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 33.2, Problem 3E
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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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- You are given an adjacency list representation of a weighted directed graph G = (V, E) with n vertices, m edges, and no negative cycles. Furthermore, you are given two designated vertices s, t ∈ V and a subset P ⊆ E of the edges are labeled as “premium” edges. Describe a O(mn)-time algorithm to find the shortest path from s to t that uses at most one premium edge (along with any number of non-premium edges).arrow_forwardRun the code to determine experimentally the distribution of the number of components in random graphs of various types by building a large number of graphs and producing a histogram.arrow_forwardThe book demonstrated that a poisoned reverse will prevent the count-to-infinity problem caused when there is a loop involving three directly connected nodes. However, other loops are possible. Will the poisoned reverse solve the general case count-to-infinity problem encountered by Bellman-Ford? -Yes, the poisoned reverse will prevent a node from offering a path that includes preceding nodes in the loop. -It will not, preceeding nodes may still be used in the computation of the distance vector offered by a given node.arrow_forward
- Give 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_forwardFully evaluate the following ʎ-term so that no further 3-reduction is possible. (ʎr yr y) (ʎr. y)) uarrow_forwardI am trying to work with some generic search algorithms in a coding homework, and I am having trouble understanding some of it. Here are my questions: 1. For this linear search algorithm below I am trying to send an array of x and y cordinate points into it and search to see if a specific x, y point is in the array, but I don't know how to send the points into the linear search function. By the way, I am using a struct point type for the array of points and the point I am looking for. (The below code is an exact example from our teacher during a lecture.) void* linearSearchG(void* key, void* arr, int size, int elemSize, int(*compare)(void* a, void* b)) { for (int i = 0; i < size; i++) { void* elementAddress = (char*)arr + i * elemSize; if (compare(elementAddress, key) == 0) return elementAddress; } return NULL; } 2. I forgot what this line of code specifically does: void* elementAddress = (char*)arr + i * elemSize; I need to code this myself, so if you could explain…arrow_forward
- For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. START FUNCTION def binary_search(f,domain, MAX =…arrow_forwardFor this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. START FUNCTION def binary_search(f,domain, MAX =…arrow_forwardThe function Ecol_M M in the Python programme that implements this approach discovers the minimum edge colours for a graph that is passed to it in the form of an incidence matrix. To discover the maximal matching in the graph, we utilise the Maximal Match function from the earlier constructed module MATCH within this function. The list edges is used to retain uncolored edges, while the list edge color is used to hold the current edge colours. The while loop continues to run until the edges list is empty, at which point all edges have been coloured. At each iteration, the graph is reduced by removing the columns associated with the matched edges.arrow_forward
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