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.
حول هذه الرزمة
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.
بطاقات هذه الرزمة
البطاقة ١
السؤال
Which input constraints should you clarify before choosing an interview algorithm?
الإجابة
Input size, value range, ordering, duplicates, allowed mutations, and the exact output. These determine which operations are affordable and which assumptions are valid.
البطاقة ٢
السؤال
What does a loop invariant describe?
الإجابة
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.
البطاقة ٣
السؤال
When analyzing nested loops, why can multiplying their written bounds overestimate runtime?
الإجابة
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.
البطاقة ٤
السؤال
What is the difference between auxiliary space and total space?
الإجابة
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.
البطاقة ٥
السؤال
What does amortized O(1) mean for an operation sequence?
الإجابة
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.
البطاقة ٦
السؤال
How does a counterexample help evaluate a proposed greedy rule?
الإجابة
One valid input where the rule fails disproves it. Try small cases that force a locally attractive choice to block a better later choice.
البطاقة ٧
السؤال
Why should an algorithm's correctness argument address termination separately?
الإجابة
Preserving the right property is not enough if the loop never stops. Identify a bounded measure that moves strictly toward termination.
البطاقة ٨
السؤال
What runtime lower bound follows from returning k separate results?
الإجابة
At least Ω(k) time to emit them, or more if each result has multiple elements. Include output size when analyzing enumeration algorithms.
البطاقة ٩
السؤال
What should you say when quoting expected O(1) hash-table lookup?
الإجابة
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.
البطاقة ١٠
السؤال
Which edge cases best expose index and boundary errors?
الإجابة
Empty input, one element, all equal elements, and answers at either end. Also check the smallest input that enters each branch.
البطاقة ١١
السؤال
Why can sorting be an invalid optimization even when it reduces later search work?
الإجابة
Sorting may destroy required order or original indices. Preserve the needed information or choose an approach that respects the input contract.
البطاقة ١٢
السؤال
What does an exchange argument establish in a greedy proof?
الإجابة
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.
البطاقة ١٣
السؤال
Why can recursion use O(n) space even without an explicit collection?
الإجابة
Each active call occupies a stack frame. A chain of n calls can therefore need O(n) auxiliary space.
البطاقة ١٤
السؤال
What evidence should accompany a faster solution after presenting brute force?
الإجابة
Name the repeated work or discarded search space, explain why the shortcut is safe, and give the resulting time and space bounds.
البطاقة ١٥
السؤال
What makes an array useful when a problem repeatedly accesses positions by index?
الإجابة
Constant-time indexed access in the usual RAM model. Inserting or removing near the front can still require shifting O(n) elements.
البطاقة ١٦
السؤال
What should 'one character' mean before solving a string problem?
الإجابة
Clarify whether the unit is a byte, code unit, Unicode code point, or user-perceived character. Indexing and length depend on that choice.
البطاقة ١٧
السؤال
An unsorted array needs a duplicate-existence check. Which structure fits?
الإجابة
A hash set of values seen so far. Stop when a value is already present; expected O(n) time and O(n) space.
البطاقة ١٨
السؤال
For two-sum on an unsorted array, what should a hash map store?
الإجابة
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.
البطاقة ١٩
السؤال
When does a frequency array beat a hash map for counting?
الإجابة
When keys come from a small known integer or character range. Direct indexing gives predictable access with space proportional to that range.
البطاقة ٢٠
السؤال
Why is repeated concatenation risky when constructing a long immutable string?
الإجابة
Each append may copy the existing prefix, producing quadratic total work. Collect pieces and join them, or use an appropriate mutable builder.
البطاقة ٢١
السؤال
How can you group anagrams without comparing every pair of words?
الإجابة
Map a canonical character signature to a group. Sorted characters work; a frequency tuple works when the alphabet and character rules are fixed.
البطاقة ٢٢
السؤال
What information does a set lose compared with a frequency map?
الإجابة
Multiplicity. A set can answer whether a value exists but cannot distinguish one occurrence from several.
البطاقة ٢٣
السؤال
How can a hash set support finding the longest consecutive integer run in expected O(n) time?
الإجابة
Start scanning a run only at values whose predecessor is absent. Each distinct value then belongs to one forward scan; iterate distinct values.
البطاقة ٢٤
السؤال
Why can a mutable object be a dangerous hash-map key?
الإجابة
Changing fields used by its hash or equality can make the stored entry unreachable by ordinary lookup. Use immutable keys or stable key values.
البطاقة ٢٥
السؤال
An array contains only integers from 0 through k. When is counting sort attractive?
الإجابة
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.
البطاقة ٢٦
السؤال
How can a single scan find both the minimum value and its earliest index?
الإجابة
Keep the current minimum and index; update only on a strictly smaller value. Updating on equality would select a later occurrence.
البطاقة ٢٧
السؤال
How do you compare two strings as multisets of characters?
الإجابة
Compare character counts under the same character interpretation. Order does not matter, but every character's multiplicity does.
البطاقة ٢٨
السؤال
Why does a hash collision not imply that two keys are equal?
الإجابة
A hash compresses many possible keys into fewer codes. A correct table also checks key equality when resolving collisions.
البطاقة ٢٩
السؤال
When is sorting a useful preprocessing step for detecting duplicate values?
الإجابة
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.
البطاقة ٣٠
السؤال
What is the key distinction between a subarray and a subsequence?
الإجابة
A subarray is contiguous. A subsequence preserves relative order but may skip positions. Sliding-window methods usually depend on contiguity.
البطاقة ٣١
السؤال
For an unsorted two-sum query, how do hashing and sorting trade off?
الإجابة
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.
البطاقة ٣٢
السؤال
How can a frequency map detect whether any permutation of a string can be a palindrome?
الإجابة
Count odd frequencies. At most one character may have an odd count; all other occurrences must form mirrored pairs.
البطاقة ٣٣
السؤال
Why must compound hash keys encode boundaries unambiguously?
الإجابة
Naive concatenation can merge different tuples into the same key, such as (1, 23) and (12, 3). Use tuples or a length-aware encoding.
البطاقة ٣٤
السؤال
What does coordinate compression preserve about numeric values?
الإجابة
Their relative order and equality, by replacing distinct sorted values with ranks. It does not preserve numeric distances or sums.
البطاقة ٣٥
السؤال
How can you compute products except self without division?
الإجابة
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.
البطاقة ٣٦
السؤال
Why can a count of matching pairs overflow even when every input value fits in an integer?
الإجابة
The number of matching pairs can grow quadratically with the input length. Size the result type for the count, not just the input values.
البطاقة ٣٧
السؤال
A sorted array needs a pair with a target sum. Which search pattern fits?
الإجابة
Opposite-end two pointers. Compare the endpoint sum with the target and move the endpoint that can move the sum in the needed direction.
البطاقة ٣٨
السؤال
What invariant supports in-place removal of unwanted array values with read and write pointers?
الإجابة
The prefix before write contains exactly the retained values from the processed input, in order. Read scans every input position once.
البطاقة ٣٩
السؤال
How can two pointers check a palindrome without constructing a reversed string?
الإجابة
Compare matching elements from opposite ends and move inward. Any mismatch rejects it; the pointers meeting or crossing completes the check.
البطاقة ٤٠
السؤال
When does a fixed-size sliding window apply?
الإجابة
When every candidate is a contiguous block of the same length and its summary can be updated as one element enters and one leaves.
البطاقة ٤١
السؤال
What invariant should a longest-window algorithm restore after adding a new rightmost element?
الإجابة
The current window satisfies the required constraint. Move the left boundary and update state until validity returns, then consider its length.
البطاقة ٤٢
السؤال
Why is moving the left pointer safe when a sorted-array endpoint sum is too small?
الإجابة
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.
البطاقة ٤٣
السؤال
How does a three-way partition maintain separate regions?
الإجابة
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.
البطاقة ٤٤
السؤال
How do you update the sum when a fixed-size window moves one position?
الإجابة
Subtract the outgoing value and add the incoming value. After initializing the first window, all moves together take O(n) time.
البطاقة ٤٥
السؤال
Why can a variable sliding window run in O(n) despite a nested shrink loop?
الإجابة
Each boundary advances at most n times. With constant-time state updates, the total number of additions and removals is linear.
البطاقة ٤٦
السؤال
For the longest substring without repeated characters, what window state is useful?
الإجابة
Character counts or last-seen positions. Move the left boundary past the conflicting occurrence while ensuring it never moves backward.
البطاقة ٤٧
السؤال
Why does opposite-end target-sum search fail on a generally unsorted array?
الإجابة
Moving an endpoint no longer changes the sum predictably. The algorithm can discard a valid pair because the order-based elimination proof is missing.
البطاقة ٤٨
السؤال
A positive-number array needs the shortest nonempty subarray with sum at least a positive T. When should the left boundary move?
الإجابة
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.
البطاقة ٤٩
السؤال
For windows with at most k distinct values, what must happen when an outgoing count becomes zero?
الإجابة
Remove that value from the active distinct set or decrement the distinct counter. A zero count must not still count as present.
البطاقة ٥٠
السؤال
What changes when a fixed-window length exceeds the input length?
الإجابة
There is no complete window. Return the contract's empty or missing-result value instead of treating a partial block as a valid candidate.
البطاقة ٥١
السؤال
How do you merge two sorted arrays with forward pointers?
الإجابة
Repeatedly take the smaller unconsumed element, then append the remaining suffix. Each element is consumed once, giving O(m + n) time.
البطاقة ٥٢
السؤال
Why must a minimum-cover substring track multiplicities of required characters?
الإجابة
A target can require the same character more than once. A set of required characters would mark an undersupplied window as complete.
البطاقة ٥٣
السؤال
How can counting subarrays with exactly k distinct values, for k ≥ 1, use an at-most helper?
الإجابة
Compute atMost(k) − atMost(k − 1). The helper counts all valid subarrays ending at each right boundary after restoring the distinct-value limit.
البطاقة ٥٤
السؤال
Why can a negative value break the usual shortest-sum sliding-window argument?
الإجابة
Removing it increases the sum, and adding one can decrease the sum. The monotonic relation between window size and sum no longer holds.
البطاقة ٥٥
السؤال
What does 'fast and slow pointers' mean when removing duplicates from a sorted array?
الإجابة
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.
البطاقة ٥٦
السؤال
What invariant prevents overwriting unread data during a backward merge into spare array capacity?
الإجابة
The suffix after the write pointer already contains the largest merged elements. Filling from the end leaves the remaining source elements unread and intact.
البطاقة ٥٧
السؤال
Why is 'find a contiguous range' alone insufficient to justify a variable sliding window?
الإجابة
You also need a safe boundary-movement rule. Check how adding and removing elements affect the condition; contiguity by itself gives no such guarantee.
البطاقة ٥٨
السؤال
After restoring an at-most window's validity, why are there right − left + 1 valid subarrays ending at right?
الإجابة
Every suffix starting between left and right is valid when removing elements cannot violate the constraint. Count those starts, including the one-element suffix.
البطاقة ٥٩
السؤال
How can you avoid duplicate value pairs in a sorted two-pointer enumeration?
الإجابة
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.
البطاقة ٦٠
السؤال
When does a character-frequency sliding window detect an anagram of a pattern?
الإجابة
When the window has the pattern's length and identical character counts. Maintain count differences or a mismatch counter as the window moves.
البطاقة ٦١
السؤال
What does a prefix-sum array P mean when P[0] = 0?
الإجابة
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.
البطاقة ٦٢
السؤال
When is binary search valid on a Boolean predicate over ordered candidates?
الإجابة
When the predicate changes at most once, such as false then true. The search uses that monotonic boundary to discard a whole interval.
البطاقة ٦٣
السؤال
Which workload favors a difference array?
الإجابة
Many range additions followed by final value reconstruction. Mark each range's start and end changes, then take one prefix sum.
البطاقة ٦٤
السؤال
In a lower-bound search over [lo, hi), what does hi initially equal for an n-element array?
الإجابة
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.
البطاقة ٦٥
السؤال
For a static array, how do prefix sums answer the half-open range [l, r)?
الإجابة
Return P[r] − P[l]. Building P takes O(n) time and space; each range-sum query then takes O(1).
البطاقة ٦٦
السؤال
How can prefix sums count subarrays whose sum equals k when negative values are allowed?
الإجابة
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.
البطاقة ٦٧
السؤال
Why is binary-searching an answer different from binary-searching an input array?
الإجابة
The candidates are possible result values. A feasibility check tells which side contains the boundary, even if the original input is unsorted.
البطاقة ٦٨
السؤال
How does a difference array encode an addition of v to [l, r)?
الإجابة
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.
البطاقة ٦٩
السؤال
For lower bound, how should equality with the target move the search boundary?
الإجابة
Move hi to mid. An equal element is a candidate, but an earlier equal or qualifying element may still exist.
البطاقة ٧٠
السؤال
Why initialize the prefix-frequency map with zero appearing once?
الإجابة
It represents the empty prefix before the array. This lets a subarray starting at index 0 contribute to the count.
البطاقة ٧١
السؤال
Why are plain prefix sums inconvenient for many interleaved point updates and range-sum queries?
الإجابة
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).
البطاقة ٧٢
السؤال
How can you binary-search the minimum capacity needed to finish ordered work within a deadline?
الإجابة
Define whether a capacity suffices, prove larger capacities remain feasible, bracket a feasible answer, and search for the first feasible capacity.
البطاقة ٧٣
السؤال
What must every binary-search iteration do to guarantee termination?
الإجابة
Strictly shrink the candidate interval while preserving the boundary invariant. Mixing inclusive and exclusive update rules can leave the same interval unchanged.
البطاقة ٧٤
السؤال
For the longest subarray with a specified sum, which occurrence of each prefix sum should you retain?
الإجابة
The earliest index. For a later endpoint, it gives the longest matching span; overwriting it with a later occurrence can shorten the answer.
البطاقة ٧٥
السؤال
What runtime should you report for binary search with a nonconstant feasibility check?
الإجابة
O(C log R), where C is one check's cost and R is the number of discrete candidates. Include any preprocessing separately.
البطاقة ٧٦
السؤال
How can prefix sums turn a longest balanced binary subarray into an equal-prefix problem?
الإجابة
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.
البطاقة ٧٧
السؤال
What is upper bound in a sorted array?
الإجابة
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.
البطاقة ٧٨
السؤال
Why must a prefix-sum counting algorithm query before recording the current prefix?
الإجابة
Recording first can count the empty subarray ending at the current boundary, especially for target zero. Query only earlier prefixes for nonempty ranges.
البطاقة ٧٩
السؤال
How do you safely compute a midpoint in a fixed-width integer search?
الإجابة
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.
البطاقة ٨٠
السؤال
Why can duplicate values degrade searching a rotated sorted array to O(n)?
الإجابة
Equal endpoints and midpoint can hide which side is sorted. Some cases permit discarding only one boundary element at a time.
البطاقة ٨١
السؤال
What preprocessing usually simplifies merging overlapping intervals?
الإجابة
Sort by start coordinate. Keep the current merged interval and either extend its end or emit it when the next interval starts beyond it.
البطاقة ٨٢
السؤال
Which data structure matches nested bracket validation?
الإجابة
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.
البطاقة ٨٣
السؤال
A problem asks for each element's next greater element. Which pattern is promising?
الإجابة
A monotonic stack of unresolved positions. A new larger value resolves the smaller pending values it overtakes.
البطاقة ٨٤
السؤال
Why must interval endpoint conventions be explicit?
الإجابة
Touching endpoints overlap for closed intervals, but adjacent half-open intervals do not. The convention changes merge tests and event ordering.
البطاقة ٨٥
السؤال
How can a sweep line find the maximum number of simultaneous intervals?
الإجابة
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.
البطاقة ٨٦
السؤال
Why is one pass after sorting enough to merge intervals?
الإجابة
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.
البطاقة ٨٧
السؤال
What information should a stack store for next-greater distances?
الإجابة
Indices, so the distance is currentIndex − previousIndex. Values alone do not identify positions or distinguish repeated occurrences.
البطاقة ٨٨
السؤال
Why is counting opening and closing brackets insufficient to validate their sequence?
الإجابة
Counts ignore order and nesting. A closing bracket may appear before its opener, or bracket types may cross despite balanced totals.
البطاقة ٨٩
السؤال
For half-open intervals [start, end), how should equal-time starts and ends affect room counts?
الإجابة
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.
البطاقة ٩٠
السؤال
Why is a monotonic-stack algorithm often O(n) even though one step can pop many items?
الإجابة
Each item is pushed once and popped at most once. Summed across the scan, stack operations are linear.
البطاقة ٩١
السؤال
How can a stack help simplify an absolute filesystem path lexically?
الإجابة
Process components: ignore empty components and '.', pop for '..' when possible, and push ordinary names. This lexical result does not resolve symbolic links.
البطاقة ٩٢
السؤال
How can a monotonic deque find each sliding-window maximum?
الإجابة
Keep candidate indices in decreasing value order. Remove expired indices from the front and dominated values from the back; the front gives the maximum.
البطاقة ٩٣
السؤال
What mistake can lose coverage when merging an interval contained inside the current one?
الإجابة
Replacing the current end with the new end. Use the larger end so a nested interval cannot shrink the merged coverage.
البطاقة ٩٤
السؤال
For a strictly next-greater query, what should happen to an equal-valued stack entry?
الإجابة
Do not resolve it with the equal value. With a decreasing stack of unresolved indices, pop only when the new value is strictly greater.
البطاقة ٩٥
السؤال
What event allows a monotonic stack to finalize a rectangle in a histogram?
الإجابة
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.
البطاقة ٩٦
السؤال
What comparison detects overlap between two nonempty half-open intervals?
الإجابة
max(start1, start2) < min(end1, end2). A strict comparison excludes intervals that only touch.
البطاقة ٩٧
السؤال
How does a stack support evaluating a postfix arithmetic expression?
الإجابة
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.
البطاقة ٩٨
السؤال
Why can a newer value dominate an older value in a sliding-window maximum deque?
الإجابة
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.
البطاقة ٩٩
السؤال
How can you merge two already sorted lists of disjoint intervals to find their intersections?
الإجابة
Compare one interval from each list, emit any overlap, then advance the one with the earlier end. Total time is O(m + n).
البطاقة ١٠٠
السؤال
Why must a histogram stack algorithm handle bars still pending after the scan?
الإجابة
Those bars may extend to the array's end and contain the largest rectangle. Flush them using the end boundary or a suitable sentinel.
البطاقة ١٠١
السؤال
What must you save before reversing a singly linked list node's next pointer?
الإجابة
Its original next node. Otherwise rewiring can lose access to the remaining list.
البطاقة ١٠٢
السؤال
Why does a dummy head simplify linked-list insertion and deletion?
الإجابة
It supplies a predecessor even when the real head changes. The same pointer update can handle both the first node and interior nodes.
البطاقة ١٠٣
السؤال
How do fast and slow pointers detect a cycle in a singly linked list?
الإجابة
Advance one pointer one step and the other two. A meeting implies a cycle; reaching null with the fast pointer means the list terminates.
البطاقة ١٠٤
السؤال
What does a recursive binary-tree traversal use for auxiliary space?
الإجابة
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.
البطاقة ١٠٥
السؤال
During iterative list reversal, what do prev and current represent?
الإجابة
prev heads the reversed processed prefix; current heads the unprocessed suffix. Rewire one node while preserving access to the suffix.
٢١٠ بطاقات
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البطاقة ١٠٦
السؤال
How can you remove the nth node from the end of a list in one pass?
الإجابة
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.
البطاقة ١٠٧
السؤال
Which tree traversal naturally computes a value that depends on both children's results?
الإجابة
Postorder. Process left and right subtrees before combining their results at the parent.
البطاقة ١٠٨
السؤال
How can you locate a cycle's entry after Floyd's two-speed pointers meet?
الإجابة
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.
البطاقة ١٠٩
السؤال
What is the difference between tree depth and tree height?
الإجابة
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.
البطاقة ١١٠
السؤال
How can you merge two sorted linked lists using O(1) auxiliary node storage?
الإجابة
Relink the smaller current node onto the result tail, advancing that list. Attach the remaining suffix when one list ends; existing nodes are reused.
البطاقة ١١١
السؤال
When is breadth-first traversal more natural than depth-first traversal on a tree?
الإجابة
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.
البطاقة ١١٢
السؤال
Why must linked-list intersection compare node identity rather than node value?
الإجابة
Intersection means sharing the same node object and suffix. Separate nodes can hold equal values without the lists intersecting.
البطاقة ١١٣
السؤال
Why is checking only immediate children insufficient to validate a binary search tree?
الإجابة
A descendant can satisfy its parent yet violate an ancestor's constraint. Carry inherited lower and upper bounds, with an explicit duplicate policy.
البطاقة ١١٤
السؤال
What is the lowest common ancestor of two nodes in a rooted tree?
الإجابة
The deepest node that is an ancestor of both, allowing a node to be its own ancestor.
البطاقة ١١٥
السؤال
What property makes inorder traversal useful in a binary search tree?
الإجابة
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.
البطاقة ١١٦
السؤال
Why must maximum tree-path sum separate its returned value from its global candidate?
الإجابة
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.
البطاقة ١١٧
السؤال
How can two pointers find the intersection of two acyclic singly linked lists without measuring lengths?
الإجابة
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.
البطاقة ١١٨
السؤال
What extra information makes preorder serialization unambiguous for an arbitrary binary tree?
الإجابة
Explicit null-child markers or another equivalent shape encoding. Values in preorder alone do not determine the structure.
البطاقة ١١٩
السؤال
Why can repeated subtree-height calculations make a tree-balance check O(n²)?
الإجابة
The same descendants may be scanned from many ancestors. Return height and balance together in one postorder traversal to visit each node once.
البطاقة ١٢٠
السؤال
How does BST ordering guide a lowest-common-ancestor search for two existing distinct keys?
الإجابة
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.
البطاقة ١٢١
السؤال
What runtime does a search in an ordinary unbalanced BST guarantee?
الإجابة
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.
البطاقة ١٢٢
السؤال
When computing a root-to-leaf path sum, why is reaching a null child insufficient for success?
الإجابة
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.
البطاقة ١٢٣
السؤال
What does a min-heap guarantee about its root and children?
الإجابة
The root is a minimum element, and each parent is no larger than its children. The whole array representation is not sorted.
البطاقة ١٢٤
السؤال
A stream needs the k largest values seen so far. Which heap should you maintain?
الإجابة
A min-heap of at most k values. Its root is the smallest retained value, so a larger arrival can replace it.
البطاقة ١٢٥
السؤال
What shared structure does a trie store?
الإجابة
Prefixes of keys. Following one edge per symbol reaches a key's prefix node, while a terminal marker distinguishes a complete stored key.
البطاقة ١٢٦
السؤال
What are the usual binary-heap costs for peek, insertion, and root removal?
الإجابة
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.
البطاقة ١٢٧
السؤال
How can a heap merge k sorted input streams?
الإجابة
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.
البطاقة ١٢٨
السؤال
Why is bottom-up heap construction O(n), not O(n log n)?
الإجابة
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.
البطاقة ١٢٩
السؤال
How do two heaps support a running median?
الإجابة
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.
البطاقة ١٣٠
السؤال
What is a trie's lookup cost for a key of length L?
الإجابة
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.
البطاقة ١٣١
السؤال
Why does a trie node need a terminal marker even if it has children?
الإجابة
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.
البطاقة ١٣٢
السؤال
When does sorting make more sense than a top-k heap?
الإجابة
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.
البطاقة ١٣٣
السؤال
Why does a priority queue not by itself support efficient arbitrary deletion?
الإجابة
The heap efficiently exposes only its root. Removing another item needs its position, an indexed-heap design, or a lazy-deletion scheme with cleanup.
البطاقة ١٣٤
السؤال
What output cost remains after a trie reaches a requested prefix?
الإجابة
Enumerating matching completions still costs time proportional to the visited subtree and emitted text. Prefix lookup does not make all autocomplete results free.
البطاقة ١٣٥
السؤال
How can a priority queue break tied priorities without comparing the payloads?
الإجابة
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.
البطاقة ١٣٦
السؤال
Why can a trie use more memory than a hash set of complete strings?
الإجابة
Nodes and child containers have overhead, especially for sparse branches. Shared prefixes save repeated symbols but do not guarantee a smaller representation.
البطاقة ١٣٧
السؤال
What should graph modeling identify before choosing a traversal?
الإجابة
The states as vertices and legal transitions as edges, including direction and cost. A grid cell, word, or puzzle configuration can be a vertex.
البطاقة ١٣٨
السؤال
When does ordinary BFS find a shortest path?
الإجابة
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.
البطاقة ١٣٩
السؤال
What is the space cost of an adjacency list compared with an adjacency matrix?
الإجابة
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.
البطاقة ١٤٠
السؤال
Which pattern finds all vertices reachable from a start vertex?
الإجابة
DFS or BFS with a visited set. Each reachable vertex and edge is processed a bounded number of times with adjacency lists.
البطاقة ١٤١
السؤال
What role does a parent map play in shortest-path traversal?
الإجابة
It records the predecessor used to reach each state. After reaching the target, follow parents backward and reverse the sequence to recover a path.
البطاقة ١٤٢
السؤال
Why should BFS mark a vertex visited when enqueuing it?
الإجابة
To prevent several parents from adding it before its first removal. First enqueue already fixes its distance in an unweighted graph.
البطاقة ١٤٣
السؤال
When is Dijkstra's algorithm appropriate?
الإجابة
For shortest paths with nonnegative edge weights. Its greedy finalization relies on no later path reducing a settled distance through a negative edge.
البطاقة ١٤٤
السؤال
How can a grid traversal avoid confusing physical cells with full search states?
الإجابة
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.
البطاقة ١٤٥
السؤال
How do you detect a directed cycle with DFS?
الإجابة
Track unvisited, active, and finished vertices. An edge to an active vertex closes a cycle on the current recursion path.
البطاقة ١٤٦
السؤال
Why can DFS with a visited set fail to find a shortest unweighted path?
الإجابة
Its first discovered route may follow a deep detour. DFS reachability order is not distance order; BFS provides that guarantee.
البطاقة ١٤٧
السؤال
What does a topological ordering guarantee?
الإجابة
For every directed edge u → v, u appears before v. Such an ordering exists exactly when the directed graph is acyclic.
البطاقة ١٤٨
السؤال
Why should stale priority-queue entries be skipped in a common Dijkstra implementation?
الإجابة
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.
البطاقة ١٤٩
السؤال
For an undirected simple graph, why does DFS ignore the edge back to its parent when detecting cycles?
الإجابة
That edge is the same tree edge traversed in reverse, not a new cycle. A different already-visited neighbor indicates a cycle.
البطاقة ١٥٠
السؤال
What does union-find answer efficiently?
الإجابة
Whether elements belong to the same connected component while components are merged. It does not store the actual connecting paths.
البطاقة ١٥١
السؤال
How does Kahn's algorithm build a topological ordering?
الإجابة
Enqueue all zero-indegree vertices, repeatedly remove one, and decrement its outgoing neighbors' indegrees. Enqueue each neighbor when its indegree becomes zero.
البطاقة ١٥٢
السؤال
Which shortest-path algorithm handles edges weighted only 0 or 1 without a heap?
الإجابة
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.
البطاقة ١٥٣
السؤال
Why is a boolean visited flag usually wrong for Dijkstra at first enqueue?
الإجابة
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.
البطاقة ١٥٤
السؤال
How do path compression and union by size or rank affect union-find complexity?
الإجابة
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.
البطاقة ١٥٥
السؤال
What does processing fewer than V vertices in Kahn's algorithm reveal?
الإجابة
A directed cycle remains. No vertex in the cyclic remainder can reach indegree zero after all removable dependencies are processed.
البطاقة ١٥٦
السؤال
How can BFS compute distance from every grid cell to the nearest source?
الإجابة
Initialize the queue with all sources at distance zero. This multi-source BFS expands the nearest-source distance layers together.
البطاقة ١٥٧
السؤال
Why can a topological ordering be nonunique?
الإجابة
Several vertices may currently have no remaining prerequisites. Choosing them in different orders can produce different valid orderings.
البطاقة ١٥٨
السؤال
What happens when union-find receives an edge whose endpoints already share a representative?
الإجابة
The edge connects vertices already in one component. In incremental construction of an undirected forest, adding it creates a cycle.
البطاقة ١٥٩
السؤال
Which algorithm can handle negative edge weights and detect a reachable negative cycle?
الإجابة
Bellman–Ford. Repeatedly relax all edges; an improvement after V − 1 full rounds indicates a negative cycle reachable from the source.
البطاقة ١٦٠
السؤال
Why does traversal need an outer loop to count every connected component of an undirected graph?
الإجابة
One traversal reaches only one component. Start another traversal from each still-unvisited vertex and increment the component count.
البطاقة ١٦١
السؤال
How can topological order simplify shortest paths in a weighted DAG?
الإجابة
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).
البطاقة ١٦٢
السؤال
When should you use BFS or DFS instead of union-find for connectivity?
الإجابة
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.
البطاقة ١٦٣
السؤال
What is the difference between a minimum spanning tree and a shortest-path tree?
الإجابة
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.
البطاقة ١٦٤
السؤال
Why can stopping at the first meeting be unsafe in bidirectional BFS with arbitrary node-by-node expansion?
الإجابة
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.
البطاقة ١٦٥
السؤال
Which signal suggests backtracking rather than a single greedy choice?
الإجابة
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.
البطاقة ١٦٦
السؤال
What belongs in a backtracking state?
الإجابة
Enough information to determine legal next choices and recognize completion, such as the current position, chosen items, and remaining constraints.
البطاقة ١٦٧
السؤال
What makes a pruning condition safe?
الإجابة
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.
البطاقة ١٦٨
السؤال
How do combinations differ from permutations during generation?
الإجابة
Combinations ignore order, so restrict future choices to later positions. Permutations care about order, so track which positions are already used.
البطاقة ١٦٩
السؤال
What should be true after a backtracking recursive call returns?
الإجابة
The caller's mutable search state is restored exactly to its pre-choice state. Undo additions and constraint updates before trying a sibling choice.
البطاقة ١٧٠
السؤال
When generating unique subsets from sorted values, how do you skip duplicates safely?
الإجابة
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.
البطاقة ١٧١
السؤال
Why can backtracking output alone require exponential time?
الإجابة
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.
البطاقة ١٧٢
السؤال
Why should a completed mutable candidate usually be copied before saving it?
الإجابة
Later backtracking steps will modify the working candidate. Saving only a reference can make all recorded answers reflect subsequent changes.
البطاقة ١٧٣
السؤال
What is the main risk of memoizing backtracking solely by the current index?
الإجابة
Different histories can leave different remaining choices or constraints. The memo key must include every part of the state that affects future results.
البطاقة ١٧٤
السؤال
For selecting the most nonoverlapping intervals, which greedy choice is justified?
الإجابة
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.
البطاقة ١٧٥
السؤال
What is the difference between greedy choice and dynamic programming?
الإجابة
Greedy commits to a choice proven safe without exploring all alternatives. DP evaluates and combines subproblem alternatives when that local commitment is not justified.
البطاقة ١٧٦
السؤال
Why does choosing the largest coin repeatedly fail for some coin systems?
الإجابة
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.
البطاقة ١٧٧
السؤال
How does a farthest-reachable frontier solve reachability in a nonnegative jump-length array?
الإجابة
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.
البطاقة ١٧٨
السؤال
Why does choosing the shortest interval not always maximize the number of nonoverlapping intervals?
الإجابة
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.
البطاقة ١٧٩
السؤال
What must be proved before pruning a combination-sum branch because its sum exceeds the target?
الإجابة
Remaining choices cannot reduce the sum. The pruning is safe for nonnegative additions under the stated goal, but negative numbers can make it invalid.
البطاقة ١٨٠
السؤال
How does branch and bound differ from ordinary feasibility pruning?
الإجابة
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.
البطاقة ١٨١
السؤال
What question distinguishes a greedy proof from evidence that a heuristic often works?
الإجابة
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.
البطاقة ١٨٢
السؤال
Why is earliest-finish interval scheduling insufficient when intervals have different rewards?
الإجابة
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.
البطاقة ١٨٣
السؤال
Which combination of properties makes dynamic programming promising?
الإجابة
Repeated subproblems and a recurrence that combines their results. Define a state whose answer is independent of the path used to reach it.
البطاقة ١٨٤
السؤال
What should a DP state definition say before you write a recurrence?
الإجابة
Exactly what one table entry means, including its input boundary and any remaining resource or constraint. Ambiguous states lead to mismatched transitions.
البطاقة ١٨٥
السؤال
How do top-down memoization and bottom-up tabulation differ?
الإجابة
Memoization computes states on demand through calls and caches them. Tabulation processes states in an explicit dependency order, often avoiding recursion overhead.
البطاقة ١٨٦
السؤال
What determines the runtime of a DP with a finite state table?
الإجابة
The number of states actually evaluated times the work per state, plus preprocessing and output reconstruction. Count transitions rather than just table dimensions.
البطاقة ١٨٧
السؤال
Why are base cases part of a DP's meaning rather than convenient initial values?
الإجابة
They encode valid empty or smallest subproblems. A wrong base value can invent impossible solutions or remove legitimate ones from every later transition.
البطاقة ١٨٨
السؤال
For 0/1 knapsack compressed to one capacity array, why iterate capacities downward?
الإجابة
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.
البطاقة ١٨٩
السؤال
When can a DP table be compressed to a few rows or variables?
الإجابة
When future states depend only on a bounded slice of earlier states. Keep those dependencies until their last use; reconstruction may need additional storage.
البطاقة ١٩٠
السؤال
What recurrence models choosing nonadjacent values for maximum sum?
الإجابة
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.
البطاقة ١٩١
السؤال
What DP state counts paths through a blocked grid when moves are only right or down?
الإجابة
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.
البطاقة ١٩٢
السؤال
For unbounded knapsack, why can capacities run upward within an item's pass?
الإجابة
Reusing the current item's updated smaller-capacity result is allowed. Ascending order lets that item contribute more than once.
البطاقة ١٩٣
السؤال
How can loop order change coin-change counting from combinations to ordered sequences?
الإجابة
Processing coin types outside amounts builds combinations without ordering them. Processing amounts outside all coin choices counts different last-coin sequences separately.
البطاقة ١٩٤
السؤال
What is the key distinction between longest common subsequence and longest common substring?
الإجابة
A subsequence may skip characters; a substring must stay contiguous. Their DP transitions differ because a substring match cannot carry through a mismatch.
البطاقة ١٩٥
السؤال
Why is O(nW) knapsack called pseudopolynomial?
الإجابة
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.
البطاقة ١٩٦
السؤال
For longest increasing subsequence, what does tails[length − 1] represent in the O(n log n) method?
الإجابة
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.
البطاقة ١٩٧
السؤال
Why do counting and minimization DPs use different unreachable-state values?
الإجابة
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.
البطاقة ١٩٨
السؤال
What state supports edit distance between two strings?
الإجابة
The minimum edits needed to transform one prefix into the other. Transitions account for insertion, deletion, and replacement or a matching final character.
البطاقة ١٩٩
السؤال
How can a DP recover one chosen solution instead of only its score?
الإجابة
Store predecessor or choice information, or recompute choices from the full table. Walk backward from the final state to reconstruct the selected decisions.
البطاقة ٢٠٠
السؤال
Why must an LIS implementation choose its binary-search boundary according to strictness?
الإجابة
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.
البطاقة ٢٠١
السؤال
What operation tests whether bit i of a nonnegative integer mask is set?
الإجابة
Check whether mask AND (1 shifted left by i) is nonzero. Ensure i is inside the integer representation's supported bit range.
البطاقة ٢٠٢
السؤال
Why does XOR recover a unique value when every other value occurs exactly twice?
الإجابة
Equal values cancel because x XOR x = 0, and XOR is associative and commutative. XORing all values leaves the single unpaired value.
البطاقة ٢٠٣
السؤال
What does x AND (x − 1) do for a positive integer x?
الإجابة
It clears x's lowest set bit. Repeating it counts set bits in time proportional to the number of set bits.
البطاقة ٢٠٤
السؤال
When does a bitmask make a useful DP state?
الإجابة
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.
البطاقة ٢٠٥
السؤال
How do you set a bit and clear a bit without changing the others?
الإجابة
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.
البطاقة ٢٠٦
السؤال
What makes a memoized recurrence invalid when it depends on mutable global state omitted from the key?
الإجابة
The same key can have different answers under different global conditions. Include the relevant state in the key or remove that dependency.
البطاقة ٢٠٧
السؤال
What condition recognizes a power of two among integers?
الإجابة
x > 0 and x AND (x − 1) = 0. The positivity check excludes zero, which also makes the bitwise expression zero.
البطاقة ٢٠٨
السؤال
Why does bitwise complement need a width convention in language-agnostic reasoning?
الإجابة
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.
البطاقة ٢٠٩
السؤال
How can two unique values be recovered when every other value occurs twice?
الإجابة
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.
البطاقة ٢١٠
السؤال
Why is memoization alone insufficient to handle cyclic state dependencies?
الإجابة
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.
٢١٠ بطاقات
Coding Interview Patterns Flashcards: Signals, Invariants & Complexity
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