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Unformatted text preview: except perhaps the last o Indeed, if a search passes a pillar at level l, it would have passed it at a higher level, so would not have returned to t at level l o Each pillar w/ max level >= l has max level exactly l w/ probability Pr(Max level = l | max level >= l) = ½ (1/2) l+1 /(1/2) l o Chance that j pillars in a row of max level >= l are at max level exactly =(1/2) j Define Y = # pillars in a row that reach level l but fail to reach level l+1 E(Y) = sum from j=0 to inf of j*(1/2) j == (1/2)/(1-(1/2)) 2 = 2 o Conclude: at level l, we pass an average of 2 pillars of height = l+1 before seeing a pillar of height >l+1, which causes us to stop and go down to the next level o Therefore, expected number of pillars inspected at level l is 2+1 = 3 o...
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- Spring '11
- Computer Science, max level