Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 33.4, Problem 1E
Program Plan Intro
To identify the flaw in Professor W’s scheme which states that at most 6 points can reside in
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Given an integer n and an array a of length n, your task is to apply the following mutation to a:
Array a mutates into a new array b of length n. For each i from 0 to n - 1, b[i] = a[i - 1] + a[i] + a[i + 1]. If some element in the sum a[i - 1] + a[i] + a[i + 1] does not exist, it should be set to 0. For example, b[0] should be equal to 0 + a[0] + a[1].
Let A be an array of numbers. In the maximum sub-array problem, your goal is to determine the sub-array A[x . . . y] of consecutive terms for which the sum of the entries is as large as possible.
For example, if A = [−2, −3, 4, −1, −2, 1, 5, −3], the maximum sub-array is [4, −1, 2, 1, 5], and the largest possible sum is S = 4 − 1 − 2 + 1 + 5 = 7.
Suppose A = [1, 2, −4, 8, 16, −32, 64, 128, −256, 512, 1024, −2048]. Determine S, the largest possible sum of a sub-array of A.
Consider an array A of N values (N entered by the user). Write a C program that creates a second array B such that the i-th element of B, i.e., B[i] is equal to A[0] *A[1] * A[2] * ... A[i]; In other words:- B[0] = A[0]- B[1] = A[0] * A[1];- B[2] = A[0] * A[1] * A[2];- B[3] = A[0] * A[1] * A[2] * A[3]- ....etc.For this exercise, we would like to implement two solutions and compare their complexity /performance in terms of computation time.Solution 1: Implement blindly the following algorithms: for each element B[i], compute A[0] *A[1] * A[2] * .... *A[i] and save the result in B[i];To test the solution, create an array A of 1000 elements and initialize each of its elements with arandom value (instead of asking the user to . To do that, use the function rand, which, every timecalled, returns a random number
Questions:- How long does your program take to produce the solution?- Analyze the solution above and explain why it is taking long time. What are the mainfactors that affect how long…
Chapter 33 Solutions
Introduction to Algorithms
Ch. 33.1 - Prob. 1ECh. 33.1 - Prob. 2ECh. 33.1 - Prob. 3ECh. 33.1 - Prob. 4ECh. 33.1 - Prob. 5ECh. 33.1 - Prob. 6ECh. 33.1 - Prob. 7ECh. 33.1 - Prob. 8ECh. 33.2 - Prob. 1ECh. 33.2 - Prob. 2E
Ch. 33.2 - Prob. 3ECh. 33.2 - Prob. 4ECh. 33.2 - Prob. 5ECh. 33.2 - Prob. 6ECh. 33.2 - Prob. 7ECh. 33.2 - Prob. 8ECh. 33.2 - Prob. 9ECh. 33.3 - Prob. 1ECh. 33.3 - Prob. 2ECh. 33.3 - Prob. 3ECh. 33.3 - Prob. 4ECh. 33.3 - Prob. 5ECh. 33.3 - Prob. 6ECh. 33.4 - Prob. 1ECh. 33.4 - Prob. 2ECh. 33.4 - Prob. 3ECh. 33.4 - Prob. 4ECh. 33.4 - Prob. 5ECh. 33.4 - Prob. 6ECh. 33 - Prob. 1PCh. 33 - Prob. 2PCh. 33 - Prob. 3PCh. 33 - Prob. 4PCh. 33 - Prob. 5P
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