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