Question

1. (50) [Dynamic programming: Bellman-Ford shortest path algorithm tracing] Consider the directed graph shown below, and provide answers as specified below. a) Run the Bellman-Ford shortest path algorithm we studied in class to find the shortest path from each node to the node d, and fill in the two-dimensional memoization array M[0..n, V] (provided below, where n = 5 is the number of nodes and V = {a, b, c, d, e} is the set of nodes in the graph). Write the completed memoization table, where each array entry should show the shortest path length and the immediate successor node (e.g., “8/e”). b) For each node v in the graph, backtrack in the memoization table (filled in the previous exercise) from the last entry of the node (i.e., M[n, v]) and write the shortest path and its path length. Write your answer in the following format: “Shortest path from x to d: x - y - z -d (path length = 8)”, where x ? {a, b, c, e}. Note that path length is the sum of the weights of edges in the path. Memoization table: a b c d e 0 1 2 3 4

          1. (50) [Dynamic programming: Bellman-Ford shortest path algorithm tracing] Consider the
directed graph shown below, and provide answers as specified below.
a) Run the Bellman-Ford shortest path algorithm we studied in class to find the shortest path from
each node to the node d, and fill in the two-dimensional memoization array M[0..n, V]
(provided below, where n = 5 is the number of nodes and V = {a, b, c, d, e} is the set of nodes
in the graph). Write the completed memoization table, where each array entry should show the
shortest path length and the immediate successor node (e.g., “8/e”).
b) For each node v in the graph, backtrack in the memoization table (filled in the previous exercise)
from the last entry of the node (i.e., M[n, v]) and write the shortest path and its path length.
Write your answer in the following format: “Shortest path from x to d: x - y - z -d (path
length = 8)”, where x ? {a, b, c, e}. Note that path length is the sum of the weights of edges
in the path.
Memoization table:
a
b
c
d
e
0
1
2
3
4

1. (50) [Dynamic programming: Bellman-Ford shortest path algorithm tracing] Consider the
directed graph shown below, and provide answers as specified below.
a) Run the Bellman-Ford shortest path algorithm we studied in class to find the shortest path from
each node to the node d, and fill in the two-dimensional memoization array M[0..n, V]
(provided below, where n = 5 is the number of nodes and V = a, b, c, d, e is the set of nodes
in the graph). Write the completed memoization table, where each array entry should show the
shortest path length and the immediate successor node (e.g., “8/e”).
b) For each node v in the graph, backtrack in the memoization table (filled in the previous exercise)
from the last entry of the node (i.e., M[n, v]) and write the shortest path and its path length.
Write your answer in the following format: “Shortest path from x to d: x - y - z -d (path
length = 8)”, where x ? a, b, c, e. Note that path length is the sum of the weights of edges
in the path.
Memoization table:
a
b
c
d
e
0
1
2
3
4

Added by Christine G.

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