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 <113218619+FabianaCampanari@users.noreply.github.com>
Date: Wed, 14 May 2025 12:54:44 -0300
Subject: [PATCH] Delete class__12- Shortest Path-Dijkstra's
 Algorithm/exec_2-Applying Dijkstra's Algorithm to the Shortest Path
 Problem/Example 2- Applying Dijkstra's Algorithm to the Shortest Path
 Problem.md
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Signed-off-by: Fabiana 🚀  Campanari <113218619+FabianaCampanari@users.noreply.github.com>
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-
-## Exercise 2: 
-
-### Statement:
-
-Applying Dijkstra's Algorithm to the Shortest Path Problem
-
-**Step 1:** Assign the value 0 to the source node (1) and ∞ (infinity) to all other nodes, as shown in the graph:
-
-
-INSERIR O GRAFO
-
-
-### Dijkstra's Algorithm – Node Labeling Process
-
-- **Node labeling** is the process of assigning values to nodes to represent the shortest known distance from the source node at each step of the algorithm.
-- At each iteration, nodes are divided into two sets:
-    - **Labeled nodes (closed):** Nodes for which the shortest path from the source has been definitively found.
-    - **Unlabeled nodes (open):** Nodes for which the shortest path is still being determined.
-
-
-#### Steps:
-
-1. **Initialization:**
-    - Set \$ R = \{\} \$ (the set of labeled nodes is empty).
-    - Set \$ NR = \{1, 2, 3, ..., n\} \$ (all nodes are initially unlabeled).
-    - Assign 0 to the source node and ∞ to all others.
-2. **While \$ NR \neq \emptyset \$:**
-    - Select the unlabeled node with the smallest value (node \$ k \$).
-    - Move node \$ k \$ to the set of labeled nodes \$ R \$.
-    - For each unlabeled successor node \$ j \$ of \$ k \$:
-        - Add the value of node \$ k \$ to the cost of the arc from \$ k \$ to \$ j \$.
-        - If this new value is less than the current value of node \$ j \$, update node \$ j \$ with the new value and set \$ k \$ as its predecessor.
-
-#### Importance of "Where I Came From" and "Where I Am":
-
-- **Where I came from:** In the tableau, the rows indicate the predecessor node, which is crucial for reconstructing the shortest path at the end.
-- **Where I am:** The columns represent the current node being evaluated in each iteration.
-
----
-
-### Step-by-Step Tableaus
-
-| 1* | 2* | 3* | 4* | 5* | 6 | 7* | 8* | 9* |
-| :-- | :-- | :-- | :-- | :-- | :-- | :-- | :-- | :-- |
-| 0 | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
-| - | (1, 11) | (1, 9) | ∞ | ∞ | ∞ | ∞ | ∞ | ∞ |
-| - | (1, 11) | - | (3, 17) | (3, 15) | ∞ | ∞ | ∞ | ∞ |
-| - | - | - | (2, 15) | (3, 15) | ∞ | ∞ | ∞ | ∞ |
-| - | - | - | - | (3, 15) | (4, 21) | (4, 21) | (5, 19) | ∞ |
-| - | - | - | - | - | (4, 21) | (4, 20) | (5, 19) | (8, 25) |
-| - | - | - | - | - | (4, 21) | (4, 20) | - | (7, 24) |
-
-**Minimum Path:**
-1 → 2 → 4 → 7 → 9 = 24
-
----
-
-### Summary
-
-- **Node labeling** (rotulação dos nós) is a fundamental part of Dijkstra's algorithm, systematically updating the shortest distances and predecessors for each node.
-- The tableau tracks, for each node, both the current shortest distance and the node from which that distance was reached.
-- At the end, by tracing back from the destination node using the predecessors, you reconstruct the shortest path.
-
-