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[search] dominance typo
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search/informed.md

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@@ -100,7 +100,7 @@ A couple of important highlights from the discussion above before we proceed: fo
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## 1.4.5 Dominance
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Now that we've established the property of admissibility and its role in maintaining the optimality of A* search, we can return to our original problem of creating "good" heuristics, and how to tell if one heuristic is better than another. The standard metric for this is that of **dominance**. If heuristic $$$$ is dominant over heuristic $$b$$, then the estimated goal distance for $$a$$ is greater than the estimated goal distance for $$b$$ for every node in the state space graph. Mathematically,
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Now that we've established the property of admissibility and its role in maintaining the optimality of A* search, we can return to our original problem of creating "good" heuristics, and how to tell if one heuristic is better than another. The standard metric for this is that of **dominance**. If heuristic $$a$$ is dominant over heuristic $$b$$, then the estimated goal distance for $$a$$ is greater than the estimated goal distance for $$b$$ for every node in the state space graph. Mathematically,
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$$\forall n: h_a(n) \geq h_b(n)$$
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As a general rule, the max function applied to multiple admissible heuristics will also always be admissible. This is simply a consequence of all values output by the heuristics for any given state being constrained by the admissibility condition, $$0 \leq h(n) \leq h^*(n)$$. The maximum of numbers in this range must also fall in the same range. It's common practice to generate multiple admissible heuristics for any given search problem and compute the max over the values output by them to generate a heuristic that dominates (and hence is better than) all of them individually.
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[^1]: In other courses, such as CS70 and CS170, you may have been introduced to "trees" and "graphs" in the graph theory context. Specifically, a tree being a type of graph that satisfies certain constraints (connected and acyclic). This is not the distinction between tree search and graph search that we make in this course.
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[^1]: In other courses, such as CS70 and CS170, you may have been introduced to "trees" and "graphs" in the graph theory context. Specifically, a tree being a type of graph that satisfies certain constraints (connected and acyclic). This is not the distinction between tree search and graph search that we make in this course.

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