I have a problem that looks like this: partial solution found
I want to calculate the minimum number of roads required to connect all sources (yellow) to the destination (green). However, I also want to ensure that there is the minimum path length from each source to destination. Diagonals are same move cost as up/down/left/right.
Greedy doesn't work, it won't guarantee min total roads, got any other suggestions? Shown in the image is the possible min paths from each source to the destination, with overlap shown as larger circles.
Edit: greedy example failing:
