How Search Algorithms Work — From DFS and BFS to A*

Search algorithms look simple until the state space gets huge.

Then the real question becomes:

Do you explore everything, or do you choose smarter paths first?

That is the core idea behind search in AI.

Core Idea

Search is about moving from a start state to a goal state.

You have:

a current state
possible actions
next states
a goal condition

The algorithm decides which state to explore next.

That one decision changes everything.

The Basic Structure

Most search algorithms follow this pattern:

start from the initial state

while there are states to explore:
    choose the next state

    if it is the goal:
        return solution

    expand possible next states

return failure

The difference between DFS, BFS, Greedy Search, and A* is mostly this:

How do we choose the next state?

DFS vs BFS

The first important comparison is DFS vs BFS.

DFS goes deep first.

BFS expands level by level.

DFS:

follows one path as far as possible
uses less memory in many cases
can get stuck exploring a bad deep branch

BFS:

explores nearby states first
finds the shortest path in unweighted graphs
can use a lot of memory

So the trade-off is simple:

DFS is memory-friendly.

BFS is distance-friendly.

Concrete Example

Imagine a maze.

DFS may run down one corridor until it hits a dead end.

Then it backtracks.

BFS explores all nearby positions first.

Then it expands outward step by step.

If the shortest path matters, BFS is safer.

If memory matters more, DFS may be more practical.

Where IDS Fits

Iterative Deepening Search tries to combine both ideas.

It runs DFS with a depth limit.

Then it increases the limit gradually.

In simple form:

for depth_limit from 0 to max_depth:
    run DFS only up to depth_limit

This gives you:

DFS-style memory usage
BFS-style level-by-level discovery

IDS is useful because it shows that search strategies are not always separate boxes.

Sometimes they are trade-offs.

Uninformed vs Informed Search

Basic search does not know where the goal is.

It only follows structure.

That is called uninformed search.

Examples:

Informed search uses extra information.

It asks:

“Which direction looks more promising?”

That extra information is usually a heuristic.

Greedy Search vs A*

This is the key comparison for heuristic search.

Greedy Search uses only the heuristic.

It chooses the node that looks closest to the goal.

A* uses both cost and heuristic.

It chooses the node with the best total estimated path.

The structure is:

Greedy:

h(n)

A*:

f(n) = g(n) + h(n)

Where:

g(n) = cost from start to current node
h(n) = estimated cost from current node to goal
f(n) = total estimated cost

Greedy is fast and intuitive.

But it can be fooled.

A* is more careful because it also remembers the cost already paid.

Why This Matters in Practice

In real problems, the state space can explode.

A small grid, puzzle, route map, or game tree can quickly produce thousands or millions of possible states.

So implementation is not just about “finding a path.”

It is about choosing what not to explore.

That is why the search strategy matters.

A bad strategy wastes time.

A good strategy turns a massive problem into a manageable one.

Recommended Learning Order

If you are learning search algorithms, this order works well:

State Space Search
DFS
BFS
IDS
Informed Search
Heuristic Function
Greedy Search
A* Algorithm

This order helps because you first learn the basic search structure.

Then you learn the trade-offs.

Then you learn how heuristics make search more efficient.

Takeaway

Search algorithms are not just different ways to traverse graphs.

They are different strategies for deciding what to explore next.

DFS goes deep.

BFS expands nearby states.

IDS balances depth and memory.

Greedy follows what looks best.

A* balances actual cost and estimated future cost.

If you remember one idea, remember this:

Search performance depends on the rule used to choose the next state.

Discussion

When solving search problems, do you usually start with BFS or DFS first, or do you jump directly to heuristic search like Greedy Search or A*?

Originally published at zeromathai.com.
Original article: https://zeromathai.com/en/search-algorithms-hub-en/

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