Data Structures and Algorithms

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Questions and Answers

Consider a scenario where you need to efficiently retrieve data based on unique keys. Which data structure is most suitable for this purpose?

  • Queue
  • Linked List
  • Stack
  • Hash Table (correct)

You're tasked with implementing a system where tasks are processed in the order they are received. Which data structure is most appropriate for managing these tasks?

  • Hash Table
  • Tree
  • Stack
  • Queue (correct)

Given an array, what is the time complexity of inserting an element at a specific index in the middle of the array requiring shifting of existing elements?

  • $O(n)$ (correct)
  • $O(log n)$
  • $O(n log n)$
  • $O(1)$

In a call stack, which element is removed first when a function completes its execution?

<p>The last function call (A)</p> Signup and view all the answers

Which characteristic is most vital when evaluating the efficiency of an algorithm designed to process large datasets?

<p>Time complexity (C)</p> Signup and view all the answers

Given an unsorted array, what is the time complexity of determining if a specific element is present in the array?

<p>$O(n)$ (B)</p> Signup and view all the answers

What does Big-O notation primarily describe about an algorithm?

<p>The upper bound of the algorithm's runtime (D)</p> Signup and view all the answers

Under which condition does QuickSort exhibit its worst-case time complexity?

<p>When the pivot is always the smallest or largest element (D)</p> Signup and view all the answers

Which scenario best illustrates the use of average-case time complexity, denoted as Θ(n), in algorithm analysis?

<p>Estimating the typical execution time of an algorithm over many runs (D)</p> Signup and view all the answers

If the input size of an algorithm with $O(log n)$ complexity increases from 16 to 256, how many times does the execution time approximately increase?

<p>2 times (D)</p> Signup and view all the answers

Flashcards

What is a data structure?

A method to store and organize data in an efficient way.

What is a non-linear data structure?

A data structure where elements do not form a sequential order.

Array O(1) operation

Inserting an element at the end of the array.

LIFO data structure

Last In, First Out (LIFO) principle.

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What is an algorithm?

A sequence of steps to solve a problem.

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Unsorted array search complexity

O(n) - each element must be checked.

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What Big-O notation represents

Represents the upper bound of the algorithm's growth rate.

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QuickSort best-case time complexity

O(n log n) - efficient partitioning on average.

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Average-case complexity

Θ(n) represents the average-case complexity.

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O(log n) impact

Increases logarithmically, not linearly.

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Study Notes

  • Data structures are used to store and organize data efficiently.
  • Stacks, queues, and arrays are linear data structures, while trees are not.
  • Insertion at the end of an array has O(1) time complexity.
  • Stacks operate on the Last In, First Out (LIFO) principle.
  • An algorithm is a set of well-defined steps for solving a problem.
  • Searching an element in an unsorted array has a time complexity of O(n).
  • Big-O notation represents the worst-case time complexity.
  • QuickSort has a best-case time complexity of O(n log n).
  • Θ(n) notation represents average-case complexity.
  • An algorithm with O(log n) complexity experiences a logarithmic increase in execution time when the input size doubles.
  • Bubble Sort has a worst-case time complexity of O(n²).
  • Binary Search has a time complexity of O(log n).
  • Counting Sort is not based on comparison.
  • Insertion Sort is effective for nearly sorted data.
  • Binary Search is efficient on sorted data.

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