Added 6.006 lec 15

6.006/fall-2011/index.md

@@ -35,6 +35,7 @@ problems.
 12. [Square Roots, Newton's Method]({% link 6.006/fall-2011/lec12.md %})
 13. [Breadth-First Search]({% link 6.006/fall-2011/lec13.md %})
 14. [Depth-First Search, Topological Sort]({% link 6.006/fall-2011/lec14.md %})
+15. [Single Source Shortest Paths Problem]({% link 6.006/fall-2011/lec15.md %})
 16. [Dijkstra]({% link 6.006/fall-2011/lec16.md %})
 17. [Bellman-Ford]({% link 6.006/fall-2011/lec17.md %})
 18. [Speeding up Dijkstra]({% link 6.006/fall-2011/lec18.md %})

6.006/fall-2011/lec15.md

@@ -0,0 +1,28 @@
+---
+layout: default
+title: Lecture 15 - Single Source Shortest Paths Problem
+parent: MIT 6.006 - Introduction to Algorithms
+nav_order: 15
+---
+
+# Lecture 15 - Single Source Shortest Paths Problem
+This lecture discusses the single source shortest paths problem and presents the general strategies algorithms follow to solve it.
+
+The single source shortest paths problem is defined as follows: given a graph $G = (V, E)$ and a source vertex $s \in V$, find the shortest path from $s$ to every other vertex in $V$.
+
+## General Strategies
+Given that your graph does not have any negative weight cycles, there is a general approach to solve the single source shortest paths problem:
+
+```
+Initialize the distance of the source vertex to 0 and the distance of all other vertices to infinity.
+Repeat until no more updates are possible:
+    For each edge (u, v) in E:
+        Relax the edge (u, v)
+```
+
+"Relaxing" an edge means updating the distance of the destination vertex $v$ to the minimum of its current distance and the sum of the distance of the source vertex $u$ and the weight of the edge $(u, v)$.
+
+```python
+if d[v] > d[u] + w(u, v):
+    d[v] = d[u] + w(u, v)
+```