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thereamp;#39;s a very interesting principle in mathematics which is worth discussing in the context of binary heaps because it has a pretty interesting application so suppose that we have a function and we have hereamp;#39;s the x axis and this is the f of x axis and our task is to compute the minimum of f of x over some valid interval all right and letamp;#39;s make another assumption right letamp;#39;s assume that weamp;#39;re lazy and most mathematicians and computer programmers are naturally lazy people they they like code reuse and they like proof reuse and letamp;#39;s assume that we know how to compute minus f of x and the question is can we use our knowledge of minus f of x to actually get us the minimum of f of x okay so this is this is the minus f of x and it turns out that you think about it so if we can find the maximum of minus f of x right on the assumption that we know how to deal with minus f of x so letamp;#39;s say that we take the maximum find the maximum of m
