Alice is the manager of a cafe which supplies n different kinds of drink and m different kinds of dessert. One day the materials are in short supply, so she can only make ai cups of each drink. type i and bj servings of each dessert type j.
On this day, k customers come to the caf e and the ith of them has pi favourite drinks(ci,1, ci,2. . . , ci,pi) and qi favourite desserts (di,1, di,2, . . . , di,qi). Each customer wants to order one cup of any one of their favourite drinks and one serving of any one of their favourite desserts. If Alice refuses to serve them, or if all their favourite drinks or all their favourite desserts are unavailable, the customer will instead leave the cafeand provide a poor rating.
Alice wants to save the restaurant’s rating. From her extensive experience with these k customers, she has listed out the favourite drinks and desserts of each customer, and she wants your help to decide which customers’ orders should be fulfilled.
Design a polynomial time algorithm which determines the smallest possible number of poor ratings that Alice can receive. A solution for the case where pi= qi= 1 for alli(i.e. all customers have only one favourite drink and one favourite dessert) will earn up to 10 points.
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