CF1012B Chemical table

Innopolis University scientists continue to investigate the periodic table. There are $ n·m $ known elements and they form a periodic table: a rectangle with $ n $ rows and $ m $ columns. Each element can be described by its coordinates $ (r,c) $ ( $ 1

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For each example you have a picture which illustrates it. The first picture for each example describes the initial set of element samples available. Black crosses represent elements available in the lab initially. The second picture describes how remaining samples can be obtained. Red dashed circles denote elements that should be purchased from other labs (the optimal solution should minimize the number of red circles). Blue dashed circles are elements that can be produced with nuclear fusion. They are numbered in order in which they can be produced. Test 1 We can use nuclear fusion and get the element from three other samples, so we don't need to purchase anything. Test 2 We cannot use any nuclear fusion at all as there is only one row, so we have to purchase all missing elements. Test 3 There are several possible solutions. One of them is illustrated below. Note that after purchasing one element marked as red it's still not possible to immidiately produce the middle element in the bottom row (marked as 4). So we produce the element in the left-top corner first (marked as 1), and then use it in future fusions.