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4) For each of the following assume m, n, a, b are positive integers. a. Write...
Show Work P4. (25 pts) [Ch5. Divide and Conquer] a. (10 pts) Briefly describe a divide...
Show Work
P4. (25 pts) [Ch5. Divide and Conquer] a. (10 pts) Briefly describe a divide and conquer algorithm for computing the sum of n positive integers. You may assume the integers all have the same number of digits which is a constant. b. (5 pts) Write out a recurrence for your solution, and identify which case of the Master method applies. c. (10 pts) Solve the recurrence in (b) using back-substitution. Show your work. Is the divide and conquer...
7. (10) Given an array of integers A[1..n], such that, for all i, 1 <i< n,...
7. (10) Given an array of integers A[1..n], such that, for all i, 1 <i< n, we have |Ali]- Ali+1]| < 1. Let A[1] = and Alny such that r < y. Using the divide-and-conquer technique, describe in English algorithm to find j such that Alj] z for a given value z, xz < y. Show that your algorithm's running time is o(n) and that it is correct o(n) search an 2 8. (10) Solve the recurrence in asymptotically tight...
Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a...
Suppose that, in a divide-and-conquer algorithm, we always
divide an instance of size n of a problem into 5 sub-instances of
size n/3, and the dividing and combining steps take a time
in Θ(n n). Write a recurrence equation for the running time T
(n) , and solve the
equation for T (n)
2. Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into 5 sub-instances of size n/3, and the dividing...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n...
Suppose the following is a divide-and-conquer algorithm for some problem. "Make the input of size n into 3 subproblems of sizes n/2 , n/4 , n/8 , respectively with O(n) time; Recursively call on these subproblems; and then combine the results in O(n) time. The recursive call returns when the problems become of size 1 and the time in this case is constant." (a) Let T(n) denote the worst-case running time of this approach on the problem of size n....
(13 pts) Given an array AlI,2,. .. ,n] integers, design and analyze an efficient Divide-and-Conqu...
(13 pts) Given an array AlI,2,. .. ,n] integers, design and analyze an efficient Divide-and-Conquer algorithm to find some i and j, where j > 1, such that A[j]-Ali] is maximized. For example, given A 6, 1,3,8,4,5, 12,6], the maximum value of AL] - Ali] for j > i is 12-1 11 where j -7 and i 2. Give the underlying recurrence relation for your algorithm and analyze its running time. You should carefully state all details of your algorithm:...
1. Design and write a Divide& Conquer algorithm that, given an array A of n distinct...
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.
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers,...
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers, you want to find out whether there is an index i for which Al = i. Give a divide-and-conquer algorithm that runs in time O(log n). Provide only the main idea and the runtime analysis.
I already solved part A and I just need help with part B 1. Matrix Multiplication...
I already solved part A and I just need help with part B
1. Matrix Multiplication The product of two n xn matrices X and Y is a third n x n matrix 2 = XY, with entries 2 - 21; = xixYk x k=1 There are n’ entries to compute, each one at a cost of O(n). The formula implies an algorithm with O(nº) running time. For a long time this was widely believed to be the best running...
Let A be an array containing n numbers (positive and negative). Develop a divide and conquer algo...
need help in this algorithm question
Let A be an array containing n numbers (positive and negative). Develop a divide and conquer algorithm that finds the two indices 1 sisjsn such that A[k] (the sum of the elements from i to j) is maximized. For example, in the array A [10,-5,-6,5, 7,-2,4, -11], the sub-array A[4:6] has the sum 5+ 7-2+4-14 and no other sub-array contains elements that sum to a value greater than 14, so for this input the...
Consider an array of length n containing positive and negative integers in random. Write a C++...
Consider an array of length n containing positive and negative integers in random. Write a C++ code that rearranges the integers so that the negative integers appear before the positive integers. Your solution should use: a. O(n^2) b. O(n)
Show Work
P4. (25 pts) [Ch5. Divide and Conquer] a. (10 pts) Briefly describe a divide and conquer algorithm for computing the sum of n positive integers. You may assume the integers all have the same number of digits which is a constant. b. (5 pts) Write out a recurrence for your solution, and identify which case of the Master method applies. c. (10 pts) Solve the recurrence in (b) using back-substitution. Show your work. Is the divide and conquer...
7. (10) Given an array of integers A[1..n], such that, for all i, 1 <i< n, we have |Ali]- Ali+1]| < 1. Let A[1] = and Alny such that r < y. Using the divide-and-conquer technique, describe in English algorithm to find j such that Alj] z for a given value z, xz < y. Show that your algorithm's running time is o(n) and that it is correct o(n) search an 2 8. (10) Solve the recurrence in asymptotically tight...
Suppose that, in a divide-and-conquer algorithm, we always
divide an instance of size n of a problem into 5 sub-instances of
size n/3, and the dividing and combining steps take a time
in Θ(n n). Write a recurrence equation for the running time T
(n) , and solve the
equation for T (n)
2. Suppose that, in a divide-and-conquer algorithm, we always divide an instance of size n of a problem into 5 sub-instances of size n/3, and the dividing...
(13 pts) Given an array AlI,2,. .. ,n] integers, design and analyze an efficient Divide-and-Conquer algorithm to find some i and j, where j > 1, such that A[j]-Ali] is maximized. For example, given A 6, 1,3,8,4,5, 12,6], the maximum value of AL] - Ali] for j > i is 12-1 11 where j -7 and i 2. Give the underlying recurrence relation for your algorithm and analyze its running time. You should carefully state all details of your algorithm:...
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.
1. (16 pts.) Sorted Array Given a sorted array A of n (possibly negative) distinct integers, you want to find out whether there is an index i for which Al = i. Give a divide-and-conquer algorithm that runs in time O(log n). Provide only the main idea and the runtime analysis.
I already solved part A and I just need help with part B
1. Matrix Multiplication The product of two n xn matrices X and Y is a third n x n matrix 2 = XY, with entries 2 - 21; = xixYk x k=1 There are n’ entries to compute, each one at a cost of O(n). The formula implies an algorithm with O(nº) running time. For a long time this was widely believed to be the best running...
need help in this algorithm question
Let A be an array containing n numbers (positive and negative). Develop a divide and conquer algorithm that finds the two indices 1 sisjsn such that A[k] (the sum of the elements from i to j) is maximized. For example, in the array A [10,-5,-6,5, 7,-2,4, -11], the sub-array A[4:6] has the sum 5+ 7-2+4-14 and no other sub-array contains elements that sum to a value greater than 14, so for this input the...
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