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I want to create a function and possibly use Arcmap tools to create something similar to Cost Path. Instead of just choosing the LCP, it must cross through the most different integers. Let's say I have a raster with values 1-5. I want this path to use all five values but still use the shortest path in relation to number of cells. The raster values do not represent any sort of cost.

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This generalizes the Traveling Salesman Problem (which is the case when there is exactly one cell with each value to visit) and can be approached with similar methods (such as binary integer linear programs). ArcMap has no tools that will solve this exactly. I wouldn't rule out being able to compute an approximate solution using the tools it has, but this seems unlikely. – whuber♦ Jul 31 '12 at 21:06

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