Higher School of Economics & Computer Science in Cracow Entrance Exam Set

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new learning management system. The team is employing an agile methodology, specifically Scrum. The core of the question lies in understanding the role of the Product Owner in Scrum and how they manage the product backlog. The Product Owner is responsible for maximizing the value of the product resulting from the work of the Development Team. This is achieved primarily through managing the Product Backlog, which is an ordered list of everything that might be needed in the product and is the single source of requirements for any changes to be made to the product. The Product Owner is solely accountable for the Product Backlog, including its content, availability, and ordering. They must ensure the backlog is transparent, visible, and understood. In this context, the Product Owner would prioritize features based on business value, stakeholder feedback, and technical feasibility, continuously refining and updating the backlog to reflect evolving needs. Therefore, the most critical responsibility of the Product Owner in this scenario is to meticulously manage and prioritize the Product Backlog to ensure the development team is working on the most valuable features for the new learning management system.

The scenario describes a situation where a new software development project at the Higher School of Economics & Computer Science in Cracow faces a critical bottleneck. The project aims to integrate a novel data analytics module with the existing student information system. The core issue is the dependency on a legacy database system that lacks robust API support and has a poorly documented schema. The development team is experiencing significant delays because extracting and transforming data from this legacy system for the new module is proving far more complex and time-consuming than initially estimated. This complexity arises from the need to manually reverse-engineer data structures and write custom scripts for each data point, leading to a high risk of data integrity issues and increased debugging time. The question asks to identify the most appropriate strategic approach to mitigate this risk, considering the principles of efficient project management and software engineering best practices relevant to academic institutions like the Higher School of Economics & Computer Science in Cracow. Option A, focusing on developing a comprehensive data abstraction layer, directly addresses the root cause of the problem. This layer would act as an intermediary between the new analytics module and the legacy database. It would encapsulate the complexities of accessing and transforming data from the old system, providing a clean, well-defined interface for the new module. This approach promotes modularity, reduces direct dependencies on the legacy system’s intricacies, and allows the development of the analytics module to proceed with greater independence. Furthermore, it aligns with principles of software architecture that emphasize decoupling and maintainability, crucial for long-term project success and potential future system upgrades at the university. Option B, advocating for immediate replacement of the legacy system, is a drastic measure that, while potentially ideal in the long run, is often impractical due to budget constraints, institutional inertia, and the significant disruption it would cause to ongoing operations. It doesn’t offer an immediate solution to the current development bottleneck. Option C, suggesting a reduction in the scope of the analytics module to avoid the legacy system, would compromise the project’s primary objectives and the intended benefits for the Higher School of Economics & Computer Science in Cracow. It represents a retreat rather than a solution. Option D, proposing extensive manual data entry into a new system, is highly inefficient, prone to human error, and completely bypasses the opportunity to leverage existing data. It would be a retrograde step in terms of data management and would not address the core technical challenge of integrating with the legacy system. Therefore, the most strategic and technically sound approach to manage the risk posed by the legacy database is to build a data abstraction layer.

The scenario describes a digital transformation initiative at the Higher School of Economics & Computer Science in Cracow, focusing on integrating a new learning management system (LMS) with existing administrative databases. The core challenge lies in ensuring data integrity and interoperability between disparate systems. The question probes the understanding of architectural principles for such integrations. The correct approach involves establishing a robust data governance framework and employing middleware solutions for seamless data exchange. A data governance framework defines policies, standards, and processes for managing data throughout its lifecycle, ensuring accuracy, consistency, and security. Middleware, such as Enterprise Service Bus (ESB) or API gateways, acts as an intermediary layer, facilitating communication and data transformation between the new LMS and legacy systems. This architectural pattern promotes loose coupling, allowing systems to evolve independently while maintaining interoperability. Option (a) correctly identifies the need for a comprehensive data governance strategy coupled with middleware for effective integration. This aligns with best practices in enterprise architecture and information systems management, crucial for institutions like the Higher School of Economics & Computer Science in Cracow that rely on efficient data flow for academic and administrative operations. Option (b) suggests a direct database-to-database migration without middleware. This approach is prone to creating tight coupling, making future system updates difficult and increasing the risk of data inconsistencies. It often leads to a monolithic architecture that is hard to maintain and scale. Option (c) proposes a phased approach focusing solely on user training for the new LMS. While user adoption is important, it does not address the fundamental technical challenge of system integration and data interoperability, which is the primary bottleneck in the described scenario. Option (d) advocates for a complete overhaul of all existing administrative systems to match the LMS’s architecture. This is often prohibitively expensive, time-consuming, and disruptive, and may not be the most efficient or practical solution for integrating a single new system.

The core of this question lies in understanding the principles of data integrity and the potential vulnerabilities introduced by different data processing methodologies. When a dataset is subjected to multiple transformations, each step carries a risk of introducing noise, bias, or outright errors. The concept of “data provenance” is crucial here, as it tracks the origin and history of data, allowing for the identification of potential points of degradation. In the context of the Higher School of Economics & Computer Science in Cracow, understanding how to maintain data quality through rigorous validation and auditing processes is paramount for reliable research and analysis. Consider a scenario where a raw dataset undergoes the following sequence of operations: 1. **Initial Cleaning:** Removal of duplicate entries and imputation of missing values using the mean. 2. **Feature Engineering:** Creation of new features by combining existing ones through arithmetic operations. 3. **Normalization:** Scaling all features to a range between 0 and 1. 4. **Dimensionality Reduction:** Application of Principal Component Analysis (PCA) to reduce the number of features. Each of these steps, while often necessary, can impact the original data’s fidelity. Imputing with the mean can distort variance and correlations. Feature engineering can introduce spurious relationships if not carefully considered. Normalization, while standard, can obscure the original scale and magnitude. PCA, by its nature, creates new, synthetic features that are linear combinations of the original ones, meaning the transformed data is no longer directly interpretable in terms of the initial measurements. The question asks which of these operations is *least* likely to preserve the original data’s inherent structure and relationships without introducing significant distortion or abstraction. While all steps can alter the data, the creation of entirely new, abstract features through dimensionality reduction techniques like PCA fundamentally changes the nature of the data representation. The resulting components are not directly observable variables but rather mathematical constructs designed to capture variance, which can obscure the original data’s granular characteristics and causal relationships. Therefore, PCA represents the most significant departure from the original data’s structure.

The core of this question lies in understanding the principles of distributed systems and consensus mechanisms, particularly in the context of fault tolerance and achieving agreement among nodes. In a system where nodes might fail or exhibit Byzantine behavior, ensuring that all non-faulty nodes agree on a single value is paramount. The question presents a scenario involving a distributed system with a specific number of nodes and a threshold for consensus. Let \(n\) be the total number of nodes in the system, and \(f\) be the maximum number of faulty nodes. For a distributed system to reach consensus even in the presence of faulty nodes, the number of non-faulty nodes must be strictly greater than the number of faulty nodes. This is a fundamental requirement for many consensus algorithms, including those designed to tolerate Byzantine failures. The condition for achieving consensus is typically expressed as \(n > 2f\). This inequality ensures that even if all \(f\) faulty nodes collude to disrupt the consensus process, the remaining \(n-f\) non-faulty nodes will still constitute a majority, allowing them to outvote the faulty nodes and agree on a value. In the given scenario, we have \(n = 7\) nodes and the system is designed to tolerate up to \(f = 2\) faulty nodes. Let’s check if the condition \(n > 2f\) is met: \(7 > 2 \times 2\) \(7 > 4\) This inequality holds true, indicating that consensus can be achieved. The question asks about the minimum number of nodes that must agree on a value for consensus to be guaranteed, assuming the system can tolerate up to 2 faulty nodes. To guarantee consensus, the number of nodes that must agree must be sufficient to overcome the maximum number of potential faulty nodes. If \(k\) nodes agree on a value, and we want to be sure this agreement is valid despite up to \(f\) faulty nodes, then the number of agreeing nodes \(k\) must be greater than the number of faulty nodes \(f\). More precisely, for a system with \(n\) nodes and \(f\) faulty nodes, consensus is guaranteed if a majority of the *total* nodes agree, or if a sufficient number of nodes agree such that even if all faulty nodes are among those who *disagree*, the agreeing group still represents a valid consensus. The most robust condition for guaranteed consensus in a system with \(f\) faulty nodes is that at least \(f+1\) non-faulty nodes must agree. This is because if \(f+1\) nodes agree, and at most \(f\) nodes are faulty, then even if all \(f\) faulty nodes are among the \(f+1\) who agree, there is still at least one non-faulty node in that group. However, a stronger guarantee, and the one typically associated with reaching a definitive consensus state that all non-faulty nodes can adopt, requires a majority of the *total* nodes to agree. In a system with \(n\) nodes and \(f\) faulty nodes, the number of non-faulty nodes is \(n-f\). To ensure that the agreeing set is definitively composed of non-faulty nodes and represents a true consensus, the number of agreeing nodes must be such that even if all faulty nodes are *not* in the agreeing set, the agreeing set is still a majority of the non-faulty nodes, or more commonly, a majority of the total nodes. The critical threshold for guaranteed consensus in a system with \(n\) nodes and \(f\) faulty nodes is when \(n-f\) nodes agree. This is because if \(n-f\) nodes agree, and at most \(f\) nodes are faulty, then even if all \(f\) faulty nodes are among those who *disagree*, the \(n-f\) agreeing nodes must all be non-faulty. This is the minimum number of nodes that *must* agree to guarantee that the consensus value is held by a set of non-faulty nodes, irrespective of how the faulty nodes behave. In this specific case, \(n=7\) and \(f=2\). The number of non-faulty nodes is \(n-f = 7-2 = 5\). Therefore, if 5 nodes agree on a value, we can be certain that these 5 nodes are non-faulty, and thus a valid consensus has been reached. This aligns with the requirement that the number of agreeing nodes must be greater than the number of faulty nodes plus one, i.e., \(f+1\), to ensure that the agreeing group is not entirely composed of faulty nodes. However, the question asks for the minimum number of nodes that *must* agree to guarantee consensus, which implies a state where all non-faulty nodes can confidently adopt this value. This is achieved when the number of agreeing nodes is at least \(n-f\). Calculation: Total nodes \(n = 7\) Maximum faulty nodes \(f = 2\) Minimum number of nodes that must agree for guaranteed consensus = \(n – f\) Minimum number of nodes that must agree = \(7 – 2 = 5\) The correct answer is 5. This is because if 5 nodes agree, and at most 2 are faulty, then the 5 agreeing nodes must all be non-faulty. This ensures that the consensus is based on the state of the majority of operational nodes, which is a fundamental principle in distributed systems for achieving reliable agreement. This concept is crucial for applications at the Higher School of Economics & Computer Science in Cracow, where robust data management and synchronized operations are essential, especially in areas like distributed databases, blockchain technologies, and fault-tolerant computing. Understanding these thresholds is vital for designing systems that can maintain integrity and availability even when components fail.

The core of this question lies in understanding the principles of agile software development, specifically the concept of Minimum Viable Product (MVP) and its role in iterative development, a cornerstone of modern software engineering practices often emphasized at institutions like the Higher School of Economics & Computer Science in Cracow. An MVP is the version of a new product which allows a team to collect the maximum amount of validated learning about customers with the least effort. It is not simply a stripped-down version of the final product; rather, it is a functional product that addresses a core user need and allows for early feedback. In the scenario presented, the development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new online learning platform. Instead of building the entire platform with all envisioned features (e.g., advanced analytics, personalized learning paths, gamification elements, extensive multimedia support), they decide to focus on the essential functionality that allows students to access course materials, submit assignments, and receive basic feedback. This focused approach is characteristic of an MVP. The rationale behind this strategy is to validate the core assumptions about user needs and platform usability early in the development cycle. By releasing this minimal but functional version, the team can gather real-world data on how students interact with the platform, identify pain points, and prioritize future development based on actual user feedback rather than speculative design. This iterative process, often guided by frameworks like Scrum or Kanban, allows for flexibility and adaptation, reducing the risk of building a product that doesn’t meet market demands. The MVP serves as a learning tool, enabling the team to pivot or persevere based on empirical evidence. The other options represent less effective or incomplete strategies. Building the full-featured product upfront (option b) is resource-intensive and carries a high risk of misalignment with user needs. Focusing solely on user interface design without core functionality (option c) neglects the essential purpose of the platform. Developing a prototype that is not intended for actual user interaction (option d) limits the scope of validated learning. Therefore, the strategy described aligns with the principles of developing a Minimum Viable Product.

The scenario describes a distributed system where nodes communicate using a gossip protocol. The core of the problem lies in understanding how information propagates and the conditions under which a node can be considered “fully informed.” In a gossip protocol, a node periodically selects another random node to share its information with. If a node has received new information, it will eventually share it with other nodes it contacts. Consider a network of \(N\) nodes. Let \(p\) be the probability that a node, upon receiving new information, will successfully transmit it to another randomly chosen node in the next time step. Conversely, \(1-p\) is the probability of failure. A node is considered fully informed if it has received the information from at least one other node. We are interested in the probability that a specific node, say Node A, becomes fully informed after \(k\) time steps, given that it starts with no information. Node A becomes fully informed if, in any of the \(k\) time steps, it receives the information from another node. It is easier to calculate the complementary probability: the probability that Node A *never* receives the information within \(k\) time steps. In each time step, Node A interacts with one other randomly chosen node. There are \(N-1\) other nodes it could interact with. The probability that Node A *does not* receive the information from the node it interacts with in a single time step is the probability that the contacted node *does not* have the information AND the transmission fails. However, the question simplifies this by focusing on Node A’s perspective: in each step, Node A either receives the information or it doesn’t. The probability that Node A *does not* receive the information in a single time step, assuming the other node has the information, is \(1-p\). The probability that Node A does not receive the information from *any* of the \(N-1\) other nodes in a single time step is the probability that it contacts a node that *doesn’t* have the information, or it contacts a node that *does* have the information but the transmission fails. This is complex. A simpler model for gossip protocols often assumes that if a node has information, it will eventually transmit it. The critical factor is the probability of *contact* and successful *transmission*. Let’s reframe: Node A starts uninformed. In each time step, it contacts one random node out of \(N-1\) other nodes. For Node A to become informed, it must contact a node that *already has* the information, and the transmission must be successful. The question implies a simplified model where the probability of receiving information in a single step, given that the information exists in the network and Node A is contacted, is \(p\). The probability that Node A *does not* receive the information in a single time step is \(1-p\). The probability that Node A *does not* receive the information in \(k\) time steps is \((1-p)^k\). Therefore, the probability that Node A *does* receive the information within \(k\) time steps is \(1 – (1-p)^k\). The question asks for the probability that Node A is *not* fully informed after \(k\) steps. This is the probability that it never receives the information. Assuming that in each of the \(k\) steps, Node A has a probability \(p\) of receiving the information (if it’s available from the contacted node and transmission is successful), the probability of *not* receiving it in one step is \(1-p\). Over \(k\) independent steps, the probability of not receiving it in any of those steps is \((1-p)^k\). Let’s consider the context of the Higher School of Economics & Computer Science in Cracow. Understanding distributed systems, network protocols like gossip, and information propagation is crucial for areas like peer-to-peer networks, distributed databases, and fault-tolerant systems. The ability to model and analyze the efficiency and reliability of such protocols is a key skill. This question tests the understanding of probabilistic processes in distributed computing, a fundamental concept for students pursuing advanced studies in computer science and related fields at the university. The ability to derive such probabilities is essential for designing and optimizing distributed algorithms. The calculation is: Probability of not receiving information in one step = \(1-p\) Probability of not receiving information in \(k\) steps = \((1-p)^k\) So, the probability that Node A is *not* fully informed after \(k\) steps is \((1-p)^k\).

The core of this question lies in understanding the principles of agile software development, specifically the concept of Minimum Viable Product (MVP) and its role in iterative development and feedback loops, which are central to the curriculum at the Higher School of Economics & Computer Science in Cracow. An MVP is the version of a new product which allows a team to collect the maximum amount of validated learning about customers with the least effort. It’s not about delivering a half-finished product, but a product with just enough features to satisfy early adopters and provide feedback for future development. In the given scenario, the development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a novel data visualization platform. They have identified core functionalities: data ingestion, basic chart rendering, and user authentication. To adhere to agile principles and gather early user feedback efficiently, the team should prioritize delivering a version of the platform that includes these essential features, allowing users to upload a limited dataset, generate a single type of basic chart (e.g., a bar chart), and log in. This initial release, while not exhaustive, serves as the MVP. It enables the team to test their fundamental assumptions about user needs and technical feasibility. Subsequent iterations would then build upon this foundation, adding more complex visualizations, data sources, and features based on the feedback received. Option A correctly identifies this approach by focusing on delivering a functional core with essential features for early validation. Option B is incorrect because a “fully featured, polished product” contradicts the MVP philosophy of iterative development and learning. Option C is incorrect as “extensive market research without any product development” delays the crucial feedback loop and is not an MVP strategy. Option D is incorrect because “focusing solely on backend infrastructure without user interaction” bypasses the primary goal of an MVP, which is to validate user value and gather feedback on the user experience. The calculation here is conceptual: identifying the most appropriate agile strategy for early validation.

The core of this question lies in understanding the principles of agile software development, specifically how the Higher School of Economics & Computer Science in Cracow might leverage them for project management and curriculum development. The scenario describes a situation where a new interdisciplinary program is being designed. Agile methodologies emphasize iterative development, continuous feedback, and adaptability. In this context, the most effective approach would be to adopt a phased rollout with regular stakeholder reviews. This aligns with the agile principle of delivering working software (or in this case, program components) frequently and gathering feedback to inform subsequent iterations. Let’s break down why this is the optimal strategy: 1. **Iterative Development:** The program can be developed in modules or phases. For instance, the foundational economics courses could be finalized and piloted, followed by the computer science components, and then the interdisciplinary elements. This allows for learning and adjustment at each stage. 2. **Continuous Feedback:** Regular reviews with faculty from both departments, potential students, and industry advisors are crucial. This feedback loop ensures that the program remains relevant, addresses emerging needs, and incorporates best practices from both fields. 3. **Adaptability:** The dynamic nature of economics and computer science necessitates a flexible approach. An agile strategy allows the Higher School of Economics & Computer Science in Cracow to pivot based on feedback, technological advancements, or shifts in industry demand without a complete overhaul. Consider the alternatives: * A “big bang” launch without iterative testing would be highly risky, potentially leading to a program that is outdated or misaligned with student and industry expectations upon its initial release. * Focusing solely on one discipline’s development cycle would neglect the interdisciplinary nature of the program and the synergistic benefits it aims to provide. * A rigid, long-term plan without built-in review points would stifle innovation and prevent the program from adapting to the rapidly evolving academic and professional landscapes that the Higher School of Economics & Computer Science in Cracow is known for. Therefore, the strategy that best embodies agile principles for this scenario at the Higher School of Economics & Computer Science in Cracow is a phased implementation with continuous stakeholder engagement and iterative refinement.

The core of this question lies in understanding the principles of agile software development, specifically the concept of Minimum Viable Product (MVP) and its role in iterative development. An MVP is the version of a new product which allows a team to collect the maximum amount of validated learning about customers with the least effort. It’s not about building a fully featured product, but rather the smallest possible version that can be released to gather feedback. In the context of the Higher School of Economics & Computer Science in Cracow, where innovation and practical application are emphasized, understanding how to efficiently validate ideas is crucial. Building a complete, feature-rich application before market testing is inefficient and risky. It delays feedback, increases development costs, and may result in a product that doesn’t meet user needs. Therefore, the most effective strategy for a startup aiming to launch a novel data analytics platform, as described, would be to focus on developing a core set of functionalities that address the primary pain point of their target users. This allows for early user engagement, iterative refinement based on real-world usage, and a more agile response to market demands. This approach aligns with the principles of lean startup methodologies, which are often discussed in the context of entrepreneurship and technology management, areas relevant to the curriculum at the Higher School of Economics & Computer Science in Cracow. The goal is to learn and adapt, not to perfect in isolation.

The scenario describes a situation where a newly developed algorithm for optimizing resource allocation in a simulated smart city environment, designed by students at the Higher School of Economics & Computer Science in Cracow, exhibits unexpected behavior. Specifically, when the simulation scales to a larger number of interconnected nodes representing urban infrastructure, the algorithm’s efficiency degrades significantly, leading to suboptimal resource distribution. This degradation is not due to a simple increase in computational complexity, which would be a predictable outcome of scaling. Instead, the problem lies in the algorithm’s inherent assumption about the homogeneity of network traffic patterns. In reality, as the network grows, emergent properties arise, creating localized traffic congestion and unpredictable data flow dynamics that the algorithm, with its static parameterization, fails to adapt to. The core issue is the algorithm’s inability to dynamically reconfigure its decision-making heuristics based on real-time, localized network states. This points to a fundamental limitation in its adaptive learning or feedback mechanisms. The most fitting description for this problem, within the context of computer science principles relevant to the Higher School of Economics & Computer Science in Cracow, is a failure to account for emergent system properties and the lack of robust adaptive control mechanisms. The algorithm’s design, while effective for smaller, controlled environments, lacks the sophisticated state-space exploration and dynamic parameter tuning necessary for complex, emergent systems. This is analogous to issues encountered in distributed systems and artificial intelligence where static models struggle with dynamic, unpredictable environments.

The scenario describes a situation where a new software development project at the Higher School of Economics & Computer Science in Cracow faces a critical bottleneck due to an unforeseen dependency on a legacy system. The core issue is that the legacy system’s data export functionality is unreliable and produces inconsistent output formats. To address this, the development team needs to implement a robust data validation and transformation layer. The most effective approach, considering the need for accuracy, adaptability, and maintainability within an academic and research-oriented environment like the Higher School of Economics & Computer Science in Cracow, is to develop a custom parsing and validation engine. This engine would be designed to handle the variability in the legacy data, identify and flag anomalies, and transform the data into a standardized, machine-readable format suitable for the new software. This approach allows for granular control over the data processing, ensuring that the new system receives clean and consistent input, thereby mitigating the risks associated with the legacy system’s unreliability. A custom engine offers superior flexibility compared to off-the-shelf ETL tools, which might not adequately address the specific nuances of the legacy system’s output or might introduce licensing complexities. While manual data correction is impractical for large datasets and iterative development, and simply documenting the inconsistencies would not solve the integration problem, building a dedicated engine directly tackles the root cause of the data quality issue. This aligns with the Higher School of Economics & Computer Science in Cracow’s emphasis on developing sophisticated, in-house solutions and fostering deep understanding of data engineering principles. The development of such an engine also provides valuable learning opportunities for students involved in the project, reinforcing concepts in data structures, algorithms, and software engineering best practices, which are central to the curriculum.

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new learning management system. They are considering different architectural patterns. The core of the problem lies in understanding the trade-offs between monolithic, microservices, and service-oriented architectures (SOA) in the context of scalability, maintainability, and development agility, which are crucial for a university’s IT infrastructure. A monolithic architecture, while simpler to develop initially, can become unwieldy as the system grows, leading to deployment challenges and slower innovation cycles. Microservices, on the other hand, offer independent deployability and scalability for individual components, but introduce complexity in inter-service communication and distributed system management. SOA provides a middle ground, emphasizing reusable services with well-defined interfaces, which can be beneficial for integrating with existing university systems. Considering the need for flexibility to adapt to evolving pedagogical needs and integrate with diverse university databases and administrative systems, a microservices architecture, despite its initial complexity, offers the greatest long-term advantage in terms of independent scaling of specific functionalities (e.g., student enrollment, course material delivery, assessment grading) and allows different teams to work on different services concurrently, fostering faster development and deployment cycles. This aligns with the dynamic nature of academic technology and the Higher School of Economics & Computer Science in Cracow’s commitment to cutting-edge solutions. The ability to independently update and scale specific modules without affecting the entire system is paramount for a university environment that requires continuous improvement and adaptation.

The core of this question lies in understanding the principles of agile software development, specifically the concept of Minimum Viable Product (MVP) and its role in iterative development and feedback loops. An MVP is the version of a new product which allows a team to collect the maximum amount of validated learning about customers with the least effort. For the Higher School of Economics & Computer Science in Cracow, which emphasizes practical application and innovation, understanding how to efficiently bring a product to market while gathering crucial user insights is paramount. Consider a scenario where a development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new online learning platform. They decide to adopt an agile methodology. The initial phase involves defining the core functionalities that address the most critical user needs for a pilot group of students. This means identifying the essential features that allow students to access course materials, submit assignments, and receive basic feedback from instructors. This initial release, containing only these fundamental features, is the Minimum Viable Product. The purpose of this MVP is not to be a complete, feature-rich product, but rather a functional prototype that can be tested with real users. The feedback gathered from this pilot group on the usability, effectiveness, and desirability of these core features is invaluable. This feedback then informs the subsequent iterations of development. For instance, if students find the assignment submission process cumbersome, the team can prioritize improving that aspect in the next sprint. Conversely, if they discover an unexpected but highly valued use case, that can be incorporated into the product roadmap. This iterative process of building, measuring, and learning, driven by the MVP, allows the team to adapt to user needs and market demands efficiently, minimizing wasted development effort on features that might not be used or valued. This approach aligns with the Higher School of Economics & Computer Science in Cracow’s commitment to producing graduates who can navigate complex projects with adaptability and a user-centric focus.

The scenario describes a situation where a new software development project at the Higher School of Economics & Computer Science in Cracow faces a critical bottleneck. The project aims to create an innovative platform for collaborative research, integrating data analysis tools with secure communication channels. The development team has encountered significant delays due to the integration of a third-party machine learning library, which is essential for the platform’s predictive analytics capabilities. This library, while powerful, has a complex API and requires specialized knowledge for efficient implementation. The project manager is considering two primary strategies to overcome this: either investing in extensive in-house training for the existing developers or hiring external consultants with proven expertise in the specific library. To determine the most effective approach, we need to consider the long-term goals and constraints of the Higher School of Economics & Computer Science in Cracow. The school emphasizes fostering internal talent and building sustainable expertise within its faculty and student body. While external consultants offer immediate solutions and can accelerate the project, their involvement is typically temporary and does not contribute to the school’s long-term capacity building. In-house training, conversely, although potentially slower initially, empowers the existing team, enhances their skill sets, and creates a knowledge base that can be leveraged for future projects. This aligns with the educational philosophy of the Higher School of Economics & Computer Science in Cracow, which prioritizes the development of its human capital and the creation of enduring academic and technical resources. Therefore, prioritizing the development of internal expertise, even with a potentially longer initial timeline, is the more strategically sound decision for the institution. This approach not only resolves the immediate project challenge but also strengthens the school’s overall technical proficiency and research potential.

The scenario describes a situation where a newly developed algorithm for optimizing resource allocation in a simulated environment for the Higher School of Economics & Computer Science in Cracow has been deployed. The algorithm’s performance is being evaluated against a baseline. The key metric is the “efficiency score,” which is calculated as the ratio of successfully allocated resources to the total resources available, multiplied by a factor representing the speed of allocation. The initial deployment resulted in an efficiency score of \(0.85\). A subsequent modification to the algorithm, aimed at improving its predictive accuracy for resource demand, led to a new efficiency score of \(0.92\). The question asks to identify the most appropriate interpretation of this change in the context of the Higher School of Economics & Computer Science in Cracow’s focus on practical application and rigorous evaluation. The increase in the efficiency score from \(0.85\) to \(0.92\) indicates a positive impact of the algorithmic modification. This improvement suggests that the enhanced predictive accuracy has indeed translated into better resource utilization and/or faster allocation, directly aligning with the school’s emphasis on developing and evaluating practical computational solutions. The core concept being tested is the understanding of how algorithmic improvements, particularly those related to predictive modeling in resource management, manifest in measurable performance gains. This is crucial for students at the Higher School of Economics & Computer Science in Cracow, as it bridges theoretical computer science with real-world problem-solving in economics and computer science domains. The improved score signifies a more effective and potentially faster allocation of simulated resources, demonstrating a successful iterative development process.

The core of this question lies in understanding the principles of algorithmic efficiency and data structure selection in the context of a dynamic, evolving dataset. Consider a scenario where the Higher School of Economics & Computer Science in Cracow needs to manage a continuously updated database of student project submissions. Each submission includes metadata such as submission timestamp, project topic category, and a unique identifier. The system must support two primary operations: efficiently retrieving all submissions within a specified time range and quickly identifying submissions belonging to a particular topic category. To analyze the efficiency, we can think about the worst-case time complexity for each operation. For retrieving submissions within a time range, a data structure that allows for ordered access based on the timestamp is crucial. A balanced binary search tree (BST) or a B-tree, indexed by timestamp, would allow for range queries in \(O(\log n + k)\) time, where \(n\) is the total number of submissions and \(k\) is the number of submissions within the range. A simple unsorted list would require \(O(n)\) for this operation. For retrieving submissions by topic category, a hash table or a dictionary, where the keys are topic categories and the values are lists of submission identifiers (or pointers to submission objects), would provide average \(O(1)\) access. If the values are lists of identifiers, retrieving all submissions for a category would take \(O(m)\) time, where \(m\) is the number of submissions in that category. Now, let’s consider the combined requirement and the need for efficient updates. If we use a single data structure to index both by timestamp and by topic category, we might face trade-offs. A multi-dimensional data structure like a k-d tree could handle range queries on multiple attributes, but updates can be complex, and performance can degrade with high dimensionality or skewed data distributions. The question asks for the most suitable approach for *both* operations, implying a need for a balanced solution. Using two separate, optimized data structures—one for time-based retrieval and another for category-based retrieval—often provides the best overall performance for these distinct query types. A sorted list or a BST for timestamps and a hash map for topic categories is a common and effective pattern. Let’s evaluate the options based on this: Option 1: A single, highly specialized multi-dimensional index. While potentially elegant, the complexity of implementation and maintenance, especially with frequent updates, can be substantial. The performance guarantees for both types of queries might not be optimal compared to separate structures. Option 2: Two independent, optimized data structures. This approach leverages the strengths of different structures for each query type. A time-ordered structure (like a balanced BST or a skip list) for temporal queries and a hash-based structure for categorical queries offers excellent average-case performance for both operations and manageable update complexity. Option 3: A simple linear scan of all submissions for both query types. This is clearly inefficient, especially as the number of submissions grows, leading to \(O(n)\) complexity for both operations. Option 4: A single, generic data structure without specific indexing for either attribute. This would likely result in poor performance for both time-range and category-based queries, similar to the linear scan. Therefore, the most robust and efficient strategy for the Higher School of Economics & Computer Science in Cracow to manage its student project database, supporting both time-range and category-based retrieval with reasonable update efficiency, is to employ two distinct, optimized data structures. Specifically, a structure optimized for ordered data (like a balanced binary search tree or a skip list) for timestamps and a hash map for topic categories. This allows for efficient \(O(\log n + k)\) or \(O(n)\) for time-range queries (depending on the structure and \(k\)) and average \(O(m)\) for category queries, with manageable update costs. The final answer is \(\boxed{Two independent, optimized data structures}\)

The core of this question lies in understanding the ethical implications of data utilization in a university setting, specifically concerning student privacy and the responsible application of AI. The Higher School of Economics & Computer Science in Cracow, like many institutions, emphasizes academic integrity and the ethical treatment of information. When a university implements an AI system to analyze student performance data, several ethical considerations arise. The primary concern is ensuring that the data collected and analyzed is done so with explicit consent and for clearly defined, beneficial purposes that do not infringe upon individual privacy. Furthermore, the algorithms used must be transparent and free from bias to ensure fair evaluation and prevent discriminatory outcomes. The potential for misuse of sensitive student information, such as academic records or personal learning patterns, necessitates robust data security measures and strict access controls. Therefore, the most ethically sound approach involves a comprehensive framework that prioritizes transparency, consent, data security, and bias mitigation, all while aligning with the university’s commitment to student welfare and academic excellence. This framework would involve clear communication with students about data usage, anonymization techniques where appropriate, and regular audits of the AI system’s performance and ethical compliance.

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow Entrance Exam is tasked with creating a new educational platform. The core challenge lies in balancing the need for rapid feature deployment with the imperative of maintaining code integrity and long-term system stability. The team is considering adopting a new version control strategy. To determine the most effective strategy, we must analyze the trade-offs between different approaches in the context of a university’s academic and research environment, which often involves collaborative projects with evolving requirements and a need for reproducible research. Consider the following: 1. **Centralized Version Control (e.g., SVN):** Offers a single source of truth but can become a bottleneck for distributed teams and lacks robust branching capabilities for parallel development, which is common in academic projects. 2. **Distributed Version Control (e.g., Git):** Provides excellent branching and merging, enabling parallel development and offline work, which is highly beneficial for students and researchers. However, it requires a clear branching strategy to manage contributions effectively. 3. **Feature Branching:** Isolates development of new features into separate branches, reducing merge conflicts and allowing for independent testing before integration. This aligns well with the iterative development cycles often seen in academic software projects. 4. **Gitflow Workflow:** A more structured branching model that defines specific branches for features, releases, and hotfixes, promoting a disciplined workflow. While robust, it can introduce complexity for simpler projects or teams new to distributed version control. The question asks for the strategy that best supports both rapid iteration and robust code management in an academic setting. A distributed system like Git, combined with a feature branching strategy, allows individual researchers or student groups to work on specific components without disrupting the main codebase. This facilitates experimentation and parallel development, crucial for academic innovation. Furthermore, the ability to create isolated branches for experimental features or bug fixes ensures that the main development line remains stable. This approach directly addresses the dual requirements of agility and stability. The correct answer is the adoption of a distributed version control system that supports a feature branching workflow. This combination provides the flexibility for individual or small-group development (common in academic research and coursework) while maintaining a clear path for integrating tested features into a stable main branch, thus supporting both rapid iteration and robust code management.

The scenario describes a digital transformation initiative at the Higher School of Economics & Computer Science in Cracow, focusing on integrating a new learning management system (LMS) with existing administrative databases. The core challenge lies in ensuring data integrity and seamless information flow between disparate systems. The question probes the understanding of architectural principles for such integrations. The correct approach involves establishing a robust data governance framework and utilizing an Enterprise Service Bus (ESB) or a similar middleware solution. An ESB acts as a central hub, facilitating communication and data transformation between different applications. This allows for standardized data exchange protocols, error handling, and monitoring, crucial for maintaining consistency and reliability. Data mapping and transformation rules are essential to ensure that information from the legacy systems is correctly interpreted and integrated into the new LMS, and vice versa. Furthermore, a phased rollout strategy, coupled with rigorous testing at each stage, mitigates risks associated with large-scale system changes. Implementing a data catalog and metadata management system also supports long-term maintainability and understanding of the integrated data landscape. Incorrect options often propose less integrated or more simplistic solutions that fail to address the complexity of inter-system dependencies and data governance. For instance, direct point-to-point integrations, while seemingly simpler initially, become unmanageable as the number of systems grows, leading to a “spaghetti architecture” with high maintenance costs and increased risk of data inconsistencies. Relying solely on manual data reconciliation is inefficient and prone to human error, especially in an academic environment with a high volume of student and course data. A complete overhaul without considering the existing infrastructure’s strengths and weaknesses, or focusing only on front-end user experience without addressing the underlying data architecture, would also be suboptimal.

The core of this question lies in understanding the principles of agile software development, specifically how a team prioritizes and manages its backlog in response to evolving project requirements and stakeholder feedback. In an agile environment, the product owner is primarily responsible for the product backlog, which is a dynamic, ordered list of everything that might be needed in the product. When new, high-priority features emerge, or existing ones are re-evaluated based on market shifts or user testing, the product owner must adapt the backlog accordingly. This involves not just adding new items but also re-prioritizing existing ones, refining their descriptions, and potentially removing less critical items to maintain focus. The scenario describes a situation where the Higher School of Economics & Computer Science in Cracow has received feedback indicating a strong demand for a new data visualization module, which is deemed more critical than several previously planned features. Therefore, the most effective and agile response is to update the product backlog by incorporating this new module and reordering existing items to reflect its higher priority. This ensures that development efforts are aligned with the most current and valuable objectives, a fundamental tenet of agile methodologies taught and practiced at institutions like the Higher School of Economics & Computer Science in Cracow. The other options represent less agile or less effective approaches. Simply adding the new feature without re-prioritization would lead to a cluttered and inefficient backlog. Delegating backlog management to the development team, while collaboration is key, bypasses the product owner’s crucial role in strategic decision-making. Postponing the new feature until the next development cycle ignores the immediate feedback and potential competitive advantage, which is counterproductive in a fast-paced academic or industry setting.

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new learning management system (LMS). The team is considering different architectural patterns. The question asks to identify the most suitable pattern given the project’s requirements: scalability to accommodate a growing student body, modularity for independent feature development and updates, and robust data integrity for academic records. A monolithic architecture, while simpler to develop initially, would struggle with scalability and modularity. As the system grows, it becomes harder to update or scale individual components without affecting the entire application. This directly contradicts the need for accommodating a growing student body and allowing independent feature development. A microservices architecture, on the other hand, breaks down the application into small, independent services that communicate with each other. This inherently supports scalability, as individual services can be scaled up or down based on demand. It also promotes modularity, allowing different teams to work on and deploy services independently, facilitating faster development cycles and easier updates. The emphasis on data integrity can be managed through careful service design and inter-service communication protocols, ensuring that critical academic data remains consistent. A client-server architecture is a broad category and doesn’t specify the internal structure of the server, so it’s less precise than microservices in addressing the specific needs for modularity and independent scaling of components within the server-side logic. A peer-to-peer architecture is generally not suitable for a centralized LMS where a single source of truth for academic data is required and where centralized management and security are paramount. Therefore, the microservices architecture best aligns with the stated requirements of scalability, modularity, and the ability to manage complex data integrity within the context of an educational institution like the Higher School of Economics & Computer Science in Cracow.

The core of this question lies in understanding the principles of data integrity and the potential vulnerabilities introduced by different data processing stages. When a dataset is initially collected, it is assumed to be in its most pristine state, representing the raw, unadulterated truth of the observed phenomena. However, as data moves through various transformations – cleaning, normalization, feature engineering, and aggregation – the risk of introducing errors or biases increases. Data cleaning, while essential for removing noise and inconsistencies, can inadvertently alter valid data points if the cleaning heuristics are too aggressive or misapplied. Normalization, often used to scale features to a common range, can obscure original distributions. Feature engineering, the process of creating new variables from existing ones, can introduce complex relationships that might not accurately reflect the underlying reality or might be artifacts of the chosen methodology. Aggregation, by summarizing data, inherently loses granular detail and can mask outliers or specific patterns present in the raw data. Therefore, the stage most susceptible to the introduction of subtle, yet significant, deviations from the original truth, without necessarily being outright errors, is the transformation and feature engineering phase, as it involves interpretation and manipulation of the data’s structure and meaning. This aligns with the Higher School of Economics & Computer Science in Cracow’s emphasis on rigorous data handling and understanding the lifecycle of data in analytical processes.

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new application. The core challenge lies in managing the inherent uncertainty and evolving requirements typical of innovative projects. The team is considering different methodologies. Agile methodologies, such as Scrum or Kanban, are designed to embrace change and deliver value incrementally. They prioritize flexibility, collaboration, and rapid feedback loops, which are crucial when the final product vision is not fully defined at the outset. Waterfall, on the other hand, is a linear, sequential approach that requires all requirements to be finalized before development begins. This makes it ill-suited for projects with high uncertainty and a need for adaptation. Lean principles focus on eliminating waste and maximizing customer value, often through iterative development and continuous improvement, which aligns well with agile practices. DevOps aims to streamline the software development lifecycle by fostering collaboration between development and operations teams, but it’s more about the operational aspect of delivery rather than the core project management methodology for handling evolving requirements. Therefore, an approach that emphasizes iterative development, continuous feedback, and adaptability to change is most appropriate. This directly points to the principles underpinning agile and lean software development.

The core of this question lies in understanding the principles of agile software development, specifically the concept of Minimum Viable Product (MVP) and its role in iterative development and feedback loops, which are central to the curriculum at the Higher School of Economics & Computer Science in Cracow. An MVP is not merely a stripped-down version of a product; it is a version of a new product which allows a team to collect the maximum amount of validated learning about customers with the least effort. This validated learning is crucial for guiding future product development. Consider a scenario where a team at the Higher School of Economics & Computer Science in Cracow is developing a novel educational platform. They decide to launch with only the core functionality of user registration and basic content viewing, foregoing advanced features like interactive quizzes, personalized learning paths, and community forums for the initial release. This approach allows them to gather immediate feedback on the user interface, registration process, and the fundamental content delivery mechanism. The data collected from early adopters regarding usability, engagement with the core content, and any technical issues encountered forms the basis for the next iteration. This iterative process, driven by empirical data and user insights, is a hallmark of agile methodologies and directly informs the product roadmap, ensuring that development efforts are aligned with actual user needs and market demands. The success of this strategy hinges on the ability to quickly iterate based on this feedback, making the MVP a strategic tool for risk mitigation and efficient resource allocation in product development, a key consideration in modern computer science and economics.

The core of this question lies in understanding the principles of agile software development, specifically the concept of “technical debt” and its management within a continuous integration and continuous delivery (CI/CD) pipeline. Technical debt, in essence, represents the implied cost of additional rework caused by choosing an easy (limited) solution now instead of using a better approach that would take longer. In the context of the Higher School of Economics & Computer Science in Cracow, understanding how to balance rapid feature delivery with maintaining code quality is crucial for developing robust and scalable software systems. When a development team at the Higher School of Economics & Computer Science in Cracow prioritizes speed over thoroughness in code refactoring during a sprint, they are effectively accumulating technical debt. This debt manifests as code that is harder to understand, modify, and test. If this debt is not addressed, it can lead to slower development cycles, increased bug rates, and higher maintenance costs in the future. A CI/CD pipeline, designed to automate the software release process, can either exacerbate or help manage this debt. If the CI/CD pipeline includes automated tests (unit, integration, and end-to-end) that are designed to catch regressions and code quality issues, then the accumulation of technical debt will be more readily apparent. When a build fails due to a new bug introduced by a quick fix or a lack of refactoring, the pipeline signals a problem. The team must then decide how to address this failure. The most effective approach, aligned with agile principles and the need for sustainable development, is to fix the underlying issue that caused the pipeline to fail. This often involves refactoring the problematic code, thereby paying down the technical debt. Therefore, the scenario where the CI/CD pipeline flags a build failure due to a regression directly linked to a previously deferred refactoring task necessitates addressing that specific regression. This action directly tackles the accumulated technical debt that caused the failure.

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow is transitioning from a monolithic architecture to a microservices approach. The core challenge is managing the increased complexity of inter-service communication, data consistency, and deployment orchestration. The question probes the understanding of architectural patterns that address these challenges. A monolithic architecture, while simpler to develop initially, suffers from scalability issues and tight coupling. Microservices break down an application into smaller, independent services, each responsible for a specific business capability. This promotes agility, independent deployment, and technology diversity. However, it introduces complexities in how these services interact. Event-driven architecture (EDA) is a paradigm where the flow of information is dictated by the occurrence of events. Services communicate asynchronously by publishing and subscribing to events. This decouples services, enhances resilience (as services can operate even if others are temporarily unavailable), and facilitates scalability. For instance, when a new order is placed (an event), the order service publishes an “OrderPlaced” event. Other services, like the inventory service or the notification service, subscribe to this event and react accordingly. This asynchronous communication pattern is crucial for managing the distributed nature of microservices. Consider the following: 1. **Service Discovery:** How do services find each other? 2. **Inter-service Communication:** How do they exchange data? 3. **Data Consistency:** How is data kept consistent across multiple services? 4. **Deployment and Orchestration:** How are these independent services managed? While other patterns like API Gateways are essential for managing external access, and CQRS (Command Query Responsibility Segregation) can optimize read/write operations, Event-Driven Architecture directly addresses the fundamental challenge of asynchronous, decoupled communication and data flow in a distributed microservices environment, which is a key consideration for modern software engineering practices taught at institutions like the Higher School of Economics & Computer Science in Cracow. The ability to handle state changes and propagate them efficiently across independent units is paramount.

The core of this question lies in understanding the principles of agile software development, specifically how it addresses the challenges of evolving requirements and the need for rapid feedback in complex projects. The Higher School of Economics & Computer Science in Cracow emphasizes practical application and adaptability in its curriculum. When a project faces a significant shift in market demand mid-development, as described, the most effective response within an agile framework is to embrace this change. This involves re-prioritizing the product backlog, potentially dropping or significantly altering existing features to accommodate the new direction, and then iterating through development cycles (sprints) to deliver the updated functionality. This approach prioritizes delivering value that aligns with current market needs over rigidly adhering to an outdated plan. A rigid adherence to the original scope, even with a strong justification for the initial plan, would be counterproductive in an agile environment. Similarly, halting development entirely or focusing solely on documentation without adapting the product would fail to leverage the inherent flexibility of agile methodologies. The key is to integrate the new requirements into the ongoing development process, using the feedback loops inherent in agile to ensure the product remains relevant and valuable. This reflects the Higher School of Economics & Computer Science in Cracow’s focus on producing graduates who can navigate and lead in dynamic technological landscapes.

The scenario describes a situation where a software development team at the Higher School of Economics & Computer Science in Cracow is tasked with creating a new learning management system. The team is employing an agile methodology, specifically Scrum. The core of the problem lies in understanding how to effectively manage the backlog and ensure that the most valuable features are prioritized for development. The question asks about the primary responsibility of the Product Owner in this context. In Scrum, the Product Owner is accountable for maximizing the value of the product resulting from the work of the Development Team. This is achieved by managing the Product Backlog, which is a prioritized list of everything that might be needed in the product. The Product Owner’s role involves clearly expressing Product Backlog items, ordering them to best achieve goals and missions, ensuring the Product Backlog is visible, transparent, and clear to all, and showing what the Development Team will work on next. They also ensure that the Development Team understands items in the Product Backlog to the level needed. Therefore, the primary responsibility is to define and prioritize the work that the team will undertake, ensuring it aligns with the overall product vision and stakeholder needs.

The scenario describes a software development project at the Higher School of Economics & Computer Science in Cracow where a team is using an agile methodology. The core issue is the team’s inability to consistently deliver working software increments by the end of each sprint, leading to a backlog of unfinished tasks and a decline in stakeholder confidence. This directly impacts the iterative and incremental nature of agile development, which relies on frequent delivery of value. The explanation for the correct answer lies in understanding the fundamental principles of agile and common pitfalls. In agile, the “Definition of Done” (DoD) is a critical artifact that establishes a shared understanding of what it means for a piece of work to be complete. If the DoD is unclear, too lenient, or not consistently applied, tasks may appear “done” from a developer’s perspective but still require significant further work to be truly shippable or meet quality standards. This leads to the accumulation of partially completed work and the inability to deliver a potentially shippable increment. Addressing this requires a re-evaluation and reinforcement of the DoD. This involves the team collaboratively defining clear, objective, and measurable criteria for completion. These criteria typically include aspects like code completion, unit testing, integration testing, documentation, and adherence to coding standards. By making the DoD explicit and ensuring every team member understands and adheres to it, the team can improve the predictability of their sprint outcomes and build trust with stakeholders. The other options, while potentially related to project management, do not directly address the root cause of unfinished increments in an agile context as effectively as reinforcing the DoD. For instance, increasing sprint length might mask the problem rather than solve it, changing the development methodology might be an overreaction, and focusing solely on individual performance metrics ignores the systemic issue of a poorly defined or enforced completion standard.