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Frontier and Visited State on Graphs

Keep repeat skips, waiting frontier nodes, and already-expanded nodes visible together so cycle handling feels like honest bookkeeping on one graph bench.

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Featured setups

Bridge cycle BFS

Use a looped graph where the frontier and visited state have to stay distinct.

Bridge cycle DFS

Compare the same looped graph under a branch-first run.

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Starter track

Step 6 of 60 / 6 complete

Algorithms and Search Foundations

Earlier steps still set up Frontier and Visited State on Graphs.

1. Sorting and Algorithmic Trade-offs2. Binary Search / Halving the Search Space3. Graph Representation and Adjacency Intuition4. Breadth-First Search and Layered Frontiers+2 more steps

Previous step: Depth-First Search and Backtracking Paths.

Start from track beginning

Why it behaves this way

Explanation

On a graph with cycles, the frontier and the visited state are not the same thing. The frontier holds nodes that have already been claimed but are still waiting to be expanded. The visited state marks nodes whose neighborhoods have already been used.

That separation is what stops graph traversal from wasting time on the same loop over and over. This bench keeps repeat skips, frontier size, and visited nodes visible together so cycle handling feels like visible bookkeeping rather than hidden magic.

Key ideas

01Frontier nodes are waiting work, not finished work.
02Visited state means a node's neighborhood has already been expanded, so repeat edges can be skipped honestly.
03Cycles become manageable when the search keeps claimed, waiting, and finished nodes distinct.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Read the frontier and visited sets directly from the bridge-cycle bench.

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Frozen valuesUsing frozen parameters

On the bridge-cycle graph, why are frontier and visited state both needed?

Graph layout

Bridge cycle

Frontier role

claimed but waiting

Visited role

already expanded

1. Read the frontier honestly

Nodes on the frontier have already been discovered, but they are still waiting for their neighborhoods to be expanded.

2. Read the visited role honestly

Visited nodes are the ones whose edges have already been used, so repeat edges back into them can be skipped.

3. Read the cycle consequence

That separation keeps the bridge-cycle graph from reopening the same diamond loops every time one edge points backward.

Cycle-control read

Frontier means waiting; visited means already expanded.
Keeping those roles separate is what turns cycles into manageable bookkeeping instead of repeated work.

Common misconception

Frontier and visited state are basically the same set with two different names.

A frontier node has been claimed but not expanded yet. A visited node has already had its neighborhood used.

That difference is exactly what makes repeat skips and clean backtracking possible on looped graphs.

Mini challenge

Build a graph run where repeat skips become visible before the frontier is empty.

Make a prediction before you reveal the next step.

Decide whether you need a looped graph or a tree-like graph before you change the preset.

Check your reasoning against the live bench.

Use the bridge-cycle graph so backward edges appear while there is still frontier work waiting.
Repeat skips become visible when the graph contains cycles and the traversal has enough time to encounter them.

Quick test

Reasoning

Question 1 of 2

Answer from the visible cycle bookkeeping, not from memorized vocabulary.

What is the clearest difference between the frontier and the visited state?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one labeled graph with the current node, the frontier nodes, and the visited nodes colored differently so waiting work and finished work stay separate.

A readout card reports the traversal mode, current node, frontier size, visited count, and target, while a cue panel shows the frontier order and the current neighbor list.

Graph summary

One graph tracks visited nodes against frontier size, a second tracks current depth against the deepest claimed depth, and a third compares new discoveries with repeat skips.

Together they show how cycle-handling depends on keeping frontier and visited state distinct.