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Unformatted text preview: we argue that S’ is legal (i.e. you never run out of gas). By definition of the greedy choice you can reach g. Finally, since S is optimal and the distance between g and s2 is no more than the distance between s1 and s2, there is enough gas to get from g to s2. The rest of S’ is like S and thus legal. Optimal Substructure Property: Let P be the original problem with an optimal solution S. Then after stopping at the station g at distance di the subproblem P’ that remains is given by di+1, . . . , dn (i.e. you start at the current city instead of USC). Let S’ be an optimal solution to P’. Since, cost(S) = cost(S’) + 1, clearly an optimal solution to P includes within it an optimal solution to P’....
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 Spring '08
 SHAHRIARSHAMSIAN
 Greedy algorithm, optimal solution, Stop consonant, Optimal substructure

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