Contents

- 1 Which algorithm will always guarantee the optimal solution?
- 2 Do heuristics guarantee A solution?
- 3 What are the four heuristic methods?
- 4 How can you tell if a heuristic is admissible?
- 5 Can an admissible heuristic guarantee final optimality?
- 6 Which is the best definition of a consistent heuristic?
- 7 How is the admissible heuristic used in the search algorithm?
- 8 Why is the Manhattan distance an admissible heuristic?

## Which algorithm will always guarantee the optimal solution?

Kruskal’s algorithm and Prim’s algorithm are greedy algorithms for constructing minimum spanning trees of a given connected graph. They always find an optimal solution, which may not be unique in general.

## Do heuristics guarantee A solution?

A heuristic is a mental shortcut that allows people to quickly make judgments and solve problems. These mental shortcuts are typically informed by our past experiences and allow us to act quickly. However, heuristics are really more of a rule-of-thumb; they don’t always guarantee a correct solution.

## What are the four heuristic methods?

Each type of heuristic is used for the purpose of reducing the mental effort needed to make a decision, but they occur in different contexts.

- Availability heuristic.
- Representativeness heuristic.
- Anchoring and adjustment heuristic.
- Quick and easy.

## How can you tell if a heuristic is admissible?

In computer science, specifically in algorithms related to pathfinding, a heuristic function is said to be admissible if it never overestimates the cost of reaching the goal, i.e. the cost it estimates to reach the goal is not higher than the lowest possible cost from the current point in the path.

## Can an admissible heuristic guarantee final optimality?

This way, an admissible heuristic can ensure optimality. However, note that although an admissible heuristic can guarantee final optimality, it is not necessarily efficient. While all consistent heuristics are admissible, not all admissible heuristics are consistent.

## Which is the best definition of a consistent heuristic?

A consistent heuristic is one where your prior beliefs about the distances between states are self-consistent. That is, you don’t think that it costs 5 from B to the goal, 2 from A to B, and yet 20 from A to the goal. You are allowed to be overly optimistic though.

## How is the admissible heuristic used in the search algorithm?

The search algorithm uses the admissible heuristic to find an estimated optimal path to the goal state from the current node. For example, in A* search the evaluation function (where = the evaluation function. = estimated cost from current node to goal. is calculated using the heuristic function.

## Why is the Manhattan distance an admissible heuristic?

Consider the puzzle below in which the player wishes to move each tile such that the numbers are ordered. The Manhattan distance is an admissible heuristic in this case because every tile will have to be moved at least the number of spots in between itself and its correct position.