Consider the following statements
- S1: A heuristic is admissible if it never overestimates the cost to reach the goal.
- S2: A heuristic is monotonous if it follows triangle inequality property.
Which one of the following is true referencing the above statements ?
(A) Statement S1 is true but statement S2 is false.
(B) Statement S1 is false but statement S2 is true.
(C) Neither of the statements S1 and S2 are true.
(D) Both the statements S1 and S2 are true.
Explanation: 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.
It’s necessary and sufficient for a heuristic to obey the triangle inequality in order to be consistent or monotone. The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
So, both statements are correct.
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