Charlottesville is known for some of its locally-roasted coffees, each with its own unique flavor combination. Suppose a group of coffee enthusiasts are given n samples C1, C2, ..., Cn of freshly- brewed Charlottesville coffee by 4 coffee-skeptic. Each sample is either a Snowing In Space roast or a Milli Joe roast. The enthusiasts are given each pair (C1,c) of coffees to taste, and they must collectively decide whether: (a) both are the same brand of coffee, (b) they are from different brands, or (c) they cannot agree (i.e., they are unsure whether the coffees are the same or different). Note: all pairings are tested, including (C,C),(G,G), and (Cjeci), but not all pairs have "same" or "different decisions. At the end of the tasting, suppose the coffee enthusiasts have made m judgments of "same" or "different." Give an algorithm that takes these m judgments and determines whether they are consistent. The mjudgments are consistent if there is a way to label each coffee sample cas either Snowing In Space or Milli Joe such that for every taste-comparison ( c) labeled "same," both and have the same label, and for every taste-comparison labeled "different," both and are labeled differently. Your algorithm should run in Om + n) time. Prove the correctness and running time of your algorithm. Note: you do not need to determine the brand of each sample e only whether the coffee enthusiasts are consistent in their labelings. Charlottesville is known for some of its locally-roasted coffees, each with its own unique flavor combination. Suppose a group of coffee enthusiasts are given n samples C1, C2, ..., Cn of freshly- brewed Charlottesville coffee by 4 coffee-skeptic. Each sample is either a Snowing In Space roast or a Milli Joe roast. The enthusiasts are given each pair (C1,c) of coffees to taste, and they must collectively decide whether: (a) both are the same brand of coffee, (b) they are from different brands, or (c) they cannot agree (i.e., they are unsure whether the coffees are the same or different). Note: all pairings are tested, including (C,C),(G,G), and (Cjeci), but not all pairs have "same" or "different decisions. At the end of the tasting, suppose the coffee enthusiasts have made m judgments of "same" or "different." Give an algorithm that takes these m judgments and determines whether they are consistent. The mjudgments are consistent if there is a way to label each coffee sample cas either Snowing In Space or Milli Joe such that for every taste-comparison ( c) labeled "same," both and have the same label, and for every taste-comparison labeled "different," both and are labeled differently. Your algorithm should run in Om + n) time. Prove the correctness and running time of your algorithm. Note: you do not need to determine the brand of each sample e only whether the coffee enthusiasts are consistent in their labelings