Page Reference: 6,1,0,2,5,3,4,7,8,3,2,9,7 Apply the following algorithms: d. First In First Out e. Optimal Page Replacement f. Least Replacement Used
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- Dijkstra's single-source shortest-path algorithm returns a results grid that contains the lengths of the shortest paths from a given vertex to the other vertices reachable from it. Develop a pseudocode algorithm that uses the results grid to build and return the actual path, as a list of vertices, from the source vertex to a given vertex. (Hint: This algorithm starts with a given vertex in the grid's first column and gathers ancestor vertices, until the source vertex is reached.)1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}This algorithm terminates in O(log n)rounds with good probability. The stepsof the algorithm between lines 7–10 can be performed in parallel which will providea speedup.Make Python Implementation this algorithm in sequential form1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}This algorithm terminates in O(log n)rounds with good probability [3]. The stepsof the algorithm between lines 7–10 can be performed in parallel which will providea speedup.Make a Python Implementation of given algorithm?
- c) Given the following Graph and after applying Dijkstra algorithm, the final table looks as given below. 1 Vertex A B с D E F G H I J K L M 16 3 4 5 T T T T T T T T H known T T T T T 10 18 d. 19 41 11 6 2 20 7 0 15 H с M P G J 10 K 30 D 5 G 7 J 14 K 31 T 10 560 From this information, find out the shortest path from the source vertex B to vertex I. trace the path and also find out the shortest distance.1. Linear Search Algorithm (a) Consider the elements 8 28 38 2 15 49 20 76 4 79 5 81. Show the location of the number 76 on the list by performing analysis using Linear Search Algorithm. while ( ( i ≤ n ) && ( x != ai ) ) a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 8 28 38 2 15 49 20 76 4 79 5 81 (b) Consider the elements 15 9 78 54 13 19 6 2 1 52 87 91 while ( ( i ≤ n ) && ( x != ai ) ) a1 a2 a3 a4 a5 a6 a7 a8 a9 a10 a11 a12 15 9 78 54 13 19 6 2 1 52 87 9113 6. D 20 10 Show the execution of Dijkstra's shortest path algorithm, starting from vertex A. Draw the graph. After each relaxation, you will cross the previous best length and assign a new best length. Which list below shows the list of "best lengths" of the node C? О а. оо,6,5 O b. 0,5 O c. 6,5 O d. c0,6
- The Floyd-Warshall algorithm is a dynamic algorithm for searching the shortest path in a graph. Each vertex pair has its assigned weight. You are asked to draw the initial directed graph and show the tables for each vertex from Mo to Ms by finding all the shortest paths. Below is the algorithm as a guide. Algorithm 1: Pseudocode of Floyd-Warshall Algorithm Data: A directed weighted graph G(V, E) Result: Shortest path between each pair of vertices in G for each de V do | distance|d][d] «= 0; end for each edge (s, p) € E do | distance[s][p] + weight(s, p); end n = cardinality(V); for k = 1 to n do for i = 1 to n do for j = 1 to n do if distancefi][j] > distance/i][k] + distance/k][j] then | distance i]lj] + distancefi|[k] + distance/k|[j]; end end end end Consider the relation R = {(1,4) =4, (2,1)=3, (2,5)=-3, (3,4)=2, (4,2)=1, (4,3)=1, (5,4)=2 } on A = (1,2,3,4,5) solve the Floyd-Warshall Algorithm.Computer Science Write the PSEUDOCODE for an algorithm that takes as input a list of numbers that are sorted in nondecreasing order, and finds the location(s) of the most frequently occurring element(s) in the list. If there are more than one element that is the most frequently occurring, then return the locations of all of them. Analyze the worst-case time complexity of this algorithm and give the O() estimate. (A list is in nondecreasing order if each number in the list is greater than or equal to the number preceding it.)13 D 20 Show the execution of Dijkstra's shortest path algorithm, starting from vertex A. Draw the graph. After each relaxation, you will cross the previous best length and assign a new best length. Which list below shows the list of "best lengths" of the node C? O a. 6,5 O b. 0,6,5 O c. 00,6 O d. 0,5
- Task 4: Print the optimal way to cut Implement the extended_bottom_up_cut_rod() function by following the pseudo code, so that the algorithem can now print the choices (cuts) that lead to the optimal revenue. In [ ]: def extended_bottom_up_cut_rod(prices, n): ### START YOUR CODE ### r = None # Initialize with float('-inf') and List comprehension r[e] = e s = None # Initialize with float('-inf') and List comprehension for j in None: # Specify the range 9 = float('-inf') for i in None: # Specify the range the if statement pass # Implemen r[j] = q ### END YOUR CODE ### return r, s def print_cut_rod_solution(s, n): ### START YOUR CODE ### while None: # Specify the range print(s[n-1], end=',') n = None # update n ### START YOUR CODE ### In [ ]: # Do not change the test code here prices -D [1, 5, 8, 9, 10, 17, 17, 28, 24, за] r, s = extended_bottom_up_cut_rod(prices, 9) print(s) print(r[9]) print_cut_rod_solution(s, 9) Expected output: [1, 2, 3, 2, 2, 6, 1, 2, 3] 25 3,6,a) Given a depth-first search tree T, the set of edges in T are referred to as "tree edges" while those not in T are referred to as "back edges". Modify the implementation of the Depth-First Search algorithm to print out the set of tree edges and the set of back edges for the following graph. 1(0 1 1 0 0 1 o) 210 10 0 0 31 10 1 0 0 1 40 0 10 0 0 0 50 0 0 0 0 1 1 6 10 001 70 0 10 1 1 0 0 1Luby’s Algorithm: 1. Input: G = (V, E)2. Output: MIS I of G3. I ← ∅4. V ← V5. while V = ∅6. assign a random number r(v) to each vertex v ∈ V7. for all v ∈ V in parallel8. if r(v) is minimum amongst all neighbors9. I ← I ∪ {v}10. V ← V \ {v ∪ N(v)}Make Implementation of this algorithm in sequential form in Python. dont copy ans from internet