The algorithm that efficiently calculates the single source shortest paths in a Directed Acyclic Graph (DAG) is the Topological Sort algorithm. Here are the steps:

1. Topologically sort the nodes of the graph. This can be done using Depth-First Search (DFS) or Breadth-First Search (BFS). The idea is to visit each node once and only once, and to visit a node before its successors. In a DAG, a topological sort is always possible and results in a linear ordering of the nodes.

2. Initialize the distance to the source node as 0 and the distance to all other nodes as infinity. This is because we don't know the shortest path to any node yet, except for the source node (the shortest path from a node to itself is always 0).

3. For each node in the topologically sorted order, relax all of its adjacent nodes. To "relax" an edge means to update the shortest path to the destination node of that edge if a shorter path has been found. This is done by comparing the current known distance to the destination node with the distance to the source node plus the weight of the edge. If the latter is smaller, then we have found a shorter path and we update the distance.

4. After all nodes have been processed, the shortest path to each node from the source node has been found.

This algorithm works efficiently on DAGs because the topological order allows us to process each edge once and only once, and when we process an edge, we have already processed all edges leading to the source node of that edge. This ensures that we find the shortest path to each node. The time complexity of this algorithm is O(V+E), where V is the number of nodes and E is the number of edges in the graph.

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The algorithm that efficiently calculates the single source shortest paths in a Directed Acyclic Graph (DAG) is the Topological Sort algorithm. Here are the steps:

1. Topologically sort the nodes of the graph. This can be done using Depth-First Search (DFS) or Breadth-First Search (BFS). The idea is to visit each node once and only once, and to visit a node before its successors. In a DAG, a topological sort is always possible and results in a linear ordering of the nodes.

2. Initialize the distance to the source node as 0 and the distance to all other nodes as infinity. This is because we don't know the shortest path to any node yet, except for the source node (the shortest path from a node to itself is always 0).

3. For each node in the topologically sorted order, relax all of its adjacent nodes. To "relax" an edge means to update the shortest path to the destination node of that edge if a shorter path has been found. This is done by comparing the current known distance to the destination node with the distance to the source node plus the weight of the edge. If the latter is smaller, then we have found a shorter path and we update the distance.

4. After all nodes have been processed, the shortest path to each node from the source node has been found.

This algorithm works efficiently on DAGs because the topological order allows us to process each edge once and only once, and when we process an edge, we have already processed all edges leading to the source node of that edge. This ensures that we find the shortest path to each node. The time complexity of this algorithm is O(V+E), where V is the number of nodes and E is the number of edges in the graph.

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The algorithm that efficiently calculates the single source shortest paths in a Directed Acyclic Graph (DAG) is the Topological Sort algorithm. Here are the steps:

1. Topologically sort the nodes of the graph. This can be done using Depth-First Search (DFS) or Breadth-First Search (BFS). The idea is to visit each node once and only once, and to visit a node before its successors. In a DAG, a topological sort is always possible and results in a linear ordering of the nodes.

2. Initialize the distance to the source node as 0 and the distance to all other nodes as infinity. This is because we don't know the shortest path to any node yet, except for the source node (the shortest path from a node to itself is always 0).

3. For each node in the topologically sorted order, relax all of its adjacent nodes. To "relax" an edge means to update the shortest path to the destination node of that edge if a shorter path has been found. This is done by comparing the current known distance to the destination node with the distance to the source node plus the weight of the edge. If the latter is smaller, then we have found a shorter path and we update the distance.

4. After all nodes have been processed, the shortest path to each node from the source node has been found.

This algorithm works efficiently on DAGs because the topological order allows us to process each edge once and only once, and when we process an edge, we have already processed all edges leading to the source node of that edge. This ensures that we find the shortest path to each node. The time complexity of this algorithm is O(V+E), where V is the number of nodes and E is the number of edges in the graph.

Which algorithm efficiently calculates the single source shortest paths in a Directed Acyclic Graph?

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