Coding Interviews: Essential Algorithms
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Questions and Answers

What is an example of a real-life application of BFS algorithm?

  • Insertion sort
  • Chess algorithms (correct)
  • Sorting algorithms
  • Traveling salesman problem
  • What is the best-case runtime of Insertion sort?

  • O(n log(n))
  • O(log n)
  • O(n) (correct)
  • O(n^2)
  • What is the time complexity of Merge sort?

  • O(n^2)
  • O(n log(n)) (correct)
  • O(n)
  • O(log n)
  • What is a characteristic of Quick sort?

    <p>It is a recursive algorithm</p> Signup and view all the answers

    What is the primary goal of a Greedy algorithm?

    <p>To find a relatively accurate solution</p> Signup and view all the answers

    What is the problem that involves finding the shortest route that visits each city once and returns to the starting city?

    <p>The traveling salesman problem</p> Signup and view all the answers

    What is the time complexity of binary search?

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

    What is the purpose of using depth-first search (DFS)?

    <p>To traverse through trees and graphs</p> Signup and view all the answers

    Which of the following algorithms has a runtime of O(n)?

    <p>Linear search</p> Signup and view all the answers

    What is the main difference between DFS and BFS?

    <p>DFS goes as far down one branch as possible, while BFS looks at every node at one level before continuing further down</p> Signup and view all the answers

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

    <p>Binary search has a better time complexity</p> Signup and view all the answers

    What is the time complexity of breadth-first search (BFS)?

    <p>$O(V + E)$</p> Signup and view all the answers

    Study Notes

    • There are seven essential algorithms to know for coding interviews, categorized into three search algorithms and three sorting algorithms, plus a special type of algorithm called a greedy algorithm.

    • Binary search is a search algorithm used to find the position of a specific element in a sorted list, with a runtime of O(logn), making it more efficient than linear search.

    • Linear search has a runtime of O(n), making it inefficient when scaled, whereas binary search is optimal for computer algorithms.

    • Depth-first search (DFS) is a search algorithm used to traverse through trees and graphs, with a time complexity of O(V + E), where V represents total nodes and E represents total branches.

    • DFS starts at the root node, goes as far down one branch as possible, and then backtracks to an unvisited branch, repeating the process until the entire graph is traversed.

    • One real-life example of DFS is solving a maze, where the algorithm looks through each path to find the exit, backtracking when hitting a wall.

    • Breadth-first search (BFS) is a search algorithm that looks at every node at one level before continuing further down, with a time complexity of O(V + E), similar to DFS.

    • BFS starts at the root node, adds it to the visited array, and adds all neighboring nodes to the neighbors queue, repeating the process until all nodes are visited.

    • One real-life example of BFS is in Chess algorithms, where the program predicts the best move by looking at each possible move and its subsequent possibilities.

    • Insertion sort is a simple sorting algorithm that works by comparing each element in the list and swapping them if necessary, with a best-case runtime of O(n) and worst-case runtime of O(n^2).

    • Insertion sort is best used for lists that are already mostly sorted or for smaller lists, as it becomes problematic for larger, more unordered lists.

    • Merge sort is a sorting algorithm that breaks down the problem into smaller problems, solving each smaller problem, and is better suited for larger lists.- Merge sort is a recursive algorithm with a run-time of O(n log(n)) in both best and worst cases.

    • Merge sort works by splitting an array in half, sorting each half, and then merging the sorted halves back together.

    • For smaller lists, insertion sort has a runtime closer to O(n), while merge sort has a runtime of O(n log(n)), making insertion sort a better choice.

    • For larger lists, insertion sort has a runtime closer to O(n^2), while merge sort remains at O(n log(n)), making merge sort a better choice.

    • Quick sort is a divide-and-conquer algorithm that is also recursive, with a best-case run-time of O(n log(n)) and a worst-case run-time of O(n^2).

    • Quick sort works by selecting a pivot element, partitioning the array around the pivot, and recursively sorting the sub-arrays.

    • Quick sort has a space complexity of O(log n), making it more memory-efficient than merge sort, which has a space complexity of O(n).

    • However, quick sort's performance relies heavily on optimized code, and small mistakes can greatly impact its performance.

    • Greedy algorithms make the best possible choice at each local decision point, but may not always find the optimal solution.

    • Greedy algorithms are used when finding the optimal solution is not possible, and a relatively accurate solution is acceptable.

    • The traveling salesman problem is an example of a problem where a greedy algorithm can be used to find a relatively efficient solution.

    • The traveling salesman problem involves finding the shortest route that visits each city once and returns to the starting city.

    • The number of possible routes in the traveling salesman problem grows exponentially with the number of cities, making it impractical to find the optimal solution.

    • A greedy algorithm can be used to find a relatively efficient solution by always choosing the next city that is closest to the current city.

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    Description

    Learn about the seven essential algorithms you need to know for coding interviews, including search algorithms, sorting algorithms, and a greedy algorithm. Understand the time and space complexities of each algorithm and their real-life applications.

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