then the right operand, and finally the operator at the parent, which is exactly the operand-operand-operator structure of postfix notation."},{"text":"Pre-order.","correct":false,"explanation":"Pre-order visits the operator before its operands, so it produces prefix notation. Post-order places each operator after its operands and therefore produces postfix notation."},{"text":"In-order.","correct":false,"explanation":"In-order places each operator between its left and right operands, producing infix notation. Post-order produces postfix notation by visiting the operator last."},{"text":"Level-order.","correct":false,"explanation":"Level-order visits nodes by depth and does not preserve the operand-then-operator arrangement required for postfix notation. Post-order provides the required ordering."}]},{"id":"530d3fa4-e211-4c74-b288-56f89656801d","cardType":"cloze","points":null,"front":"Infix notation puts the operator [ ] operands; postfix/RPN puts it [ ] operands.","back":"Infix notation puts the operator between operands; postfix/RPN puts it after operands.","mcqOptions":[{"text":"Infix notation puts the operator between operands; postfix/RPN puts it after operands.","correct":true,"explanation":"Infix writes an operator between its two operands, as in A + B. Postfix writes it after both operands, as in A B +."},{"text":"Infix notation puts the operator before operands; postfix/RPN puts it after operands.","correct":false,"explanation":"Placing an operator before its operands defines prefix notation, not infix. Infix places it between the operands, while postfix places it after them."},{"text":"Infix notation puts the operator between operands; postfix/RPN puts it before operands.","correct":false,"explanation":"Putting the operator before its operands describes prefix notation rather than postfix. Infix uses an operator between operands, whereas postfix places it after them."},{"text":"Infix notation puts the operator after operands; postfix/RPN puts it between operands.","correct":false,"explanation":"This reverses neither notation correctly: infix places the operator between operands, and postfix places the operator after both operands."}]},{"id":"8c5b1110-1207-4d25-bedc-a966c66bf35b","cardType":"basic","points":1,"front":"For the expression tree (A + B) * C, what postfix output does post-order produce?","back":"A B + C *","mcqOptions":[{"text":"A B + C *","correct":true,"explanation":"Post-order visits the left subtree A B +, then the right operand C, and finally the root multiplication operator."},{"text":"A B C + *","correct":false,"explanation":"This visits C before completing the addition subtree. Post-order must complete the left subtree as A B +, then visit C and *."},{"text":"A B + * C","correct":false,"explanation":"The multiplication operator appears before its right operand, which violates postfix ordering. It must follow both completed operands, giving A B + C *."},{"text":"* + A B C","correct":false,"explanation":"This is pre-order or prefix output because each operator precedes its operands. Post-order places operators after their operands, producing A B + C *."}]},{"id":"e511cd9d-e64a-4e7e-93a0-9761fdfe6fd7","cardType":"basic","points":2,"front":"Why is tree traversal time complexity $O(n)$ for $n$ nodes?","back":"

Each node is visited once.
Child-link checks take constant time.

","mcqOptions":[{"text":"

Each node is visited once.
Child-link checks take constant time.

","correct":true,"explanation":"A complete traversal performs constant work at each of the $n$ nodes. Summing that work across all nodes gives a total running time of $O(n)$."},{"text":"

Each node is compared with every node.
Child-link checks take constant time.

","correct":false,"explanation":"Comparing every node with every other node would require $O(n^2)$ work, not $O(n)$. Standard traversal visits each node once and checks links in constant time."},{"text":"

Only leaf nodes are visited.
Child-link checks take constant time.

","correct":false,"explanation":"A tree traversal processes internal nodes as well as leaves. Its linear complexity comes from visiting every node once while performing constant-time child-link checks."},{"text":"

Each node is visited once.
Child-link checks take linear time.

","correct":false,"explanation":"If checking links took linear time at every node, the total could be $O(n^2)$. Traversal is $O(n)$ because each node visit and its link checks take constant time."}]},{"id":"212e13e5-f41e-41dd-ad6f-ca074b2884b0","cardType":"cloze","points":null,"front":"The recursive call stack depends on the tree’s [ ], the longest path from [ ].","back":"The recursive call stack depends on the tree’s height, the longest path from root to leaf.","mcqOptions":[{"text":"The recursive call stack depends on the tree’s height, the longest path from root to leaf.","correct":true,"explanation":"Each recursive call represents a node on the current root-to-leaf route. The maximum number of simultaneous calls is therefore proportional to the tree’s height."},{"text":"The recursive call stack depends on the tree’s size, the longest path from root to leaf.","correct":false,"explanation":"Tree size counts all nodes, whereas the call stack contains only the current chain of recursive calls. Its maximum depth depends on height, measured from root to leaf."},{"text":"The recursive call stack depends on the tree’s height, the longest path from leaf to leaf.","correct":false,"explanation":"A longest leaf-to-leaf path describes the tree’s diameter, not its height. Recursive stack depth follows a single root-to-leaf path and therefore depends on height."},{"text":"The recursive call stack depends on the tree’s width, the longest path from one level to another.","correct":false,"explanation":"Width measures how many nodes occur at a level and does not determine recursive depth. The call stack depends on height, the longest root-to-leaf path."}]}]}],"examCountdown":{"examDate":"2027-05-11","paperLabel":"Paper 1"},"heading":"Tree-traversal","title":"Tree-traversal Flashcards","topbar":{"backHref":"/as-level/computer-science/aqa/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"5477e0e3-e2fa-5036-9c8f-f1384c8c6745","walled":"$L38"}],"$L39","$L3a"]