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Unformatted text preview: The greedy algorithm outputs an optimal A A* = i 1 ,…, i k O = j 1 ,…, j m Proof by contradiction: A is not optimal m > k i k i k j k j k j k+1 j k+1 No conflict! After i k , R was nonempty! After i k , R was nonempty! Today’s agenda Analyze runtime of the greedy algorithm Prove the claim The midterm mixup Proctors allowed early arrivals to read the exam questions Unfair to students who did not come early Proposal: I’ll add 5 points at the end of the semester if it bumps up a letter grade (but not from Ato A) Email me if you have comments The midterm story Average: 50.2 Median: 51 Remember, mid term score gets dropped if you better on the final Time pressure issues Proof of claim For every r ≤ k , f(i r ) ≤ f(j r ) i r1 i r1 j r1 j r1 j r j r By induction on r Why is r=1 OK? Why is r=1 OK? Assume true up to r1 i r i r ? Greedy can always pick j r Greedy can always pick j r...
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 Fall '11
 RUDRA
 Dynamic Programming, Greedy algorithm, Englishlanguage films, Mathematical logic

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