Kit Library / Computer Science / Data Structures
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
Data doesn't have to be a straight line.
A tree is a non-linear data structure where elements (nodes) are arranged in a hierarchy — one root, branching into children, forming levels.
↳ Trees trade linear simplicity for hierarchical speed — that's why databases and file systems rely on them.
Speak tree language fluently.
↳ Precise vocabulary is half the exam — root, leaf, depth, and height appear in almost every tree question.
Arrays walk; trees branch.
↳ Trees win when data has natural hierarchy or when fast search matters.
One less edge than nodes — always.
Every tree with $n$ nodes has exactly $n-1$ edges. This is the quickest way to verify whether a given graph is actually a tree.
↳ If edges ≠ nodes − 1, it's not a tree — it's either disconnected or has a cycle.
Visit every node — three different orders.
Traversal means visiting every node exactly once. The order depends on when you process the root relative to its subtrees.
↳ Inorder on a BST gives sorted data — that's the single most tested traversal fact.
Three lines that sort a BST.
↳ Recursion mirrors the tree's own structure — left, root, right is literally the code order.
Two children vs two rules.
↳ The BST ordering rule is what turns a plain binary tree into a searchable structure.
Same tree, opposite directions.
↳ Depth goes down from root; height goes up from leaf — memorize the direction, not just the number.
Your computer is a forest of trees.
↳ If data has hierarchy, a tree is almost always the right model.
Billions of rows, milliseconds to find one.
A B-tree is a balanced multi-way tree where each node holds many keys. Its short height means fewer disk reads per lookup.
↳ Balanced trees keep search fast at scale — that's the whole point of using them in databases.
One traversal question, guaranteed marks.
↳ Traversal questions are free marks if you trace carefully — don't rush the order.
Where's the root? That's the name.
↳ The prefix tells you exactly where the root sits — no memorizing needed.
A tree can secretly become a list.
↳ A BST is only fast if it's balanced — sorted input is the classic trap.
Height, depth, and balance — know all three.
↳ Master recursive height calculation — it unlocks half of all tree interview problems.
The null check saves your code.
↳ The base case isn't optional — it's what makes recursion on trees safe.
Trees are non-linear data structures that organize data hierarchically, with a root node branching into child nodes. Unlike linear structures such as arrays or linked lists, trees model relationships like file systems, f…
Full explanation, worked examples & memory tricks in the app
All 17 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Why is a tree classified as a non-linear data structure?
BeginnerD · Each node can have many children, giving a one-to-many shape.
Linear structures like arrays and lists are one-to-one; a tree is one-to-many because a node can point to multiple children, which is the defining non-linear property.
Q2. In a tree, what do we call a node that has no children?
BeginnerD · Leaf
A node with no children is a leaf (degree 0). The root is the topmost node, and a parent is a node with at least one child.
Q3. A tree has 15 nodes. How many edges does it contain?
BeginnerB · 14
Every node except the root has exactly one parent edge, so a tree with $n$ nodes has $n - 1$ edges: $15 - 1 = 14$.
Q4. Which traversal of a binary search tree visits nodes in ascending sorted order?
BeginnerD · Inorder
Inorder visits left subtree, node, then right subtree. Because a BST keeps smaller values on the left and larger on the right, this produces sorted output.
Q5. A file explorer where folders contain folders and files is best modeled by which structure?
BeginnerC · A tree
Nested folders form a hierarchy — each folder can contain many items, which is exactly the one-to-many shape of a tree.
Q6. A tree with $n$ nodes always has exactly $n - 1$ edges and contains no cycles.
BeginnerA · True
A tree with $n$ nodes always has exactly $n - 1$ edges and contains no cycles.
Q7. Which statement about the degree of a node is correct?
IntermediateC · It is the number of children the node has.
Degree counts a node's children. The number of edges from the root is depth, and the maximum depth is the tree's height.
Q8. A structure has 10 nodes and 12 edges. What can you conclude?
IntermediateB · It cannot be a tree because it contains at least one cycle.
A tree with $n$ nodes must have exactly $n - 1$ edges. With 10 nodes and 12 edges there are more edges than a tree allows, so at least one cycle exists.
Q9. A BST is built by inserting values in strictly increasing order. What happens to search performance?
IntermediateC · It degrades to $O(n)$ because the tree becomes list-like.
Sorted input makes every new node a right child, producing a degenerate linked-list-like tree of height $n$, so search becomes $O(n)$.
Q10. Which traversal should you use to delete an entire tree safely?
IntermediateD · Postorder, so children are removed before parents.
Postorder processes left and right subtrees before the node, so every child is freed before its parent — the safe order for deletion.
Q11. What distinguishes a binary search tree from a plain binary tree?
IntermediateD · A BST enforces left-smaller and right-larger ordering at every node.
Both limit children to two, but only a BST adds the ordering rule that makes fast search possible.
Q12. Which structure is a collection of disjoint trees with no shared nodes?
IntermediateB · A forest
A forest is exactly a set of disjoint trees. A subtree is a node plus its descendants within one tree.
Q13. Assertion (A): A tree with $n$ nodes always has exactly $n - 1$ edges. Reason (R): Every node except the root has exactly one parent, and each parent-child link is one edge.
AdvancedD · Both A and R are true, and R correctly explains A.
Each non-root node contributes exactly one edge to its parent, so edges equal non-root nodes, which is $n - 1$. The reason is the direct justification of the assertion.
Q14. Consider these statements about trees: I. A tree contains no cycles. II. Exactly one path connects any two nodes in a tree. III. Every graph is a tree. Which combination is correct?
AdvancedA · I and II only
Trees are connected and acyclic, so I and II hold. Statement III is false: graphs may contain cycles or be disconnected, so not every graph is a tree.
Q15. A team needs fast lookups on millions of records that are inserted in sorted order. Which choice is best?
AdvancedD · A self-balancing tree such as an AVL or red-black tree
Sorted insertion degenerates a naive BST to $O(n)$ search. A self-balancing tree keeps height near $\log n$, preserving $O(\log n)$ lookups.
Q16. You draw a structure and can trace a loop that returns to your starting node. What does this tell you?
AdvancedB · It is a graph but not a tree, because it contains a cycle.
A tree must be acyclic. Tracing a loop back to the start proves a cycle exists, so the structure is a general graph, not a tree.
Q17. Consider a binary search tree (BST) constructed by inserting the following values in the given order: 30, 20, 40, 10, 25, 35, 50. What will be the depth of the node containing the value 25?
AdvancedD · 2
The depth of a node in a tree is defined as the number of edges from the root to that node. In this BST, the root is 30 (depth 0), 20 is the left child of 30 (depth 1), and 25 is the right child of 20 (depth 2). Therefore, the depth of the node containing the value 25 is 2.
31 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
Word Match
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True False
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Memory Match
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Flashcard Battle
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Speed Quiz
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Guess Term
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Sequence Builder
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Categorization
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Revision Battle
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