think-cell technical report TC2003/01 A GUI-based Interaction ...

5.2 An Application of Dynamic Programming IMPLEMENTATION
Algorithm: MergeGridlines (recursive shortest path)
Input: listSource, listDest : List of Gridline
Output: minimalCost : Accumulated cost for the optimal path
optimalPath : A list of source, dest, identify that describes
the optimal path
Variables: costSource, costDest, costIdentify, minimalCost : Cost
pathSource, pathDest, pathIdentify, optimalPath : List of Choice
Begin
costSource ← 0, costDest ← 0, costIdentify ← 0
If Not IsEmpty(listSource) Then
(costSource, pathSource) ← MergeGridlines(Tail(listSource), listDest)
// Tail((a, b, c)) ↦→ (b, c)
costSource ← costSource + CostNext(source, . . .)
End If
If Not IsEmpty(listDest) Then
(costDest, pathDest) ← MergeGridlines(listSource, Tail(listDest))
costDest ← costDest + CostNext(dest, . . .)
End If
If Not (IsEmpty(listSource) Or IsEmpty(listDest)) Then
(costIdentify, pathIdentify) ← MergeGridlines(Tail(listSource), Tail(listDest))
costIdentify ← costIdentify + CostNext(identify, . . .)
End If
If costDest < costSource Then
If costDest < costIdentify Then
minimalCost ← costDest
optimalP ath ← dest.pathDest // a.(b, c) ↦→ (a, b, c)
Else
minimalCost ← costIdentify
optimalP ath ← identify.pathIdentify
End If
Else
If costSource < costIdentify Then
minimalCost ← costSource
optimalP ath ← source.pathSource
Else
minimalCost ← costIdentify
optimalP ath ← identify.pathIdentify
End If
End If
Return (minimalCost, optimalP ath)
End
Figure 43: An exponential-time recursive algorithm for gridline matching
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