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 29.2, Problem 1E
Program Plan Intro
To determinethesingle-pair shortest-path linear program from (29.44)-(29.46) into standard form.
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Use K-map to obtain the minimized product of sums form of the function
f(a,b,c,d) = SEGMA (Q. 1. 2. 3. 4. 6. 8. 9. 10. 11. 3, 15).
Use the editor to format your answer
Simplify the given function using K map
f(a,b,c,d)= ∑m (1, 2, 4, 11, 13, 14, 15) + d (0, 5, 7, 8, 10)
Q2/ Simplify using K- map for the
following :
Simplify the Boolean function
F(A, B, C, D, E) = (0, 2, 4, 6, 9, 13, 21, 23, 25, 29, 31)
%3D
Chapter 29 Solutions
Introduction to Algorithms
Ch. 29.1 - Prob. 1ECh. 29.1 - Prob. 2ECh. 29.1 - Prob. 3ECh. 29.1 - Prob. 4ECh. 29.1 - Prob. 5ECh. 29.1 - Prob. 6ECh. 29.1 - Prob. 7ECh. 29.1 - Prob. 8ECh. 29.1 - Prob. 9ECh. 29.2 - Prob. 1E
Ch. 29.2 - Prob. 2ECh. 29.2 - Prob. 3ECh. 29.2 - Prob. 4ECh. 29.2 - Prob. 5ECh. 29.2 - Prob. 6ECh. 29.2 - Prob. 7ECh. 29.3 - Prob. 1ECh. 29.3 - Prob. 2ECh. 29.3 - Prob. 3ECh. 29.3 - Prob. 4ECh. 29.3 - Prob. 5ECh. 29.3 - Prob. 6ECh. 29.3 - Prob. 7ECh. 29.3 - Prob. 8ECh. 29.4 - Prob. 1ECh. 29.4 - Prob. 2ECh. 29.4 - Prob. 3ECh. 29.4 - Prob. 4ECh. 29.4 - Prob. 5ECh. 29.4 - Prob. 6ECh. 29.5 - Prob. 1ECh. 29.5 - Prob. 2ECh. 29.5 - Prob. 3ECh. 29.5 - Prob. 4ECh. 29.5 - Prob. 5ECh. 29.5 - Prob. 6ECh. 29.5 - Prob. 7ECh. 29.5 - Prob. 8ECh. 29.5 - Prob. 9ECh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5P
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- Q4// Simplify and then implement the Boolean function F(A,B,C,D) = N (1,2,3,5,6,7,9,11,13,15) using POS karnough map , draw the implementation. %3Darrow_forwardthe shortest path from S to C indeed has distance 7, and this path is S -> E -> D -> A -> C.arrow_forwardReduce the following function using k-map technique, F(A, B, C, D) = π(0, 2, 3, 8, 9, 12, 13, 15).arrow_forward
- simplify the following functions using k-map f(a, b, c, d, e) = 1,2, 4, 7, 10, 18, 22, 23, 27, 30.arrow_forwardMinimize the function using Karnaugh map method. F(A, B, C, D) = E(1, 2, 3, 8, 9, 10, 11, 14) + Ed(7, 15).arrow_forwardConsider eight points on the Cartesian two-dimensional x-y plane. a g C For each pair of vertices u and v, the weight of edge uv is the Euclidean (Pythagorean) distance between those two points. For example, dist(a, h) : V4? + 1? = /17 and dist(a, b) = v2? + 0² = 2. Because many pairs of points have identical distances (e.g. dist(h, c) V5), the above diagram has more than one minimum-weight spanning tree. dist(h, b) = dist(h, f) Determine the total number of minimum-weight spanning trees that exist in the above diagram. Clearly justify your answer.arrow_forward
- Simplify the following function into product of sums form using a K-map. F(x,y,z) = ∑(0,5,7)arrow_forwardSimplify the following Boolean functions, using three-variable K-maps: F(A,B,C)= ∑(3,4,5,6,7)arrow_forwardFor the following graph, apply Floyd-Warshall’salgorithm to find out All-pair shortest path. Show step-by-step relaxations for all the nodes as shown in the lecture.Finally, draw the shortest-path graph.arrow_forward
- Consider the following graph G.arrow_forward3. Given the following minterm expansion: F(a, b, c, d) = Em(0, 2, 3, 4, 8, 10, 11, 15) Draw the K-Map Find out all essential prime implicants, do it systematically. Do you need additional loops to cover all the minterms. If yes, find the additional prime implicants. Get the minimum SOP.arrow_forwardDraw a Karnaugh map for the following function; X = Em(0, 2, 3, 6, 7, 8, 10, 11, 14, 15) Then encircle all the octets(groups of 8), quads(Groups of 4) and pairs you can find. Using the circled groups what is X.arrow_forward
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