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 4.1, Problem 5E
Program Plan Intro
To determine the maximum subarray of the form
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We have a MxN 2D matrix. Initialize the array with user inputs. First, find the transpose of the matrix. Additionally, if it’s a square matrix, calculate the sum of right diagonal. Write an algorithm to solve this problem. Additionally, find the time complexity of the algorithm you have written. DO NOT WRITE THE CODE.
4.1-5
Use the following ideas to develop a nonrecursive, linear-time algorithm for the
maximum-subarray problem. Start at the left end of the array, and progress toward
the right, keeping track of the maximum subarray seen so far. Knowing a maximum
subarray of A[1.. j], extend the answer to find a maximum subarray ending at in-
dex j +1 by using the following observation: a maximum subarray of A[1 .. j + 1]
is either a maximum subarray of A[1…. j] or a subarray A[i …. j + 1], for some
1 ≤ i ≤ j + 1. Determine a maximum subarray of the form A[i.. j + 1] in
constant time based on knowing a maximum subarray ending at index j.
20. Given a 4-element array with distinct elements, say {x1, x2, x3, x4}, it is known that x1 is not the minimum. How to use 2 comparisons to find an element that is neither the maximum nor the minimum? Solution:
Chapter 4 Solutions
Introduction to Algorithms
Ch. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5E
Ch. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.4 - Prob. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Prob. 8ECh. 4.4 - Prob. 9ECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4 - Prob. 1PCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6P
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- Run mergesort for large random arrays, and make an empirical determination of the average length of the other subarray when the first subarray exhausts, as a function of N (the sum of the two subarray sizes for a given merge).arrow_forwardCreate a 3-by-3 matrix. A = [1 7 3; 2 9 12; 5 22 7]; Calculate the right eigenvectors, V, the eigenvalues, D, and the left eigenvectors, W. [V,D,W] eig(A) %3!arrow_forwardGive a clear description of an efficient algorithm for finding the k smallest elements of a very large n-element vector. Compare its running time with that of other plausible ways of achieving the same result, including that of applying k times your solution for part (a). [Note that in part (a) the result of the function consists of one element, whereas here it consists of k elements. As above, you may assume for simplicity that all the elements of the vector are different.]arrow_forward
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