SAT1000 - P907

The image shows all of the available roads for road construction, where the letters represent cities and the numbers denote the corresponding cost for certain road.

What's the minimum total cost to construct roads so that one can travel from any city to every other one?


Have a look at my problem set: SAT 1000 problems


The answer is 16.

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1 solution

Ved Pradhan
Jun 30, 2020

Going through each city, choosing the least costly road for each one, and connecting the grid will get you this result:

Counting the prices will give you a total cost of 16 \boxed{16} units of currency.

Great! Actually, you have discovered a famous algorithm for finding minimum spanning tree - Kruskal's algorithm.

Alice Smith - 11 months, 2 weeks ago

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Interesting, I have never heard of that. I'll search it up.

Ved Pradhan - 11 months, 2 weeks ago

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