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11.2-1. Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. f2(A)=11 5 9 ₤3(D)=6 7 D 6 6 (origin) (destination) f2(C)=13 6 ƒ³(E)=7 (a) What are the stages and states for the dynamic programming formulation of this problem? (b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically (similar to Fig. 11.2). In particular, start with the given network, where the answers already are given for fr* (Sn) for four of the nodes; then solve for and fill in f2* (B) and f₁* (O). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use dynamic programming to solve this problem by manually constructing the usual tables for n=3, n=2, and n = 1. (d) Use the shortest-path algorithm presented in Sec. 9.3 to solve this problem. Compare and contrast this approach with the one in parts (b) and (c).

11.2-1. Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. f2(A)=11 5 9 ₤3(D)=6 7 D 6 6 (origin) (destination) f2(C)=13 6 ƒ³(E)=7 (a) What are the stages and states for the dynamic programming formulation of this problem? (b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically (similar to Fig. 11.2). In particular, start with the given network, where the answers already are given for fr* (Sn) for four of the nodes; then solve for and fill in f2* (B) and f₁* (O). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use dynamic programming to solve this problem by manually constructing the usual tables for n=3, n=2, and n = 1. (d) Use the shortest-path algorithm presented in Sec. 9.3 to solve this problem. Compare and contrast this approach with the one in parts (b) and (c).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I know the answer the question a. Kindly give me a nuanced response to the rest. I want to understand what is being done so I can replicate. Thank you very much.
11.2-1. Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. f2(A)=11 5 9 ₤3(D)=6 7 D 6 6 (origin) (destination) f2(C)=13 6 ƒ³(E)=7 (a) What are the stages and states for the dynamic programming formulation of this problem? (b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically (similar to Fig. 11.2). In particular, start with the given network, where the answers already are given for fr* (Sn) for four of the nodes; then solve for and fill in f2* (B) and f₁* (O). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use dynamic programming to solve this problem by manually constructing the usual tables for n=3, n=2, and n = 1. (d) Use the shortest-path algorithm presented in Sec. 9.3 to solve this problem. Compare and contrast this approach with the one in parts (b) and (c).
Transcribed Image Text:11.2-1. Consider the following network, where each number along a link represents the actual distance between the pair of nodes connected by that link. The objective is to find the shortest path from the origin to the destination. f2(A)=11 5 9 ₤3(D)=6 7 D 6 6 (origin) (destination) f2(C)=13 6 ƒ³(E)=7 (a) What are the stages and states for the dynamic programming formulation of this problem? (b) Use dynamic programming to solve this problem. However, instead of using the usual tables, show your work graphically (similar to Fig. 11.2). In particular, start with the given network, where the answers already are given for fr* (Sn) for four of the nodes; then solve for and fill in f2* (B) and f₁* (O). Draw an arrowhead that shows the optimal link to traverse out of each of the latter two nodes. Finally, identify the optimal path by following the arrows from node O onward to node T. (c) Use dynamic programming to solve this problem by manually constructing the usual tables for n=3, n=2, and n = 1. (d) Use the shortest-path algorithm presented in Sec. 9.3 to solve this problem. Compare and contrast this approach with the one in parts (b) and (c).
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