Reconstructing the Actual Path in Shortest Path Algorithms

Systems should not only compute results, but also explain how those results were obtained.

Parent pointers are a minimal metadata layer that turns an algorithm into a usable system feature.

Shortest path algorithms are often discussed in terms of computing the minimum distance between two nodes.
However, in real systems, knowing the distance alone is rarely sufficient — we often need the actual path.

This article explains a simple but powerful technique to reconstruct the shortest path using a parent array.

The Core Idea: Storing Parent Pointers

When running BFS on an unweighted graph, we relax edges level by level.
Whenever we discover a node for the first time, we store where it came from.

vector parent(V, -1);

For every neighbor visited:

parent[neighbor] = node;

This creates an implicit shortest-path tree.

Reconstructing the Path

Once BFS completes, we can reconstruct the path by walking backwards from the destination node using the parent pointers.

vector path;
for (int v = destination; v != -1; v = parent[v]) {
path.push_back(v);
}
reverse(path.begin(), path.end());

This converts a distance-only result into an actual navigable route.

Why This Matters Beyond DSA

This pattern appears in real-world systems:

Navigation systems reconstruct routes

Workflow engines trace execution paths

Debugging tools track state transitions

Distributed systems explain decisions

Optimization without traceability is incomplete.