Coding Interview Patterns Flashcards: Signals, Invariants & Complexity
Practice coding interview patterns with 210 English flashcards on problem signals, invariants, complexity, edge cases, and choosing between approaches. Language-agnostic DSA review to pair with hands-on coding.
Par šo kavu
Coding interview patterns become useful when you can explain why an approach fits. These 210 English flashcards practice recognizing problem signals, stating invariants, checking prerequisites, comparing approaches, and diagnosing a broken assumption.
The sequence starts with constraints and complexity, then moves through arrays, strings, hashing, two pointers, sliding windows, prefix sums, binary search, intervals, stacks, linked lists, trees, heaps, tries, graphs, union-find, topological sorting, backtracking, greedy choices, dynamic programming, and bit techniques. Each topic builds from its basic idea toward the conditions that make it work.
Cards map short scenarios to candidate patterns, named patterns to invariants and costs, and failed assumptions to explanations or alternatives. Selected contrast prompts distinguish neighboring ideas such as subarrays and subsequences, BFS and DFS, or greedy choice and dynamic programming. Mechanical reverse cards, problem-number recall, language-specific API memorization, and full solution listings are excluded because they add little to this reasoning-focused review. Answer each prompt before turning the card, then test the idea by coding a fresh example.
This is a language-agnostic companion to practical DSA exercises. It complements the Blind 75 Python solutions deck by teaching reusable reasoning across problems. It was authored independently in English, not translated or paraphrased from another catalog package.
The questions, answers, organization, metadata, and original generated cover are released under CC0 1.0 to the extent applicable rights exist. Algorithm facts are common knowledge; no commercial deck text or third-party media was copied. This is an independent study resource with no affiliation to an employer or interview platform.
Kartītes šajā kavā
1. kartīte
Jautājums
Which input constraints should you clarify before choosing an interview algorithm?
Atbilde
Input size, value range, ordering, duplicates, allowed mutations, and the exact output. These determine which operations are affordable and which assumptions are valid.
2. kartīte
Jautājums
What does a loop invariant describe?
Atbilde
A property that holds at a defined point in every iteration. Show it holds initially, survives an iteration, and implies the result when the loop ends.
3. kartīte
Jautājums
When analyzing nested loops, why can multiplying their written bounds overestimate runtime?
Atbilde
The loops may share progress. If an inner pointer only advances across the input once, its total work can be O(n), even inside an outer loop.
4. kartīte
Jautājums
What is the difference between auxiliary space and total space?
Atbilde
Auxiliary space counts extra working storage. Total space also includes the input and, depending on the stated convention, the output. State which measure you report.
5. kartīte
Jautājums
What does amortized O(1) mean for an operation sequence?
Atbilde
The total cost of m operations is O(m), even if some individual operations are expensive. It is a sequence-wide bound, not a probability claim.
6. kartīte
Jautājums
How does a counterexample help evaluate a proposed greedy rule?
Atbilde
One valid input where the rule fails disproves it. Try small cases that force a locally attractive choice to block a better later choice.
7. kartīte
Jautājums
Why should an algorithm's correctness argument address termination separately?
Atbilde
Preserving the right property is not enough if the loop never stops. Identify a bounded measure that moves strictly toward termination.
8. kartīte
Jautājums
What runtime lower bound follows from returning k separate results?
Atbilde
At least Ω(k) time to emit them, or more if each result has multiple elements. Include output size when analyzing enumeration algorithms.
9. kartīte
Jautājums
What should you say when quoting expected O(1) hash-table lookup?
Atbilde
It assumes a suitable hash distribution and controlled load factor. It is not a worst-case guarantee; hashing a long key can also cost time.
10. kartīte
Jautājums
Which edge cases best expose index and boundary errors?
Atbilde
Empty input, one element, all equal elements, and answers at either end. Also check the smallest input that enters each branch.
11. kartīte
Jautājums
Why can sorting be an invalid optimization even when it reduces later search work?
Atbilde
Sorting may destroy required order or original indices. Preserve the needed information or choose an approach that respects the input contract.
12. kartīte
Jautājums
What does an exchange argument establish in a greedy proof?
Atbilde
That an optimal solution can be changed to include the greedy choice without making its objective worse. The remaining problem must still fit the same reasoning.
13. kartīte
Jautājums
Why can recursion use O(n) space even without an explicit collection?
Atbilde
Each active call occupies a stack frame. A chain of n calls can therefore need O(n) auxiliary space.
14. kartīte
Jautājums
What evidence should accompany a faster solution after presenting brute force?
Atbilde
Name the repeated work or discarded search space, explain why the shortcut is safe, and give the resulting time and space bounds.
15. kartīte
Jautājums
What makes an array useful when a problem repeatedly accesses positions by index?
Atbilde
Constant-time indexed access in the usual RAM model. Inserting or removing near the front can still require shifting O(n) elements.
16. kartīte
Jautājums
What should 'one character' mean before solving a string problem?
Atbilde
Clarify whether the unit is a byte, code unit, Unicode code point, or user-perceived character. Indexing and length depend on that choice.
17. kartīte
Jautājums
An unsorted array needs a duplicate-existence check. Which structure fits?
Atbilde
A hash set of values seen so far. Stop when a value is already present; expected O(n) time and O(n) space.
18. kartīte
Jautājums
For two-sum on an unsorted array, what should a hash map store?
Atbilde
Previously seen values mapped to their indices. For each value x, look for target − x before inserting x, so the same position is not reused.
19. kartīte
Jautājums
When does a frequency array beat a hash map for counting?
Atbilde
When keys come from a small known integer or character range. Direct indexing gives predictable access with space proportional to that range.
20. kartīte
Jautājums
Why is repeated concatenation risky when constructing a long immutable string?
Atbilde
Each append may copy the existing prefix, producing quadratic total work. Collect pieces and join them, or use an appropriate mutable builder.
21. kartīte
Jautājums
How can you group anagrams without comparing every pair of words?
Atbilde
Map a canonical character signature to a group. Sorted characters work; a frequency tuple works when the alphabet and character rules are fixed.
22. kartīte
Jautājums
What information does a set lose compared with a frequency map?
Atbilde
Multiplicity. A set can answer whether a value exists but cannot distinguish one occurrence from several.
23. kartīte
Jautājums
How can a hash set support finding the longest consecutive integer run in expected O(n) time?
Atbilde
Start scanning a run only at values whose predecessor is absent. Each distinct value then belongs to one forward scan; iterate distinct values.
24. kartīte
Jautājums
Why can a mutable object be a dangerous hash-map key?
Atbilde
Changing fields used by its hash or equality can make the stored entry unreachable by ordinary lookup. Use immutable keys or stable key values.
25. kartīte
Jautājums
An array contains only integers from 0 through k. When is counting sort attractive?
Atbilde
When k is small enough: count each value and reconstruct the order in O(n + k) time with O(k) count storage. General arbitrary keys need another approach.
26. kartīte
Jautājums
How can a single scan find both the minimum value and its earliest index?
Atbilde
Keep the current minimum and index; update only on a strictly smaller value. Updating on equality would select a later occurrence.
27. kartīte
Jautājums
How do you compare two strings as multisets of characters?
Atbilde
Compare character counts under the same character interpretation. Order does not matter, but every character's multiplicity does.
28. kartīte
Jautājums
Why does a hash collision not imply that two keys are equal?
Atbilde
A hash compresses many possible keys into fewer codes. A correct table also checks key equality when resolving collisions.
29. kartīte
Jautājums
When is sorting a useful preprocessing step for detecting duplicate values?
Atbilde
When reordering is allowed and O(n log n) time is acceptable. Equal values become adjacent, so a scan finds duplicates without a separate hash set.
30. kartīte
Jautājums
What is the key distinction between a subarray and a subsequence?
Atbilde
A subarray is contiguous. A subsequence preserves relative order but may skip positions. Sliding-window methods usually depend on contiguity.
31. kartīte
Jautājums
For an unsorted two-sum query, how do hashing and sorting trade off?
Atbilde
Hashing gives expected O(n) time with O(n) extra storage. Sorting plus two pointers costs O(n log n) time and requires care with original indices and mutation.
32. kartīte
Jautājums
How can a frequency map detect whether any permutation of a string can be a palindrome?
Atbilde
Count odd frequencies. At most one character may have an odd count; all other occurrences must form mirrored pairs.
33. kartīte
Jautājums
Why must compound hash keys encode boundaries unambiguously?
Atbilde
Naive concatenation can merge different tuples into the same key, such as (1, 23) and (12, 3). Use tuples or a length-aware encoding.
34. kartīte
Jautājums
What does coordinate compression preserve about numeric values?
Atbilde
Their relative order and equality, by replacing distinct sorted values with ranks. It does not preserve numeric distances or sums.
35. kartīte
Jautājums
How can you compute products except self without division?
Atbilde
Combine the product strictly before each position with the product strictly after it. Prefix and suffix passes handle zeros; use a numeric type large enough for the products.
36. kartīte
Jautājums
Why can a count of matching pairs overflow even when every input value fits in an integer?
Atbilde
The number of matching pairs can grow quadratically with the input length. Size the result type for the count, not just the input values.
37. kartīte
Jautājums
A sorted array needs a pair with a target sum. Which search pattern fits?
Atbilde
Opposite-end two pointers. Compare the endpoint sum with the target and move the endpoint that can move the sum in the needed direction.
38. kartīte
Jautājums
What invariant supports in-place removal of unwanted array values with read and write pointers?
Atbilde
The prefix before write contains exactly the retained values from the processed input, in order. Read scans every input position once.
39. kartīte
Jautājums
How can two pointers check a palindrome without constructing a reversed string?
Atbilde
Compare matching elements from opposite ends and move inward. Any mismatch rejects it; the pointers meeting or crossing completes the check.
40. kartīte
Jautājums
When does a fixed-size sliding window apply?
Atbilde
When every candidate is a contiguous block of the same length and its summary can be updated as one element enters and one leaves.
41. kartīte
Jautājums
What invariant should a longest-window algorithm restore after adding a new rightmost element?
Atbilde
The current window satisfies the required constraint. Move the left boundary and update state until validity returns, then consider its length.
42. kartīte
Jautājums
Why is moving the left pointer safe when a sorted-array endpoint sum is too small?
Atbilde
With that left value, every candidate at or before the current right endpoint gives an equally small or smaller sum. The left position cannot form a valid pair.
43. kartīte
Jautājums
How does a three-way partition maintain separate regions?
Atbilde
Track a low region, a middle region, an unclassified region, and a high region. Each step shrinks the unclassified region by placing one element correctly.
44. kartīte
Jautājums
How do you update the sum when a fixed-size window moves one position?
Atbilde
Subtract the outgoing value and add the incoming value. After initializing the first window, all moves together take O(n) time.
45. kartīte
Jautājums
Why can a variable sliding window run in O(n) despite a nested shrink loop?
Atbilde
Each boundary advances at most n times. With constant-time state updates, the total number of additions and removals is linear.
46. kartīte
Jautājums
For the longest substring without repeated characters, what window state is useful?
Atbilde
Character counts or last-seen positions. Move the left boundary past the conflicting occurrence while ensuring it never moves backward.
47. kartīte
Jautājums
Why does opposite-end target-sum search fail on a generally unsorted array?
Atbilde
Moving an endpoint no longer changes the sum predictably. The algorithm can discard a valid pair because the order-based elimination proof is missing.
48. kartīte
Jautājums
A positive-number array needs the shortest nonempty subarray with sum at least a positive T. When should the left boundary move?
Atbilde
While the current sum is at least T, record the length and remove the leftmost value. Positive values make further shrinking reduce the sum predictably.
49. kartīte
Jautājums
For windows with at most k distinct values, what must happen when an outgoing count becomes zero?
Atbilde
Remove that value from the active distinct set or decrement the distinct counter. A zero count must not still count as present.
50. kartīte
Jautājums
What changes when a fixed-window length exceeds the input length?
Atbilde
There is no complete window. Return the contract's empty or missing-result value instead of treating a partial block as a valid candidate.
51. kartīte
Jautājums
How do you merge two sorted arrays with forward pointers?
Atbilde
Repeatedly take the smaller unconsumed element, then append the remaining suffix. Each element is consumed once, giving O(m + n) time.
52. kartīte
Jautājums
Why must a minimum-cover substring track multiplicities of required characters?
Atbilde
A target can require the same character more than once. A set of required characters would mark an undersupplied window as complete.
53. kartīte
Jautājums
How can counting subarrays with exactly k distinct values, for k ≥ 1, use an at-most helper?
Atbilde
Compute atMost(k) − atMost(k − 1). The helper counts all valid subarrays ending at each right boundary after restoring the distinct-value limit.
54. kartīte
Jautājums
Why can a negative value break the usual shortest-sum sliding-window argument?
Atbilde
Removing it increases the sum, and adding one can decrease the sum. The monotonic relation between window size and sum no longer holds.
55. kartīte
Jautājums
What does 'fast and slow pointers' mean when removing duplicates from a sorted array?
Atbilde
A read pointer scans candidates while a write pointer marks the next unique slot. Sorting makes equal values adjacent, so the retained prefix can stay compact.
56. kartīte
Jautājums
What invariant prevents overwriting unread data during a backward merge into spare array capacity?
Atbilde
The suffix after the write pointer already contains the largest merged elements. Filling from the end leaves the remaining source elements unread and intact.
57. kartīte
Jautājums
Why is 'find a contiguous range' alone insufficient to justify a variable sliding window?
Atbilde
You also need a safe boundary-movement rule. Check how adding and removing elements affect the condition; contiguity by itself gives no such guarantee.
58. kartīte
Jautājums
After restoring an at-most window's validity, why are there right − left + 1 valid subarrays ending at right?
Atbilde
Every suffix starting between left and right is valid when removing elements cannot violate the constraint. Count those starts, including the one-element suffix.
59. kartīte
Jautājums
How can you avoid duplicate value pairs in a sorted two-pointer enumeration?
Atbilde
After emitting a pair, skip equal values on both sides. First confirm the output wants unique value pairs, since index-pair counting needs different handling.
60. kartīte
Jautājums
When does a character-frequency sliding window detect an anagram of a pattern?
Atbilde
When the window has the pattern's length and identical character counts. Maintain count differences or a mismatch counter as the window moves.
61. kartīte
Jautājums
What does a prefix-sum array P mean when P[0] = 0?
Atbilde
P[i] is the sum of the first i input elements. The extra zero represents the empty prefix and makes ranges beginning at index 0 work uniformly.
62. kartīte
Jautājums
When is binary search valid on a Boolean predicate over ordered candidates?
Atbilde
When the predicate changes at most once, such as false then true. The search uses that monotonic boundary to discard a whole interval.
63. kartīte
Jautājums
Which workload favors a difference array?
Atbilde
Many range additions followed by final value reconstruction. Mark each range's start and end changes, then take one prefix sum.
64. kartīte
Jautājums
In a lower-bound search over [lo, hi), what does hi initially equal for an n-element array?
Atbilde
n, an exclusive boundary. The result can equal n when no element is at least the target, so do not index the array without checking.
65. kartīte
Jautājums
For a static array, how do prefix sums answer the half-open range [l, r)?
Atbilde
Return P[r] − P[l]. Building P takes O(n) time and space; each range-sum query then takes O(1).
66. kartīte
Jautājums
How can prefix sums count subarrays whose sum equals k when negative values are allowed?
Atbilde
For each current prefix p, add the number of earlier prefixes equal to p − k, then record p. A frequency map gives expected O(n) time.
67. kartīte
Jautājums
Why is binary-searching an answer different from binary-searching an input array?
Atbilde
The candidates are possible result values. A feasibility check tells which side contains the boundary, even if the original input is unsorted.
68. kartīte
Jautājums
How does a difference array encode an addition of v to [l, r)?
Atbilde
Add v at l and subtract v at r, using a boundary slot when needed. The reconstructed prefix totals apply v only within that range.
69. kartīte
Jautājums
For lower bound, how should equality with the target move the search boundary?
Atbilde
Move hi to mid. An equal element is a candidate, but an earlier equal or qualifying element may still exist.
70. kartīte
Jautājums
Why initialize the prefix-frequency map with zero appearing once?
Atbilde
It represents the empty prefix before the array. This lets a subarray starting at index 0 contribute to the count.
71. kartīte
Jautājums
Why are plain prefix sums inconvenient for many interleaved point updates and range-sum queries?
Atbilde
Changing one value can invalidate a long suffix of prefix sums. A Fenwick tree or segment tree can support both operations in O(log n).
72. kartīte
Jautājums
How can you binary-search the minimum capacity needed to finish ordered work within a deadline?
Atbilde
Define whether a capacity suffices, prove larger capacities remain feasible, bracket a feasible answer, and search for the first feasible capacity.
73. kartīte
Jautājums
What must every binary-search iteration do to guarantee termination?
Atbilde
Strictly shrink the candidate interval while preserving the boundary invariant. Mixing inclusive and exclusive update rules can leave the same interval unchanged.
74. kartīte
Jautājums
For the longest subarray with a specified sum, which occurrence of each prefix sum should you retain?
Atbilde
The earliest index. For a later endpoint, it gives the longest matching span; overwriting it with a later occurrence can shorten the answer.
75. kartīte
Jautājums
What runtime should you report for binary search with a nonconstant feasibility check?
Atbilde
O(C log R), where C is one check's cost and R is the number of discrete candidates. Include any preprocessing separately.
76. kartīte
Jautājums
How can prefix sums turn a longest balanced binary subarray into an equal-prefix problem?
Atbilde
Map one symbol to +1 and the other to −1. Equal prefix sums enclose a zero-sum range with equal counts of the two symbols.
77. kartīte
Jautājums
What is upper bound in a sorted array?
Atbilde
The first position whose value is strictly greater than the target, or n if none exists. Lower bound instead finds the first value at least the target.
78. kartīte
Jautājums
Why must a prefix-sum counting algorithm query before recording the current prefix?
Atbilde
Recording first can count the empty subarray ending at the current boundary, especially for target zero. Query only earlier prefixes for nonempty ranges.
79. kartīte
Jautājums
How do you safely compute a midpoint in a fixed-width integer search?
Atbilde
Use lo + (hi − lo) / 2 with integer division when the nonnegative difference fits the type. Choose bounds or a wider type that also keep the subtraction safe.
80. kartīte
Jautājums
Why can duplicate values degrade searching a rotated sorted array to O(n)?
Atbilde
Equal endpoints and midpoint can hide which side is sorted. Some cases permit discarding only one boundary element at a time.
81. kartīte
Jautājums
What preprocessing usually simplifies merging overlapping intervals?
Atbilde
Sort by start coordinate. Keep the current merged interval and either extend its end or emit it when the next interval starts beyond it.
82. kartīte
Jautājums
Which data structure matches nested bracket validation?
Atbilde
A stack of unmatched opening brackets. Each closing bracket must match the most recent unmatched opener, and the stack must be empty at the end.
83. kartīte
Jautājums
A problem asks for each element's next greater element. Which pattern is promising?
Atbilde
A monotonic stack of unresolved positions. A new larger value resolves the smaller pending values it overtakes.
84. kartīte
Jautājums
Why must interval endpoint conventions be explicit?
Atbilde
Touching endpoints overlap for closed intervals, but adjacent half-open intervals do not. The convention changes merge tests and event ordering.
85. kartīte
Jautājums
How can a sweep line find the maximum number of simultaneous intervals?
Atbilde
Turn starts and ends into signed events, sort by coordinate, and track the running active count. Handle same-coordinate ties according to the endpoint convention.
86. kartīte
Jautājums
Why is one pass after sorting enough to merge intervals?
Atbilde
No later interval starts earlier than the next one being inspected. Once that start is beyond the current end, future intervals cannot bridge the gap.
87. kartīte
Jautājums
What information should a stack store for next-greater distances?
Atbilde
Indices, so the distance is currentIndex − previousIndex. Values alone do not identify positions or distinguish repeated occurrences.
88. kartīte
Jautājums
Why is counting opening and closing brackets insufficient to validate their sequence?
Atbilde
Counts ignore order and nesting. A closing bracket may appear before its opener, or bracket types may cross despite balanced totals.
89. kartīte
Jautājums
For half-open intervals [start, end), how should equal-time starts and ends affect room counts?
Atbilde
Process ends before starts, or aggregate their net change before evaluating the active count for the next segment. A room freed at time t can be reused at t.
90. kartīte
Jautājums
Why is a monotonic-stack algorithm often O(n) even though one step can pop many items?
Atbilde
Each item is pushed once and popped at most once. Summed across the scan, stack operations are linear.
91. kartīte
Jautājums
How can a stack help simplify an absolute filesystem path lexically?
Atbilde
Process components: ignore empty components and '.', pop for '..' when possible, and push ordinary names. This lexical result does not resolve symbolic links.
92. kartīte
Jautājums
How can a monotonic deque find each sliding-window maximum?
Atbilde
Keep candidate indices in decreasing value order. Remove expired indices from the front and dominated values from the back; the front gives the maximum.
93. kartīte
Jautājums
What mistake can lose coverage when merging an interval contained inside the current one?
Atbilde
Replacing the current end with the new end. Use the larger end so a nested interval cannot shrink the merged coverage.
94. kartīte
Jautājums
For a strictly next-greater query, what should happen to an equal-valued stack entry?
Atbilde
Do not resolve it with the equal value. With a decreasing stack of unresolved indices, pop only when the new value is strictly greater.
95. kartīte
Jautājums
What event allows a monotonic stack to finalize a rectangle in a histogram?
Atbilde
A shorter bar supplies a right limit for taller bars being popped. A popped bar's candidate span starts after the new stack top, or at index 0 if the stack is empty. Handle equal heights consistently.
96. kartīte
Jautājums
What comparison detects overlap between two nonempty half-open intervals?
Atbilde
max(start1, start2) < min(end1, end2). A strict comparison excludes intervals that only touch.
97. kartīte
Jautājums
How does a stack support evaluating a postfix arithmetic expression?
Atbilde
Push operands; for an operator, pop its right operand and then its left operand, compute, and push the result. Preserve order for subtraction and division.
98. kartīte
Jautājums
Why can a newer value dominate an older value in a sliding-window maximum deque?
Atbilde
If the newer value is at least as large, it expires no earlier and is never worse as a future maximum. The older candidate can be removed.
99. kartīte
Jautājums
How can you merge two already sorted lists of disjoint intervals to find their intersections?
Atbilde
Compare one interval from each list, emit any overlap, then advance the one with the earlier end. Total time is O(m + n).
100. kartīte
Jautājums
Why must a histogram stack algorithm handle bars still pending after the scan?
Atbilde
Those bars may extend to the array's end and contain the largest rectangle. Flush them using the end boundary or a suitable sentinel.
101. kartīte
Jautājums
What must you save before reversing a singly linked list node's next pointer?
Atbilde
Its original next node. Otherwise rewiring can lose access to the remaining list.
102. kartīte
Jautājums
Why does a dummy head simplify linked-list insertion and deletion?
Atbilde
It supplies a predecessor even when the real head changes. The same pointer update can handle both the first node and interior nodes.
103. kartīte
Jautājums
How do fast and slow pointers detect a cycle in a singly linked list?
Atbilde
Advance one pointer one step and the other two. A meeting implies a cycle; reaching null with the fast pointer means the list terminates.
104. kartīte
Jautājums
What does a recursive binary-tree traversal use for auxiliary space?
Atbilde
O(h) call-stack space, where h is tree height. This is O(log n) for a balanced tree but O(n) for a chain.
105. kartīte
Jautājums
During iterative list reversal, what do prev and current represent?
Atbilde
prev heads the reversed processed prefix; current heads the unprocessed suffix. Rewire one node while preserving access to the suffix.
210 kartīšu
Coding Interview Patterns Flashcards: Signals, Invariants & Complexity
Mācies šo kavu bez maksasAtvērsies Nibomo, lai vari sākt mācīties.
106. kartīte
Jautājums
How can you remove the nth node from the end of a list in one pass?
Atbilde
Start lead at the head and lag at a dummy head. Advance lead n nodes, then move both until lead is null; remove lag.next. Reject invalid n according to the input contract.
107. kartīte
Jautājums
Which tree traversal naturally computes a value that depends on both children's results?
Atbilde
Postorder. Process left and right subtrees before combining their results at the parent.
108. kartīte
Jautājums
How can you locate a cycle's entry after Floyd's two-speed pointers meet?
Atbilde
Reset one pointer to the head and move both one step at a time. Their next meeting is the entry; this follows from the distances modulo the cycle length.
109. kartīte
Jautājums
What is the difference between tree depth and tree height?
Atbilde
Depth measures distance from the root to a node; height measures the longest downward distance to a leaf. State whether distances count edges or nodes.
110. kartīte
Jautājums
How can you merge two sorted linked lists using O(1) auxiliary node storage?
Atbilde
Relink the smaller current node onto the result tail, advancing that list. Attach the remaining suffix when one list ends; existing nodes are reused.
111. kartīte
Jautājums
When is breadth-first traversal more natural than depth-first traversal on a tree?
Atbilde
When results are grouped by depth or you need the nearest qualifying node by edge count. A queue processes one distance layer before the next.
112. kartīte
Jautājums
Why must linked-list intersection compare node identity rather than node value?
Atbilde
Intersection means sharing the same node object and suffix. Separate nodes can hold equal values without the lists intersecting.
113. kartīte
Jautājums
Why is checking only immediate children insufficient to validate a binary search tree?
Atbilde
A descendant can satisfy its parent yet violate an ancestor's constraint. Carry inherited lower and upper bounds, with an explicit duplicate policy.
114. kartīte
Jautājums
What is the lowest common ancestor of two nodes in a rooted tree?
Atbilde
The deepest node that is an ancestor of both, allowing a node to be its own ancestor.
115. kartīte
Jautājums
What property makes inorder traversal useful in a binary search tree?
Atbilde
It visits keys in sorted order under the tree's duplicate policy. In a strict BST, each visited key must be greater than the previous one.
116. kartīte
Jautājums
Why must maximum tree-path sum separate its returned value from its global candidate?
Atbilde
The parent can extend only one downward branch. A complete path considered at the current node may join both children, but that fork cannot be extended upward.
117. kartīte
Jautājums
How can two pointers find the intersection of two acyclic singly linked lists without measuring lengths?
Atbilde
After reaching a list's end, switch that pointer to the other head. Each traverses both lengths, so they meet at the shared node or at null.
118. kartīte
Jautājums
What extra information makes preorder serialization unambiguous for an arbitrary binary tree?
Atbilde
Explicit null-child markers or another equivalent shape encoding. Values in preorder alone do not determine the structure.
119. kartīte
Jautājums
Why can repeated subtree-height calculations make a tree-balance check O(n²)?
Atbilde
The same descendants may be scanned from many ancestors. Return height and balance together in one postorder traversal to visit each node once.
120. kartīte
Jautājums
How does BST ordering guide a lowest-common-ancestor search for two existing distinct keys?
Atbilde
Move left if both keys are smaller and right if both are larger. The first split, or a node matching one key, is their lowest common ancestor.
121. kartīte
Jautājums
What runtime does a search in an ordinary unbalanced BST guarantee?
Atbilde
O(h), where h is its height, and O(n) in the worst case. Logarithmic search requires a balance guarantee or a stated expected-shape assumption.
122. kartīte
Jautājums
When computing a root-to-leaf path sum, why is reaching a null child insufficient for success?
Atbilde
A valid endpoint must be a leaf with no children. A missing child beside an existing child does not finish a root-to-leaf path.
123. kartīte
Jautājums
What does a min-heap guarantee about its root and children?
Atbilde
The root is a minimum element, and each parent is no larger than its children. The whole array representation is not sorted.
124. kartīte
Jautājums
A stream needs the k largest values seen so far. Which heap should you maintain?
Atbilde
A min-heap of at most k values. Its root is the smallest retained value, so a larger arrival can replace it.
125. kartīte
Jautājums
What shared structure does a trie store?
Atbilde
Prefixes of keys. Following one edge per symbol reaches a key's prefix node, while a terminal marker distinguishes a complete stored key.
126. kartīte
Jautājums
What are the usual binary-heap costs for peek, insertion, and root removal?
Atbilde
Peek is O(1); insertion and root removal are O(log n). Moving a changed element along one root-to-leaf path restores heap order.
127. kartīte
Jautājums
How can a heap merge k sorted input streams?
Atbilde
Keep each nonempty stream's next element in a min-heap. Emit the minimum and replace it with that stream's next item. With k streams and N total elements, O(k + N log k) time includes initialization for k ≥ 2.
128. kartīte
Jautājums
Why is bottom-up heap construction O(n), not O(n log n)?
Atbilde
Most nodes are near the leaves and can move only a short distance. Summing each node's possible sift-down work across all heights is linear.
129. kartīte
Jautājums
How do two heaps support a running median?
Atbilde
Keep the lower half in a max-heap and the upper half in a min-heap, with sizes differing by at most one and every lower value no greater than every upper value.
130. kartīte
Jautājums
What is a trie's lookup cost for a key of length L?
Atbilde
O(L) when each child transition is O(1). Child maps or ordered child containers can change that transition cost; space depends on stored prefixes and representation.
131. kartīte
Jautājums
Why does a trie node need a terminal marker even if it has children?
Atbilde
A stored key can be a prefix of another key. The marker distinguishes a complete word from a prefix that merely leads to longer words.
132. kartīte
Jautājums
When does sorting make more sense than a top-k heap?
Atbilde
When you need the entire sorted order or k is close to n and a full sort is acceptable. A heap's advantage is strongest when only a small retained subset is needed.
133. kartīte
Jautājums
Why does a priority queue not by itself support efficient arbitrary deletion?
Atbilde
The heap efficiently exposes only its root. Removing another item needs its position, an indexed-heap design, or a lazy-deletion scheme with cleanup.
134. kartīte
Jautājums
What output cost remains after a trie reaches a requested prefix?
Atbilde
Enumerating matching completions still costs time proportional to the visited subtree and emitted text. Prefix lookup does not make all autocomplete results free.
135. kartīte
Jautājums
How can a priority queue break tied priorities without comparing the payloads?
Atbilde
Attach a unique increasing sequence number and compare priority first, then sequence number. Equal-priority items can then leave in insertion order without requiring an order on their payloads.
136. kartīte
Jautājums
Why can a trie use more memory than a hash set of complete strings?
Atbilde
Nodes and child containers have overhead, especially for sparse branches. Shared prefixes save repeated symbols but do not guarantee a smaller representation.
137. kartīte
Jautājums
What should graph modeling identify before choosing a traversal?
Atbilde
The states as vertices and legal transitions as edges, including direction and cost. A grid cell, word, or puzzle configuration can be a vertex.
138. kartīte
Jautājums
When does ordinary BFS find a shortest path?
Atbilde
When every edge has the same nonnegative cost, including the unweighted case. Processing vertices by distance layer makes first discovery a shortest-edge-count path.
139. kartīte
Jautājums
What is the space cost of an adjacency list compared with an adjacency matrix?
Atbilde
A list uses O(V + E) space; a matrix uses O(V²). A matrix gives constant-time edge lookup, while lists efficiently enumerate actual neighbors.
140. kartīte
Jautājums
Which pattern finds all vertices reachable from a start vertex?
Atbilde
DFS or BFS with a visited set. Each reachable vertex and edge is processed a bounded number of times with adjacency lists.
141. kartīte
Jautājums
What role does a parent map play in shortest-path traversal?
Atbilde
It records the predecessor used to reach each state. After reaching the target, follow parents backward and reverse the sequence to recover a path.
142. kartīte
Jautājums
Why should BFS mark a vertex visited when enqueuing it?
Atbilde
To prevent several parents from adding it before its first removal. First enqueue already fixes its distance in an unweighted graph.
143. kartīte
Jautājums
When is Dijkstra's algorithm appropriate?
Atbilde
For shortest paths with nonnegative edge weights. Its greedy finalization relies on no later path reducing a settled distance through a negative edge.
144. kartīte
Jautājums
How can a grid traversal avoid confusing physical cells with full search states?
Atbilde
Include all information that changes future moves in the visited key, such as remaining obstacle removals or collected keys. Position alone may merge different states.
145. kartīte
Jautājums
How do you detect a directed cycle with DFS?
Atbilde
Track unvisited, active, and finished vertices. An edge to an active vertex closes a cycle on the current recursion path.
146. kartīte
Jautājums
Why can DFS with a visited set fail to find a shortest unweighted path?
Atbilde
Its first discovered route may follow a deep detour. DFS reachability order is not distance order; BFS provides that guarantee.
147. kartīte
Jautājums
What does a topological ordering guarantee?
Atbilde
For every directed edge u → v, u appears before v. Such an ordering exists exactly when the directed graph is acyclic.
148. kartīte
Jautājums
Why should stale priority-queue entries be skipped in a common Dijkstra implementation?
Atbilde
A vertex can receive a better distance after an older entry was pushed. Skip an entry whose stored distance differs from the current best distance.
149. kartīte
Jautājums
For an undirected simple graph, why does DFS ignore the edge back to its parent when detecting cycles?
Atbilde
That edge is the same tree edge traversed in reverse, not a new cycle. A different already-visited neighbor indicates a cycle.
150. kartīte
Jautājums
What does union-find answer efficiently?
Atbilde
Whether elements belong to the same connected component while components are merged. It does not store the actual connecting paths.
151. kartīte
Jautājums
How does Kahn's algorithm build a topological ordering?
Atbilde
Enqueue all zero-indegree vertices, repeatedly remove one, and decrement its outgoing neighbors' indegrees. Enqueue each neighbor when its indegree becomes zero.
152. kartīte
Jautājums
Which shortest-path algorithm handles edges weighted only 0 or 1 without a heap?
Atbilde
0–1 BFS with a deque. Push a relaxed zero-cost neighbor to the front and a one-cost neighbor to the back, preserving distance order.
153. kartīte
Jautājums
Why is a boolean visited flag usually wrong for Dijkstra at first enqueue?
Atbilde
The first tentative distance need not be the shortest. Allow improvements; a vertex becomes settled when its smallest current distance is removed from the queue.
154. kartīte
Jautājums
How do path compression and union by size or rank affect union-find complexity?
Atbilde
Together they give O(α(n)) amortized time per operation, where α is the inverse Ackermann function. The bound is effectively tiny for practical input sizes.
155. kartīte
Jautājums
What does processing fewer than V vertices in Kahn's algorithm reveal?
Atbilde
A directed cycle remains. No vertex in the cyclic remainder can reach indegree zero after all removable dependencies are processed.
156. kartīte
Jautājums
How can BFS compute distance from every grid cell to the nearest source?
Atbilde
Initialize the queue with all sources at distance zero. This multi-source BFS expands the nearest-source distance layers together.
157. kartīte
Jautājums
Why can a topological ordering be nonunique?
Atbilde
Several vertices may currently have no remaining prerequisites. Choosing them in different orders can produce different valid orderings.
158. kartīte
Jautājums
What happens when union-find receives an edge whose endpoints already share a representative?
Atbilde
The edge connects vertices already in one component. In incremental construction of an undirected forest, adding it creates a cycle.
159. kartīte
Jautājums
Which algorithm can handle negative edge weights and detect a reachable negative cycle?
Atbilde
Bellman–Ford. Repeatedly relax all edges; an improvement after V − 1 full rounds indicates a negative cycle reachable from the source.
160. kartīte
Jautājums
Why does traversal need an outer loop to count every connected component of an undirected graph?
Atbilde
One traversal reaches only one component. Start another traversal from each still-unvisited vertex and increment the component count.
161. kartīte
Jautājums
How can topological order simplify shortest paths in a weighted DAG?
Atbilde
Relax each vertex's outgoing edges in topological order. Every predecessor is processed first, so negative weights are allowed and total time is O(V + E).
162. kartīte
Jautājums
When should you use BFS or DFS instead of union-find for connectivity?
Atbilde
When the graph is static and you need traversal details such as paths or component members. Union-find is especially useful for repeated incremental edge additions and connectivity queries.
163. kartīte
Jautājums
What is the difference between a minimum spanning tree and a shortest-path tree?
Atbilde
A minimum spanning tree minimizes total connecting edge weight. A shortest-path tree preserves shortest routes from a chosen source; neither objective implies the other.
164. kartīte
Jautājums
Why can stopping at the first meeting be unsafe in bidirectional BFS with arbitrary node-by-node expansion?
Atbilde
A first meeting under an arbitrary expansion order may not minimize the combined distances. Use a layer-based stopping rule that accounts for both search depths.
165. kartīte
Jautājums
Which signal suggests backtracking rather than a single greedy choice?
Atbilde
The task asks for all valid arrangements, or choices must be tried and undone because no safe local choice is known. Build a partial candidate and explore legal extensions.
166. kartīte
Jautājums
What belongs in a backtracking state?
Atbilde
Enough information to determine legal next choices and recognize completion, such as the current position, chosen items, and remaining constraints.
167. kartīte
Jautājums
What makes a pruning condition safe?
Atbilde
It proves that no completion of the current partial state can satisfy the goal or improve the required objective. A guess about likely failure is insufficient.
168. kartīte
Jautājums
How do combinations differ from permutations during generation?
Atbilde
Combinations ignore order, so restrict future choices to later positions. Permutations care about order, so track which positions are already used.
169. kartīte
Jautājums
What should be true after a backtracking recursive call returns?
Atbilde
The caller's mutable search state is restored exactly to its pre-choice state. Undo additions and constraint updates before trying a sibling choice.
170. kartīte
Jautājums
When generating unique subsets from sorted values, how do you skip duplicates safely?
Atbilde
At one recursion depth, skip a value equal to the previous sibling candidate. Still allow equal values at deeper levels when the input provides multiple copies.
171. kartīte
Jautājums
Why can backtracking output alone require exponential time?
Atbilde
A set with n distinct elements has 2^n subsets. Explicitly listing all subsets cannot be polynomial in n; copying their contents adds further cost.
172. kartīte
Jautājums
Why should a completed mutable candidate usually be copied before saving it?
Atbilde
Later backtracking steps will modify the working candidate. Saving only a reference can make all recorded answers reflect subsequent changes.
173. kartīte
Jautājums
What is the main risk of memoizing backtracking solely by the current index?
Atbilde
Different histories can leave different remaining choices or constraints. The memo key must include every part of the state that affects future results.
174. kartīte
Jautājums
For selecting the most nonoverlapping intervals, which greedy choice is justified?
Atbilde
Choose the available interval with the earliest finishing time, then continue with compatible intervals. This leaves at least as much room for the remaining selections.
175. kartīte
Jautājums
What is the difference between greedy choice and dynamic programming?
Atbilde
Greedy commits to a choice proven safe without exploring all alternatives. DP evaluates and combines subproblem alternatives when that local commitment is not justified.
176. kartīte
Jautājums
Why does choosing the largest coin repeatedly fail for some coin systems?
Atbilde
The locally largest coin can leave an expensive remainder. With denominations 1, 3, 4 and amount 6, greedy uses 4 + 1 + 1, while 3 + 3 uses fewer coins.
177. kartīte
Jautājums
How does a farthest-reachable frontier solve reachability in a nonnegative jump-length array?
Atbilde
Scan positions no farther than the current frontier and extend it with each reachable index plus its jump length. If the next position lies beyond the frontier, progress is impossible.
178. kartīte
Jautājums
Why does choosing the shortest interval not always maximize the number of nonoverlapping intervals?
Atbilde
A short interval can cross the boundary between two compatible intervals and block both. Duration alone does not measure the future scheduling space it consumes.
179. kartīte
Jautājums
What must be proved before pruning a combination-sum branch because its sum exceeds the target?
Atbilde
Remaining choices cannot reduce the sum. The pruning is safe for nonnegative additions under the stated goal, but negative numbers can make it invalid.
180. kartīte
Jautājums
How does branch and bound differ from ordinary feasibility pruning?
Atbilde
It uses a bound on the best objective reachable from a partial state. Prune only when that bound cannot beat the best complete answer already found.
181. kartīte
Jautājums
What question distinguishes a greedy proof from evidence that a heuristic often works?
Atbilde
Can every discarded alternative be ruled out for all valid inputs? Examples and benchmarks support a heuristic, but do not establish the safe-choice property.
182. kartīte
Jautājums
Why is earliest-finish interval scheduling insufficient when intervals have different rewards?
Atbilde
Maximizing count and maximizing reward are different objectives. A single high-reward interval can beat several low-reward intervals, so weighted scheduling needs more information.
183. kartīte
Jautājums
Which combination of properties makes dynamic programming promising?
Atbilde
Repeated subproblems and a recurrence that combines their results. Define a state whose answer is independent of the path used to reach it.
184. kartīte
Jautājums
What should a DP state definition say before you write a recurrence?
Atbilde
Exactly what one table entry means, including its input boundary and any remaining resource or constraint. Ambiguous states lead to mismatched transitions.
185. kartīte
Jautājums
How do top-down memoization and bottom-up tabulation differ?
Atbilde
Memoization computes states on demand through calls and caches them. Tabulation processes states in an explicit dependency order, often avoiding recursion overhead.
186. kartīte
Jautājums
What determines the runtime of a DP with a finite state table?
Atbilde
The number of states actually evaluated times the work per state, plus preprocessing and output reconstruction. Count transitions rather than just table dimensions.
187. kartīte
Jautājums
Why are base cases part of a DP's meaning rather than convenient initial values?
Atbilde
They encode valid empty or smallest subproblems. A wrong base value can invent impossible solutions or remove legitimate ones from every later transition.
188. kartīte
Jautājums
For 0/1 knapsack compressed to one capacity array, why iterate capacities downward?
Atbilde
Each item must be used at most once. Descending order reads the previous item's state instead of reusing an update made for the current item.
189. kartīte
Jautājums
When can a DP table be compressed to a few rows or variables?
Atbilde
When future states depend only on a bounded slice of earlier states. Keep those dependencies until their last use; reconstruction may need additional storage.
190. kartīte
Jautājums
What recurrence models choosing nonadjacent values for maximum sum?
Atbilde
At each position, compare skipping it with taking it plus the best result before its neighbor. The base cases must specify whether choosing nothing is allowed.
191. kartīte
Jautājums
What DP state counts paths through a blocked grid when moves are only right or down?
Atbilde
The number of ways to reach each cell from above or from the left. Blocked cells contribute zero; initialize an unblocked starting cell to one.
192. kartīte
Jautājums
For unbounded knapsack, why can capacities run upward within an item's pass?
Atbilde
Reusing the current item's updated smaller-capacity result is allowed. Ascending order lets that item contribute more than once.
193. kartīte
Jautājums
How can loop order change coin-change counting from combinations to ordered sequences?
Atbilde
Processing coin types outside amounts builds combinations without ordering them. Processing amounts outside all coin choices counts different last-coin sequences separately.
194. kartīte
Jautājums
What is the key distinction between longest common subsequence and longest common substring?
Atbilde
A subsequence may skip characters; a substring must stay contiguous. Their DP transitions differ because a substring match cannot carry through a mismatch.
195. kartīte
Jautājums
Why is O(nW) knapsack called pseudopolynomial?
Atbilde
It is polynomial in the numeric capacity W, but W can be exponential in the number of bits used to encode it. It is not polynomial in input bit length.
196. kartīte
Jautājums
For longest increasing subsequence, what does tails[length − 1] represent in the O(n log n) method?
Atbilde
The smallest possible final value of an increasing subsequence of that length among processed values. The tails array itself need not be one actual subsequence.
197. kartīte
Jautājums
Why do counting and minimization DPs use different unreachable-state values?
Atbilde
A count uses zero ways. A minimization state needs an explicit unreachable marker or infinity so an impossible predecessor cannot look like a cheap solution.
198. kartīte
Jautājums
What state supports edit distance between two strings?
Atbilde
The minimum edits needed to transform one prefix into the other. Transitions account for insertion, deletion, and replacement or a matching final character.
199. kartīte
Jautājums
How can a DP recover one chosen solution instead of only its score?
Atbilde
Store predecessor or choice information, or recompute choices from the full table. Walk backward from the final state to reconstruct the selected decisions.
200. kartīte
Jautājums
Why must an LIS implementation choose its binary-search boundary according to strictness?
Atbilde
For a strictly increasing subsequence, replace the first tail at least equal to the value. A nondecreasing subsequence instead uses the first strictly greater tail.
201. kartīte
Jautājums
What operation tests whether bit i of a nonnegative integer mask is set?
Atbilde
Check whether mask AND (1 shifted left by i) is nonzero. Ensure i is inside the integer representation's supported bit range.
202. kartīte
Jautājums
Why does XOR recover a unique value when every other value occurs exactly twice?
Atbilde
Equal values cancel because x XOR x = 0, and XOR is associative and commutative. XORing all values leaves the single unpaired value.
203. kartīte
Jautājums
What does x AND (x − 1) do for a positive integer x?
Atbilde
It clears x's lowest set bit. Repeating it counts set bits in time proportional to the number of set bits.
204. kartīte
Jautājums
When does a bitmask make a useful DP state?
Atbilde
When a small set of items is either included or excluded and future choices depend on that subset. n items give 2^n possible masks, so n must be small.
205. kartīte
Jautājums
How do you set a bit and clear a bit without changing the others?
Atbilde
Set bit i with mask OR (1 shifted left by i). Clear it with mask AND the bitwise complement of that single-bit mask, respecting the chosen word width.
206. kartīte
Jautājums
What makes a memoized recurrence invalid when it depends on mutable global state omitted from the key?
Atbilde
The same key can have different answers under different global conditions. Include the relevant state in the key or remove that dependency.
207. kartīte
Jautājums
What condition recognizes a power of two among integers?
Atbilde
x > 0 and x AND (x − 1) = 0. The positivity check excludes zero, which also makes the bitwise expression zero.
208. kartīte
Jautājums
Why does bitwise complement need a width convention in language-agnostic reasoning?
Atbilde
Complement flips all bits in the representation. Fixed-width and arbitrary-precision signed integers can produce different-looking values; mask to the intended width when necessary.
209. kartīte
Jautājums
How can two unique values be recovered when every other value occurs twice?
Atbilde
XOR all values, choose a set bit in that nonzero result, and partition by that bit. XOR within each group; the two unique values fall into different groups.
210. kartīte
Jautājums
Why is memoization alone insufficient to handle cyclic state dependencies?
Atbilde
A call may revisit an unfinished state before any value is cached. Use cycle handling or a problem-specific iterative method; ordinary DAG-style DP assumes an acyclic dependency order.
210 kartīšu
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