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ExploreSims / Computer Science & Technology / Algorithms / Pathfinding
Premium experiment • graph search

COMPUTER SCIENCE & TECHNOLOGY • ALGORITHMS

Pathfinding

Compare A* and breadth-first search across deterministic obstacle grids.

● INTERACTIVEPathfinding
Path length
Visited nodes
Algorithm
Status

Reasoning inspector

live internal state
Algorithm—
Path length—
Visited nodes—
Obstacle density—
Reachable—
A* visited—
BFS visited—
A* node savings—

Explore search

Raise obstacle density and compare how A* and breadth-first search explore the same grid.

LEARN WITH THE SIMULATION

Understand Pathfinding by experimenting.

START HERE

Pathfinding turns a grid into a graph-search problem. Breadth-first search expands nodes in layers of increasing distance, while A* adds a heuristic estimate so nodes that appear promising are explored earlier. This laboratory generates one deterministic obstacle map, records the nodes actually visited, highlights the final shortest route and compares A* with BFS on exactly the same grid.

BUILD THE IDEA

What you should understand first

  • Explain why BFS finds a shortest path on an unweighted grid by expanding nodes in distance order.
  • Describe how A* combines path cost so far with a heuristic estimate of remaining distance.
  • Compare path length and visited-node count as different measures: optimality versus search effort.
  • Recognize that a heuristic can reduce exploration without changing the optimal path when it is admissible and used correctly.

TRY IT YOURSELF

When A* and BFS return the same shortest path, how much search can the heuristic save?

  1. Choose a seed and obstacle density for which the goal is reachable.
  2. Run A* and record path length and visited nodes.
  3. Switch only the algorithm to BFS and compare the visited cells while keeping the map identical.
  4. Change the map seed and repeat to see how obstacle layout changes the size of the advantage.
Read the visual:

Both algorithms can return a shortest grid path, but A* often visits fewer cells because the Manhattan-distance heuristic prioritizes progress toward the goal. The size of that saving depends on the obstacle arrangement, not merely on density.

WHY IT WORKS 01

BFS knows distance from the start; A* also estimates distance to the goal

Breadth-first search on an unweighted graph explores the frontier in increasing numbers of edges from the start, which is enough to guarantee that the first discovered route to the goal has minimum length. A* keeps the same accumulated path cost g but ranks candidates using g+h, where h estimates the remaining cost. The heuristic does not change the graph; it changes which promising frontier node is expanded next.

WHY IT WORKS 02

Visited nodes and path length answer different questions

Two searches can return paths of identical optimal length while doing very different amounts of exploratory work. Path length describes the quality of the final route, whereas visited-node count describes how much of the search space the algorithm expanded. The premium grid shows both so efficiency is not confused with solution quality.

WHY IT WORKS 03

Why Manhattan distance works here

Movement in this model is restricted to horizontal and vertical unit steps. Ignoring obstacles, the minimum number of such moves between two cells is the Manhattan distance. Because obstacles can only force a route to stay the same length or become longer, Manhattan distance does not overestimate the true remaining path cost, making it an admissible heuristic for this grid model.

DO NOT MIX THESE UP

Common misconception

A* is not automatically faster in every implementation or on every graph. Its benefit depends on the heuristic, data structures and map geometry. Fewer visited nodes is a search-effort metric, not proof of lower runtime in all environments. A heuristic that overestimates or violates required assumptions can also sacrifice shortest-path guarantees.

PRACTICE CHALLENGE

Can you reach the goal while visiting fewer than a chosen number of cells?

  • Set a visited-node target in the premium controls.
  • Compare A* and BFS on the same seed and density.
  • If both exceed the target, change the map while keeping the algorithm comparison fair.
  • Use the inspector to verify that a lower visited count did not come from accepting a longer nonoptimal path.
Reveal the reasoning

A* can often meet a lower visited-node budget because its admissible heuristic focuses expansion toward the goal. The comparison is meaningful only when both algorithms operate on the same grid and the returned route quality is checked as well as the number of expanded nodes.

MODEL BOUNDARIES

What this simulation assumes

Every simulation simplifies reality or a mathematical system. These are the assumptions and limits to keep in mind while interpreting the results.

Model assumptions

  • Movement occurs on a rectangular grid with four orthogonal neighbors.
  • Traversable moves have equal cost, and the A* heuristic is Manhattan distance.
  • Obstacle fields are generated deterministically from the selected seed and density.

Model limitations

  • Diagonal movement, weighted terrain and continuous geometry are not represented.
  • The visualization does not model robotics dynamics, sensor uncertainty or changing obstacles.

CONNECT IT

Where this matters

  • Robot and autonomous-agent navigation
  • Game pathfinding and movement planning
  • Graph-search education
  • Route and puzzle solving on discrete state spaces

WORDS THAT MATTER

Key vocabulary

Frontier
Set of discovered nodes that are candidates for future expansion.
Heuristic
Estimate of the remaining cost from a node to the goal, used by A* to prioritize its frontier.
Admissible heuristic
Heuristic that never overestimates the true minimum remaining cost.
Visited node
Node removed from the frontier and expanded by the search.
Shortest path
Route whose total graph cost is minimal among available routes.