Find the shortest path from 1 to 10.

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In summary, the shortest path in this context is the most efficient and direct route from the starting point to the destination, considering any obstacles or limitations. Factors such as distance, obstacles, and constraints are taken into account when determining the shortest path. Commonly used methods include Dijkstra's algorithm, A* search algorithm, and Bellman-Ford algorithm. Real-world applications include transportation route planning, navigation systems, and logistics and supply chain management. While it is usually possible to find the shortest path between two points, there may be certain scenarios where this is not possible due to physical barriers or restrictions.
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mathmari
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Hey! :eek:

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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  • #2
mathmari said:
Hey! :eek:

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 $1 \rightarrow 2 \rightarrow 6\rightarrow 8 \rightarrow 10$?
 

Related to Find the shortest path from 1 to 10.

1. How do you define the "shortest path" in this context?

In this context, the shortest path refers to the most efficient and direct route from the starting point (1) to the destination (10), taking into account any obstacles or limitations.

2. What factors are considered when determining the shortest path?

The factors that are typically considered when determining the shortest path include the distance between the starting and ending points, any obstacles or barriers that may need to be navigated around, and any constraints such as speed limits or terrain difficulties.

3. What methods or algorithms are commonly used to find the shortest path?

Some commonly used methods or algorithms for finding the shortest path include Dijkstra's algorithm, A* search algorithm, and Bellman-Ford algorithm. These methods use different approaches to determine the most efficient path from one point to another.

4. Are there any real-world applications for finding the shortest path?

Yes, there are many real-world applications for finding the shortest path. Some examples include route planning for transportation systems, navigation systems in cars or on mobile devices, and logistics and supply chain management for businesses.

5. Is it always possible to find the shortest path between two points?

In most cases, it is possible to find the shortest path between two points. However, there are certain scenarios where this may not be possible, such as when there are no available paths between the two points due to physical barriers or restrictions.

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