MHB Find the shortest path from 1 to 10.

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The shortest path from 1 to 10 was calculated using the formula $v(i)= \min \{c_{ij}+v(j) \}, v(N)=0$, resulting in the path $1 \rightarrow 2 \rightarrow 6 \rightarrow 9 \rightarrow 10$ with a cost of 7. A participant questioned the accuracy of this result, suggesting an alternative path of $1 \rightarrow 2 \rightarrow 6 \rightarrow 8 \rightarrow 10$. The discussion revolves around validating the shortest path and its associated cost. Clarification on the cost and path accuracy is sought. The conversation highlights the importance of verifying calculations in pathfinding problems.
mathmari
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Hey! :o

Given the following:
View attachment 1961
I have to find the shortest path from 1 to 10.
I used the formula: $v(i)= \min \{c_{ij}+v(j) \}, v(N)=0$ and I found the shortest path is $1 \rightarrow 2 \rightarrow 6\rightarrow 9 \rightarrow 10$ and the cost is $7$.
Is this correct?
 

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mathmari said:
Hey! :o

Given the following:
View attachment 1961
I have to find the shortest path from 1 to 10.
I used the formula: $v(i)= \min \{c_{ij}+v(j) \}, v(N)=0$ and I found the shortest path is $1 \rightarrow 2 \rightarrow 6\rightarrow 9 \rightarrow 10$ and the cost is $7$.
Is this correct?

Hi. Did you mean $1 \rightarrow 2 \rightarrow 6\rightarrow 8 \rightarrow 10$?
 
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