1) What is dynamic programming? How it is different than divide and conquer solutions? Which of the problems can be solved with dynamic programming?
Following is the answer:
Dynamic Programming
While in divide and conquer, It works by dividing the problem into sub-problems, and conquer each sub-problem recursively and combine these solutions.
We face many complex problems where the repetitions of the same subproblem in the recursion take place. To avoid multiple calculations of the subproblem and to save computation time, dynamic programming is used, in which problems are solved by breaking down problems into simpler subproblems, solving each of those subproblems just once, and storing their solutions and reuse it.
example:
1) What is dynamic programming? How it is different than divide and conquer solutions? Which of...
Analysis Divide & Conquer: Analyze the complexity of algorithm A1 where the problem of size n is solved by dividing into 4 subprograms of size n - 4 to be recursively solved and then combining the solutions of the subprograms takes O(n2) time. Determine the recurrence and whether it is “Subtract and Conquer” or “Divide and Conquer“ type of problem. Solve the problem to the big O notation. Use the master theorem to solve, state which theorem you are using...
7. Explain Dynamic Program ming algorithm in contrast to Divide and Conquer algorithm Discuss the advantages of Dynamic Programming over the other iophs method. 5pts) Then find the LCS of the following two strings X ABCBDAB) and Y- (BDCABA) (Explain the algorit g two strings. (He pts) thm as well 8. a) Explain the difference between recursive and iterative algorithms.(2 pts) b) The recursive Euclid algorithm is given as below: int GCD(int a, int b) f (b0) return a else...
What is dynamic programming? How to solve a dynamic-programming problem?
5. Dynamic Programming (a) Given a set of four matrices for the following dimensions: We need to compute Al* A2 A3 A4 Al=2X3; A2=3X5; A3=5X2: A4=2X4 Find the order in which the matrix pairs should be multiplied to produce the optimum number of operations. Show all your steps (10) (b) For the problems given below, determine whether it is more efficient to use a divide and conquer strategy or a dynamic programming strategy. Give the reasons for your choice (5*3=15)...
A divide-and-conquer algorithm solves a problem by dividing the input (of size n>1, T(1) =0) into two inputs half as big using n/2-1 steps. The algorithm does n steps to combine the solutions to get a solution for the original input. Write a recurrence equation for the algorithm and solve it.
A divide-and-conquer algorithm solves a problem by dividing the input (of size n>1, T(1) =0) into two inputs half as big using n/2-1 steps. The algorithm does n steps to combine the solutions to get a solution for the original input. Write a recurrence equation for the algorithm and solve it.
1) Which Design Technique was used to produce Kruskal's Algorithm? (Select the answer from the following options and prove your choice): a) Dynamic Programming b) Greedy c) Divide and Conquer d) Linear Programming PLEASE EXPLAIN IT IN DETAIL
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct integers which is already sorted into ascending order, will find if there is some i such that Ali] in worst-case 0(log n) time.
Please give me a divide and conquer algorithm that has
runtime better than O(n^2) along with justification. Also please do
a runtime analysis on this algorithm.
Please DONT copy and paste other's
solution.THANKS
3. Give the best algorithm you can to convert an n digit number base 10 into binary. Here, we are counting operations on single digits as single steps, not arithmetic operations. You can use any of the multiplication algorithms we described in class.)
Using sorting as an algorithm solving specific problem and compare their method of solving it and performances’ tradeoffs in terms of its time complexity. compare its performance using different approaches (three approaches) such as (divide and conquer, dynamic programming, brute force, greedy approach ). show which approach solve the problem best. Use sorting as an example and compare .