About this visualization
Greedy best-first search expands the node that looks closest to the goal according to a heuristic h(n), ignoring the cost already paid. It is often very fast but can follow an expensive route. Set your own heuristic values and compare the result with A*.
How it works
- Give every node a heuristic h(n) estimating its distance to the goal.
- Expand the frontier node with the smallest h.
- Because it ignores g, the path it finds can cost more than the best path.
Formulas used
Worked example
On the Romania map with straight-line distances to Bucharest as the heuristic, greedy goes Arad → Sibiu (h = 253) → Fagaras (176) → Bucharest, cost 450, expanding only 3 nodes. The optimal route costs 418, so greedy is quick but not optimal.
Enter these numbers in the simulator above to see every step.
Complexity and properties
| Worst case | |
|---|---|
| Space |
Not optimal. Complete in a finite graph when it remembers explored nodes (as here).
When to use it
- Quick, approximate path-finding when the heuristic is good.
- Understanding why a heuristic alone is not enough for optimality.
- AI course assignments comparing search strategies.
Frequently asked questions
Is greedy best-first search optimal?
No. It ignores the cost so far, so it can return a path that costs more than the cheapest one.
Is greedy best-first search complete?
Not in general; with an explored set in a finite graph it will find a path if one exists.
How is greedy search different from A*?
Greedy uses f(n) = h(n); A* uses f(n) = g(n) + h(n), adding the cost already paid, which makes A* optimal with an admissible heuristic.