When my prof introduced us to the N/NP topics, the first thing he mentioned is input size, which he defines as the number of bytes needed to describe and write a problem's input into a file. Could someone please explain to my why the input size matters to these topics? Thank you.
EDIT: I'm concerned about why this way of measuring size is important, esp. to this P/NP topic. My prof mentioned the pseudo-polynomial running time (of the knapsack problem) which is somewhat relevant to this way of counting input size. I'm not sure how it is connected to the NP picture, mostly because right after redefining input size, he went into reduction examples and there is no mentioning of input size since. And for NP-hard problems, since there is no known way to solve them efficiently, why should we care about input anyway?