CENEVAL EGEL Plus Ciencias Computacionales (EGEL Plus COMPU)

Given the recurrence T(n) = 4T(n/2) + n², which tight bound does the Master Theorem give for T(n)?

• AΘ(n² log n)
• BΘ(n²)
• CΘ(n³)
• DΘ(n log n)

What is the worst-case time complexity of inserting a key into a binary search tree with n nodes that is not self-balancing?

• AO(log n)
• BO(n)
• CO(1)
• DO(n log n)

An algorithm must find the shortest path between all pairs of vertices in a directed, edge-weighted graph with 50 vertices that contains some negative edge weights but no negative-weight cycles. Which algorithm should be chosen?

• ADijkstra's algorithm with a Fibonacci heap
• BKruskal's algorithm
• CFloyd-Warshall algorithm
• DBreadth-First Search (BFS)

A max-heap stored in an array holds n elements after a new element is appended at the end. What is the maximum number of swaps sift-up (bubble-up) can perform to restore the heap?

• An − 1
• B⌈n/2⌉
• C2^⌊log₂ n⌋
• D⌊log₂ n⌋

Which proposition is logically equivalent to the implication P → Q?

• A¬P ∨ Q
• B¬Q → P
• CP ∧ ¬Q
• D¬P → ¬Q

How many edges does the complete bipartite graph K₄,₇ have?

• A11
• B28
• C55
• D22

In dynamic programming, what two fundamental properties must a problem exhibit for dynamic programming to be applicable and optimal?

• AGreedy choice property and optimal substructure
• BDivide-and-conquer and disjoint subproblems
• COptimal substructure and overlapping subproblems
• DMonotonicity and linear convergence

A hash table of size m = 11 uses open addressing with linear probing and h(k) = k mod 11. Keys 22, 33, 44 and 55 are inserted in that order into an empty table. At which index is key 55 stored?

• A0
• B1
• C2
• D3

What is the chromatic number χ(G) of any bipartite graph that has at least one edge?

• A2
• B1
• C3
• D4

Which sorting algorithm is stable and has a worst-case time complexity of O(n log n)?

• AQuick Sort
• BMerge Sort
• CHeap Sort
• DSelection Sort

In an AVL tree, with balance factor defined as height(left subtree) − height(right subtree), a node's balance factor becomes +2 after an insertion into the right subtree of its left child. Which rotations restore balance?

• ASingle Right rotation on the unbalanced node
• BRight rotation on the left child, followed by Left rotation on the unbalanced node
• CLeft rotation on the left child, followed by Right rotation on the unbalanced node (Left-…
• DSingle Left rotation on the unbalanced node

In first-order logic, which formula is equivalent to ¬∀x (P(x) → Q(x))?

• A∃x (¬P(x) ∨ Q(x))
• B∀x (P(x) ∧ ¬Q(x))
• C∃x (¬P(x) ∧ Q(x))
• D∃x (P(x) ∧ ¬Q(x))

A disjoint-set (union-find) structure uses both union by rank and path compression. What is the tightest amortized time bound per operation over a sequence of m operations on n elements?

• AO(α(n)), where α is the inverse Ackermann function
• BO(log n)
• CO(1) in the worst case for every single operation
• DO(log* n)

How many structurally different binary search trees can be built from 4 distinct keys?

• A24
• B14
• C42
• D8

What is the worst-case running time of the Knuth-Morris-Pratt (KMP) algorithm when searching for a pattern of length m in a text of length n?

• AO(n × m)
• BO(n log m)
• CO(n + m)
• DO(m²)

A connected planar graph has 20 vertices and divides the plane into 12 faces, counting the unbounded face. How many edges does it have?

• A32
• B28
• C10
• D30

Which of the following decision problems is known to be NP-complete?

• ABoolean Satisfiability (3-SAT)
• B2-SAT
• CSingle-source shortest path with non-negative weights
• DMinimum Spanning Tree verification

Resolving the propositional clauses (A ∨ B) and (¬A ∨ C) with the resolution rule produces which clause?

• AA ∨ C
• BB ∨ C
• C¬B ∨ C
• DThe empty clause (a contradiction)

An undirected graph G has an Eulerian circuit if and only if it is connected (ignoring isolated vertices) and:

• AExactly two vertices have an odd degree
• BThe graph is bipartite
• CEvery vertex has an even degree
• DThe number of edges is equal to the number of vertices

What is the tight asymptotic bound of f(n) = 3n³ + 100n² log n + 5000n?

• AΘ(n² log n)
• BΘ(n⁴)
• CΘ(n)
• DΘ(n³)

What is the minimum number of comparisons needed in the worst case to find both the minimum and the maximum of an unsorted array of n numbers?

• A⌈3n/2⌉ − 2
• B2n − 2
• Cn log₂ n
• Dn − 1

In a red-black tree with n internal nodes, what is the maximum possible height?

• Alog₂(n + 1)
• B2 log₂(n + 1)
• CAbout 1.44 log₂(n + 2)
• Dn

What is the coefficient of x³y⁴ in the expansion of (2x − y)⁷?

• A−280
• B70
• C280
• D−560

Which algorithmic design paradigm is exemplified by the fractional knapsack problem where items can be divided?

• ADynamic programming
• BBacktracking
• CBranch and bound
• DGreedy approach

What is the time complexity of building a binary min-heap from an unsorted array of n elements with Floyd's bottom-up build-heap algorithm?

• AO(n)
• BO(n log n)
• CO(log n)
• DO(n²)

In a 5-stage classic RISC processor pipeline (IF, ID, EX, MEM, WB), a data hazard occurs when an instruction depends on the result of the immediately preceding arithmetic instruction. Which hardware mechanism allows this dependency to resolve without stalling the pipeline?

• ABranch prediction
• BOperand forwarding (bypassing)
• COut-of-order execution
• DInstruction prefetching

A virtual memory system has a 32-bit virtual address space with 4 KB page sizes. If each page table entry (PTE) requires 4 bytes, what is the size of a single-level page table for a process?

• A1 MB
• B16 MB
• C4 MB
• D4 KB

Which set lists the four Coffman conditions that must all hold at the same time for a deadlock to occur?

• AMutual exclusion, starvation, race condition, and circular wait
• BPreemption, busy waiting, hold and wait, and priority inversion
• CCritical section, bounded waiting, mutual exclusion, and progress
• DMutual exclusion, hold and wait, no preemption, and circular wait

In compiler construction, which formal grammar hierarchy category is recognized by a Deterministic Pushdown Automaton (DPDA)?

• ADeterministic Context-Free Languages
• BRegular Languages
• CContext-Sensitive Languages
• DRecursively Enumerable Languages

Which language over the alphabet {a, b} does the grammar S → aSb | ε generate?

• A{aⁿbᵐ | n, m ≥ 0}
• B{aⁿbⁿ | n ≥ 0}
• C{(ab)ⁿ | n ≥ 0}
• D{aⁿbⁿ | n ≥ 1}

An IPv4 network has the CIDR block 192.168.10.0/26. How many assignable host IP addresses are available in this subnet?

• A64
• B126
• C62
• D30

In the TCP 3-way handshake used to establish a reliable connection, what are the flags set in the three consecutive packets transmitted between Client and Server?

• ASYN → ACK → SYN-ACK
• BACK → SYN → ACK
• CSYN → DATA → ACK
• DSYN → SYN-ACK → ACK

Which CPU scheduling algorithm minimizes the average waiting time for a set of processes that all arrive at the same time?

• AShortest Job First (SJF)
• BFirst-Come, First-Served (FCFS)
• CRound Robin (RR) with a large time quantum
• DPriority Scheduling without aging

A system uses the Banker's algorithm for deadlock avoidance with three resource types (A, B, C) and Available = (3, 3, 2). Process P₁ requests (1, 0, 2). The request does not exceed Available, but granting it would leave a state with no safe sequence. What must the operating system do?

• AGrant the request and kill the lowest-priority process
• BDeny the request for now and make P₁ wait until it can be granted safely
• CPreempt all of P₁'s resources and abort it
• DGrant the request, because Available (3, 3, 2) covers the request (1, 0, 2)

In a compiler's lexical analysis phase, what theoretical model is used to recognize tokens specified by regular expressions?

• APushdown Automaton (PDA)
• BLinear Bounded Automaton (LBA)
• CDeterministic Finite Automaton (DFA)
• DTuring Machine

What is the primary purpose of the link-state routing protocol OSPF exchanging Link-State Advertisements (LSAs)?

• ATo exchange entire routing tables periodically between neighboring routers
• BTo assign dynamic IPv4 addresses to client hosts across local interfaces
• CTo establish end-to-end encrypted tunnels across intermediate routers
• DTo enable every router within an area to construct an identical topological database of t…

A 4-way set-associative cache has a total size of 64 KB with 32-byte cache lines. Assuming a 32-bit physical address, how many bits are used for the Cache Index?

• A9 bits
• B11 bits
• C5 bits
• D18 bits

Which page replacement algorithm suffers from Belady's Anomaly, where increasing the number of allocated page frames can increase the number of page faults?

• ALeast Recently Used (LRU)
• BFirst-In, First-Out (FIFO)
• COptimal Page Replacement (OPT)
• DLeast Frequently Used (LFU)

In compiler intermediate code representation, what does Static Single Assignment (SSA) form require?

• AEvery instruction executes in exactly one clock cycle
• BNo control flow branches are permitted in basic blocks
• CEach variable is assigned exactly once
• DAll memory allocations are performed statically at compile time

What is the primary function of the Address Resolution Protocol (ARP) in IPv4 networks?

• ATranslating private IP addresses to a public routable IP address
• BResolving fully qualified domain names (FQDN) into IP addresses
• CAssigning dynamic IP addresses and default gateways to local hosts
• DMapping a known IP address to a physical MAC address on a local broadcast link

What is the main advantage of the Translation Lookaside Buffer (TLB) in a paging memory management unit?

• AIt caches recent virtual-to-physical address translations
• BIt stores the actual page data in high-speed SRAM to bypass the L1 cache
• CIt provides hardware-level disk caching for swapped-out virtual memory pages
• DIt calculates error-correcting codes (ECC) for main memory data words

In process synchronization, what does a counting semaphore initialized to k = 5 represent?

• AA barrier that requires exactly 5 processes to arrive before any of them can proceed
• BUp to 5 processes can hold units of the shared resource at the same time before further r…
• CA semaphore that blocks the first 5 processes that call wait()
• DA binary mutex that can be held by 5 threads of the same parent process

An LR(0) parsing state contains both a completed item A → α· and an item B → β·aγ that expects the terminal a. Which conflict does this state have?

• AReduce-Reduce conflict
• BShift-Shift conflict
• CShift-Reduce conflict
• DAmbiguity exception

In TCP congestion control, what happens immediately when a packet loss is detected via three duplicate ACKs (Fast Retransmit)?

• ATCP sets cwnd to 1 MSS and restarts Slow Start from the beginning
• BTCP terminates the connection and returns an RST segment
• CTCP doubles the congestion window and disables flow control
• DTCP retransmits the missing segment, sets ssthresh to half of cwnd, and enters Fast Recov…

Which of the following describes an optimization performed by modern compilers called Loop Invariant Code Motion?

• AMoving expressions whose results do not change across loop iterations to the loop prehead…
• BUnrolling the loop body multiple times to decrease loop indexing overhead
• CReplacing expensive operations like multiplication with equivalent cheaper operations lik…
• DCombining two adjacent loops that iterate over the exact same range into a single loop

What is the key functional difference between a multi-threaded process and multiple independent single-threaded processes executing on an operating system?

• AThreads have separate address spaces and can only communicate via sockets or pipes
• BThreads of the same process share the same address space, heap, and file descriptors, whe…
• CProcesses share the CPU registers and call stack, whereas threads have private memory hea…
• DContext switching between processes is significantly faster than switching between user t…

What type of pipeline hazard do conditional branch instructions such as BEQ and BNE create?

• AStructural hazard
• BData hazard (RAW)
• CControl hazard (branch hazard)
• DMemory alignment hazard