Basic Bellman-Ford Implementation

Here is the basic implementation:

function bellmanFord(n, edges, source):
    dist = array of size n, all infinity
    dist[source] = 0

    for round from 1 to n - 1:
        for (u, v, w) in edges:
            if dist[u] + w < dist[v]:
                dist[v] = dist[u] + w

    return dist

After $n-1$ iterations, dist[v] contains the shortest distance from source to $v$, assuming no negative cycles. If a negative cycle exists, some distances might be incorrect, but you can detect this with one more iteration.

This runs in $O(VE)$ time and uses $O(V)$ space.