Insertion Sort Analysis
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Questions and Answers

In the worst case scenario, how does the number of comparisons in insertion sort behave?

  • Increases quadratically (correct)
  • Decreases linearly
  • Remains constant
  • Doubles exponentially

For the best case scenario in insertion sort, how many comparisons are executed per outer loop?

  • Thrice
  • Never
  • Twice
  • Once (correct)

What happens to the number of comparisons made by insertion sort in the average case compared to decreasing arrays?

  • Halved (correct)
  • Remains the same
  • Increases exponentially
  • Doubled

Which sorting algorithm is known for 'bubbling up' the largest element to the last position in each pass?

<p>Bubble sort (A)</p> Signup and view all the answers

What is the time complexity of the best and average case scenarios in Quick Sort?

<p>$O(n ext{ log } n)$ (D)</p> Signup and view all the answers

In Merge Sort, how is the original array split before sorting?

<p>Into two equal halves (A)</p> Signup and view all the answers

What is the time complexity of Prims Algorithm when using a Priority Queue?

<p>O(E log V) (B)</p> Signup and view all the answers

In preorder traversal of a binary tree, what is visited first?

<p>Root (B)</p> Signup and view all the answers

What is the main purpose of A* algorithm?

<p>Finding the shortest path in a graph from a start to a goal node (A)</p> Signup and view all the answers

What defines the weight of a tree in the context of minimum spanning trees?

<p>Sum of weights on all its edges (C)</p> Signup and view all the answers

Which algorithm is used to find the shortest paths from a single source vertex to all other vertices in a weighted graph with non-negative edge weights?

<p>Dijkstra's algorithm (D)</p> Signup and view all the answers

What kind of solution does Greedy Search construct in optimization problems?

<p>Locally optimal (C)</p> Signup and view all the answers

Flashcards

Worst Case Scenario: Insertion Sort

In the worst-case scenario, for each element in the unsorted portion of the array, insertion sort might need to compare it against all elements in the already sorted portion.

Best Case Scenario: Insertion Sort

For sorted arrays, insertion sort performs only one comparison per outer loop because it finds the correct position for an element in the first iteration.

Average Case Scenario: Insertion Sort

The average case scenario in insertion sort has about half the comparisons needed in decreasing arrays because it will find the correct position for an element faster.

Bubble Sort

Bubble sort repeatedly steps through the list, comparing adjacent elements and swapping them if they are in the wrong order, effectively 'bubbling up' the largest element to the last position.

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Best & Average Time Complexity: Quick Sort

Quick Sort's best and average case time complexity is $O(n \log n)$. This means that the time required to sort an array grows logarithmically with the size of the array.

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Merge Sort: Splitting the Array

Merge sort divides the input array into two equal halves recursively. Sorting is then performed on each half independently, and finally, the sorted halves are merged into a single sorted array.

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Prim's Algorithm with Priority Queue

When using a Priority Queue, the time complexity of Prim's Algorithm becomes $O(E \log V)$. It depends on the number of edges (E) and vertices (V) in the graph.

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Preorder Traversal: Root First

In preorder traversal, the root node of a binary tree is visited first, followed by the left subtree, and then the right subtree.

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A* Algorithm Purpose

A* algorithm aims to find the shortest path from a start to a goal node in a graph by combining information about the distance traveled so far and the estimated distance to the goal.

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Minimum Spanning Tree: Weight

The weight of a tree in the context of a minimum spanning tree is the sum of the weights of all its edges.

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Dijkstra's Algorithm

Dijkstra's algorithm is used to find the shortest paths from a single source vertex to all other vertices in a weighted graph where edge weights are non-negative.

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Greedy Search

In optimization problems, the Greedy Search algorithm always makes the locally optimal choice at each step, hoping that ultimately this will lead to a globally optimal solution. It might not always work optimally.

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