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Questions and Answers

In the context of string algorithms, which of the following best describes the primary purpose of string hashing?

To encrypt strings, ensuring secure data transmission.
To create a unique numerical representation of a string for efficient comparison and search. (correct)
To compress strings for efficient storage and transmission.
To determine the lexicographical order of two strings.

When applying Mo’s algorithm, what is the primary reason for sorting the queries?

To maximize memory usage.
To simplify the implementation of the algorithm.
To minimize the movement of the left and right pointers, thus optimizing the algorithm's overall performance. (correct)
To ensure the queries are processed in chronological order.

What is the core concept behind lazy propagation in segment trees?

Avoiding updates altogether by storing only the initial values.
Distributing updates randomly across the tree to balance the workload.
Performing all updates immediately to ensure data consistency.
Delaying updates to individual nodes until they are absolutely necessary, thus improving efficiency. (correct)

How does the Sprague-Grundy theorem relate to combinatorial game theory?

It states all impartial games are equivalent to Nim games, allowing analysis using Nim-sums. (A) Signup and view all the answers

In computational geometry, what is the primary purpose of using complex numbers to represent points?

To simplify calculations involving rotations and scaling transformations. (B) Signup and view all the answers

When estimating the efficiency of an algorithm, what is the primary factor to consider?

The size of the input data the algorithm will process. (B) Signup and view all the answers

Which of the following scenarios would benefit most from using a 'meet in the middle' approach?

A complete search problem where the search space is too large to explore exhaustively. (A) Signup and view all the answers

How does using set structures generally compare to using sorting algorithms for managing unique elements?

Sets offer faster lookups and insertions of unique elements compared to sorting. (B) Signup and view all the answers

In the context of algorithm design, what does 'pruning the search' typically involve?

Eliminating parts of the search space that cannot lead to a valid solution. (A) Signup and view all the answers

Given an unsorted array, which algorithm provides the most efficient way to find if a specific element is present?

Linear search. (D) Signup and view all the answers

What is the primary advantage of using binary search over linear search?

Binary search has a lower time complexity for large datasets. (C) Signup and view all the answers

Which of the following is NOT a typical operation associated with dynamic arrays?

Automatically sorting elements upon insertion. (C) Signup and view all the answers

Which data structure is most suitable for efficiently determining if an element is a member of a collection, without needing to maintain any specific order?

A set. (C) Signup and view all the answers

In the context of graph theory, what distinguishes Eulerian paths from Hamiltonian paths?

Eulerian paths traverse every edge exactly once, while Hamiltonian paths visit every vertex exactly once. (D) Signup and view all the answers

What is the primary purpose of the Ford-Fulkerson algorithm?

To determine the maximum flow that can be sent from a source to a sink in a network. (C) Signup and view all the answers

How do maximum matchings relate to path covers in graph theory?

A maximum matching directly provides a minimum path cover; the unmatched vertices determine the number of paths needed. (D) Signup and view all the answers

When solving linear recurrences using matrices, what does the matrix's characteristic polynomial help determine?

The closed-form solution of the recurrence. (D) Signup and view all the answers

What is a key application of De Bruijn sequences?

Generating all possible substrings of a given length from an alphabet. (B) Signup and view all the answers

In modular arithmetic, what does finding the modular inverse of an integer a modulo m allow you to do?

Solve linear congruences of the form $ax ≡ b \pmod{m}$. (D) Signup and view all the answers

How does Burnside's Lemma help in solving combinatorial problems?

By providing a method to count the number of orbits under a group action, thus solving problems involving symmetry. (C) Signup and view all the answers

Which of the following is a direct application of Cayley's formula?

Determining the number of possible spanning trees in a complete graph. (A) Signup and view all the answers

A store wants to give a customer change of $0.67 using the fewest number of coins. They have coins of denominations $0.25, $0.10, $0.05, and $0.01. Using a greedy algorithm, how many of each coin will be used?

Two $0.25, one $0.10, one $0.05, two $0.01 (A) Signup and view all the answers

Consider the problem of scheduling tasks where each task has a start time and a finish time. What strategy does a greedy algorithm typically employ to maximize the number of tasks that can be completed?

Schedule tasks in order of earliest finish time. (B) Signup and view all the answers

You're given a set of tasks, each with a deadline and a profit. What is the core idea behind using a greedy approach to maximize total profit if you can only do one task at a time?

Sort tasks by profit in descending order and pick them if you can meet the deadline. (C) Signup and view all the answers

Which of the following scenarios would be best addressed using dynamic programming rather than a greedy algorithm?

Determining the minimum number of coins to make change for a specific amount, where standard denominations may not lead to an optimal greedy solution. (B) Signup and view all the answers

In dynamic programming, what is the primary purpose of memoization?

To store the results of expensive function calls and reuse them when the same inputs occur again. (B) Signup and view all the answers

Why is amortized analysis useful when analyzing the efficiency of algorithms?

It provides a way to analyze algorithms with operations that have varying costs, by averaging the cost over a sequence of operations. (B) Signup and view all the answers

Given an array `[2, 5, 1, 4, 3]`, what would be the 'nearest smaller elements' for each position in the array?

<code>[None, 2, None, 1, 1]</code> (A) Signup and view all the answers

What is the space complexity of a segment tree constructed for an array of size $n$?

$O(4n)$ (B) Signup and view all the answers

In competitive programming, what is the most important factor to consider in addition to the correctness of the algorithm?

The efficiency of the implementation; a correct idea must be translated into correct and efficient code. (D) Signup and view all the answers

Why is C++ often favored in programming contests?

Its standard library offers a wide range of data structures and algorithms, and it is highly efficient. (B) Signup and view all the answers

When might Python be a better choice than C++ in a programming contest?

When the problem involves calculations with very large integers. (B) Signup and view all the answers

What does the `#include <bits/stdc++.h>` line do in a C++ code template for competitive programming?

It includes the entire standard library, making data structures and algorithms readily available. (A) Signup and view all the answers

What is the purpose of the `using namespace std;` line in a C++ program?

It allows you to use classes and functions from the standard library directly without prefixing them with <code>std::</code>. (D) Signup and view all the answers

Which compiler command would you use to compile a C++ file named `test.cpp` into an executable named `test`?

<code>g++ -std=c++11 -O2 -Wall test.cpp -o test</code> (D) Signup and view all the answers

In competitive programming, what does the `-O2` flag typically signify when compiling a C++ program using `g++`?

It applies a moderate level of optimization to improve the program's performance. (C) Signup and view all the answers

Why is it important to have a concise coding style in programming contests?

Concise code helps in writing programs quickly under time constraints. (B) Signup and view all the answers

Which of the following best describes the two core components of competitive programming?

Algorithm design and algorithm implementation. (B) Signup and view all the answers

What is the MOST important criteria for an algorithm in competitive programming?

Efficiency and correctness. (D) Signup and view all the answers

Why is theoretical knowledge of algorithms important for competitive programmers?

It provides a foundation for combining existing techniques with new ideas. (B) Signup and view all the answers

What is the grading process based on in competitive programming?

Testing the implemented algorithm with a set of test cases. (A) Signup and view all the answers

A competitive programmer faces a challenge where they must process a large dataset within a strict time limit. Which of the following strategies would be MOST effective?

Selecting an algorithm with a lower time complexity, even if it's more complex to implement. (D) Signup and view all the answers

A programmer is attempting to solve a problem that requires finding the shortest path in a weighted graph. They are familiar with Dijkstra's algorithm and Bellman-Ford algorithm. Which factor should MOST influence their choice of algorithm?

Whether the graph contains negative edge weights. (B) Signup and view all the answers

Which of the following is the MOST accurate description of the relationship between algorithm design and algorithm implementation in competitive programming?

Algorithm design and implementation are equally important and interdependent, as a good design is useless without a correct implementation, and vice versa. (A) Signup and view all the answers

Why is it beneficial for competitive programmers to have knowledge in a wide range of algorithmic techniques?

To efficiently combine and adapt existing algorithms to solve novel problems. (B) Signup and view all the answers

Flashcards

Random Variables

Variables whose values are the outcomes of a random phenomenon.

Markov Chains

A stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.