Heuristic Function $h(n)$ and Search Types (Random, Brute Force, Uninformed, Informed)

In AI state-space search, a [heuristic function]{def="A function $h(n)$ estimating the cost from node $n$ to a goal"} $h(n)$ guides the search by estimating how close a state is to the goal. Heuristic-guided methods are categorized as informed search methods, in contrast to uninformed search methods.

For the question “Heuristic function $h(n)$ is used in: (i) Random Search (ii) Brute Force Search (iii) Uninformed Search (iv) Informed Search”, the correct selection is:

• ✅ (iv) Informed Search

This is because random search and brute force typically do not rely on $h(n)$, and uninformed search explicitly avoids heuristic guidance, while informed search uses $h(n)$ (e.g., Greedy Best-First Search, A*).

Key related concepts:

• [heuristic estimate]{def="A numeric guess about distance/cost to the goal from $n$"}
• [greedy best-first search]{def="Uses $h(n)$ to expand the node that appears closest to goal"}
• [A* algorithm]{def="Uses $f(n)=g(n)+h(n)$ to balance path cost and heuristic estimate"}

Why $h(n)$ implies “informed” search

A search method becomes “informed” when it uses heuristic information in its node evaluation or expansion strategy. That heuristic is formalized as $h(n)$: an estimate of remaining cost to reach a goal from node $n$.2

Typical informed strategies include:

• greedy best-first search: expansion order depends directly on $h(n)$.
• A* algorithm: combines actual path cost $g(n)$ with heuristic $h(n)$.

In contrast:

• uninformed search methods (e.g., BFS, DFS, uniform-cost without heuristic) do not use $h(n)$ for ordering/selection.