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Single Source Shortest Paths
Variants
Negative Weights
Shortest Paths Tree (single source)
Shortest Path Problem Has Optimal Substructure
Relaxation
Dijkstra's Algorithm [1959] (nonnegative weights only)
Dijkstra's Algorithm
Example
Bellman-Ford Algorithm
Pseudocode
Examples
More Examples
Shortest Paths in DAGs
All-Pairs Shortest Paths
Notation
Pseudocode
Example
Matrix Multiplication Approach
Recursive Solution
Overlapping Subproblems
Apply Dynamic Programming
Bottom-Up Strategy
Extending By One More Edge
Example
Fast APSP
Floyd-Warshall APSP Algorithm
Intermediate Structure Of Shortest Path
Recursive Solution
Pseudocode
Constructing Shortest Path
Example
Example
Applications
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