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