HBC223620[NOIP1999]Cantor表,枚举,NOIP复赛KWhereHaveYouBin?题解

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Ben Bean owns Ben Bean’s Bin Bonanza which offers storage bins to the five big companies in town: a rubber band company, a Mercedes Benz dealership, a bing cherry farm, a bonbon candy store and a bu

Ben Bean owns Ben Bean’s Bin Bonanza which offers storage bins to the five big companies in town: a rubber band company, a Mercedes Benz dealership, a bing cherry farm, a bonbon candy store and a bun bakery. Together they store their bands, Benzes, bings, bonbons and buns in Ben’s bins.  Ben has n bins altogether arranged in a single row, numbered 1 to n. While not all of the bins may be in use at any given time, Ben finds it useful to keep all the bins for one company contiguous. Thus, when a company needs a new bin or relinquishes one it no longer needs, Ben may need to move items from one bin to another to make sure all of that company’s bins stay next to each other. Sometimes Ben has a choice of which bin to move, so he has assigned a cost to each bin equal to the number of items stored in the bin (removing items from a relinquished bin and/or moving items into a new bin are the company’s responsibility and do not add to Ben’s costs). Obviously when moving bins Ben wants to keep the cost as low as possible.  If a single company has to make changes Ben can usually figure out the cheapest way to move items around, but typically at the end of each business quarter all of the five companies will make additions and deletions of bins as they reassess their product lines. In cases like this, deciding the lowest-cost set of moves is more difficult. Consider the situation in Figure K.1a which shows 6 bins storing items from the five companies labeled A, E, I, O and U. The numbers in parentheses indicate the number of items in that bin (and thus the cost of moving the items from that bin to another). Suppose that at the end of the quarter company U decides it no longer needs bin 6 and company A requests a second bin. One possibility is to move E’s items from bin 2 to the empty bin 6 which frees up bin 2 for company A (Figure K.1b)—the cost of this rearrangement to Ben is 4. The optimal move though is to move U’s items from bin 5 to bin 1 and move A’s items from bin 1 to bin 5 and giving company A bin 6 (Figure K.1c)—the cost of this move is 3. Ben could also have moved A’s items from bin 1 to bin 6 to achieve the same optimal cost. Notice that in all cases removing the three items from U’s bin 6 and adding the seven items to A’s second bin does not cost anything to Ben.  Figure K.1: Sample Input 1.

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标签： HBC223620[NOIP1999]Cantor表 枚举 NOIP复赛KWhereHaveYouBin?题解