In this article, which explains the A* algorithm, it says that for that for the given problem (finding shortest distance between two points where there is a wall as an obstacle), the Manhattan distance is not admissible. See this
Why is that? Does it overestimate the distance in any case? If yes, when?
Why is this manhattan heuristic inadmissble?
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Here is a chunk from aStarLibrary.bb (following links from your link)
;Figure out its G cost If Abs(a-parentXval) = 1 And Abs(b-parentYVal) = 1 Then addedGCost = 14 ;cost of going to diagonal squares
Else
addedGCost = 10 ;cost of going to non-diagonal squares
End If Gcost(a,b) = Gcost(parentXval,parentYVal)+addedGCost
The heuristic (Hcost) for a move from (0, 0) to (1,1) will be 10 * (1 + 1) = 20. The GCost (cost of a move) treats this a single diagonal move of cost 14. So yes, it is an over-estimate.