HBC25032生涯回忆录,数学,枚举,前缀和[USACO 2007 Dec G]Sightseeing Cows题解

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Fortunately, they have a detailed city map showing the L major landmarks and the P unidirectional cow paths that join them. Farmer John will drive the cows to a starting landmark of their choice, from which they will walk along the cow paths to a series of other landmarks, ending back at their starting landmark where Farmer John will pick them up and take them back to the farm. Because space in the city is at a premium, the cow paths are very narrow and so travel along each cow path is only allowed in one fixed direction.While the cows may spend as much time as they like in the city, they do tend to get bored easily. Visiting each new landmark is fun, but walking between them takes time. The cows know the exact fun values Fi for each landmark i.The cows also know about the cowpaths. Cowpath i connects landmark. Help the cows find the maximum fun value per unit time that they can achieve.

Farmer John has decided to reward his cows for their hard work by taking them on a tour of the big city! The cows must decide how best to spend their free time. Fortunately, they have a detailed city map showing the L (2 ≤ L ≤ 1000) major landmarks (conveniently numbered 1.. L) and the P (2 ≤ P ≤ 5000) unidirectional cow paths that join them. Farmer John will drive the cows to a starting landmark of their choice, from which they will walk along the cow paths to a series of other landmarks, ending back at their starting landmark where Farmer John will pick them up and take them back to the farm. Because space in the city is at a premium, the cow paths are very narrow and so travel along each cow path is only allowed in one fixed direction. While the cows may spend as much time as they like in the city, they do tend to get bored easily. Visiting each new landmark is fun, but walking between them takes time. The cows know the exact fun values Fi (1 ≤ Fi ≤ 1000) for each landmark i. The cows also know about the cowpaths. Cowpath i connects landmark L1_i L1 i ​ to L2_i L2 i ​ (in the direction L1_i L1 i ​ -> L2_i L2 i ​ ) and requires time Ti (1 ≤ Ti ≤ 1000) to traverse. In order to have the best possible day off, the cows want to maximize the average fun value per unit time of their trip. Of course, the landmarks are only fun the first time they are visited; the cows may pass through the landmark more than once, but they do not perceive its fun value again. Furthermore, Farmer John is making the cows visit at least two landmarks, so that they get some exercise during their day off. Help the cows find the maximum fun value per unit time that they can achieve.

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标签： HBC25032生涯回忆录 数学 枚举 前缀和[USACO 2007 Dec G]Sightseeing Cows题解