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  1. Getting Started with Algorithm
    What is an Algorithm?
  2. Characteristics of Algorithm
    1 Topic
  3. Analysis Framework
  4. Performance Analysis
    3 Topics
  5. Mathematical Analysis
    2 Topics
  6. Sorting Algorithm
    Sorting Algorithm
    10 Topics
  7. Searching Algorithm
    6 Topics
  8. Fundamental of Data Structures
  9. Queues
  10. Graphs
  11. Trees
  12. Sets
  13. Dictionaries
  14. Divide and Conquer
    General Method
  15. Binary Search
  16. Recurrence Equation for Divide and Conquer
  17. Finding the Maximum and Minimum
  18. Merge Sort
  19. Quick Sort
  20. Stassen’s Matrix Multiplication
  21. Advantages and Disadvantages of Divide and Conquer
  22. Decrease and Conquer
    Insertion Sort
  23. Topological Sort
  24. Greedy Method
    General Method
  25. Coin Change Problem
  26. Knapsack Problem
  27. Job Sequencing with Deadlines
  28. Minimum Cost Spanning Trees
    2 Topics
  29. Single Source Shortest Paths
    1 Topic
  30. Optimal Tree Problem
    1 Topic
  31. Transform and Conquer Approach
    1 Topic
  32. Dynamic Programming
    General Method with Examples
  33. Multistage Graphs
  34. Transitive Closure
    1 Topic
  35. All Pairs Shortest Paths
    6 Topics
  36. Backtracking
    General Method
  37. N-Queens Problem
  38. Sum of Subsets problem
  39. Graph Coloring
  40. Hamiltonian Cycles
  41. Branch and Bound
    2 Topics
  42. 0/1 Knapsack problem
    2 Topics
  43. NP-Complete and NP-Hard Problems
    1 Topic
Lesson 29 of 43
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Single Source Shortest Paths

In this section, we consider the single-source shortest-paths problem: for a given vertex called the source in a weighted connected graph, find shortest paths to all its other vertices. It is important to stress that we are not interested here in a single shortest path that starts at the source and visits all the other vertices. This would have been a much more difficult problem.
The single-source shortest-paths problem asks for a family of paths, each leading from the source to a different vertex in the graph, though some paths may, of course, have edges in common.

A variety of practical applications of the shortest-paths problem have made the problem a very popular object of study. The obvious but probably most widely used applications are transportation planning and packet routing in communication networks, including the Internet. Multitudes of less obvious applications include finding shortest paths in social networks, speech recognition, document formatting, robotics, compilers, and airline crew scheduling. In the world of entertainment, one can mention path finding in video games and finding best solutions to puzzles using their state-space graphs

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