# dating app dansk Morsø - Define single source shortest path problem

This is done using relaxation by keeping track of a previous-vertex pointer p[v] for each vertex, so that the **shortest** **path** is found by following all the previous-vertex pointers and reversing the sequence.

We have already seen how to solve this **problem** in the case where all the edges have the the relaxation criteria gives equalities.

Additionally, the **path** to any reachable vertex can be found by starting at the vertex and following the π's back to the **source**.

(As a side effect, we might like to find the actual **shortest** **path**, but usually this can be done easily while we are computing the distances.) There are many algorithms for solving this **problem**, but most are based on the same technique, known as The reason for relaxing a **problem** is that we can start off with very high upper bounds and lower them incrementally until they settle on the correct answer.

For **shortest** **paths** this is done by setting d(s,t) initially to zero when t=s and +∞ when t≠s (this choice doesn't require looking at the graph).

MST solves the **problem** of finding a minimum total weight subset of edges that spans all the vertices.

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