1.11 Best Worst and Average Case Analysis
ฝัง
- เผยแพร่เมื่อ 20 ม.ค. 2018
- Case Analysis Discussed in this video
1. Best
2. Worst
3.Average
Examples Taken
1. Linear Search
2. Binary Search Tree
Min time in Worst Case
Max time in Worst Case
are also discussed.
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Great video. This is small adjustment, but I think a more exact answer for the average case of linear search will be Mu(n) = n/2 + n/(n+1). This is equal to n when n=1, and is just more than half otherwise. The reason for this adjustment is to count the probability of event(k not in array), when we also assume that each discrete event occurs with equal likelihood*.
(1) Let Mu(n) be the average time for problem size n
(2) The definition of mean is: Mu(x) = sum_over_x(x * p(x)), where x is the outcome and p(x) is the probability of that outcome
(3) In the case of sequential search, mu(n) = (1/(n+1))*sum_over_i( i ) + (1/(n+1))*n
NOTE: first term is outcomes where k is found in the array; second term considers the case where k is not found
(4) Substituting (1/2)*n*(n+1) for the summation, and simplifying, we get Mu(n) = n/2 + n/(n+1)
* This probably isn't a realistic assumption. P(k in array) = ? In reality we don't know and it depends on the instance of the problem. We would want to have some a priori estimate to feed into the calculations. Since k can take an infinite number of values, and i can take a finite number of values (1
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Thanks for the great video! Would be even better if you can do a Worst-Case analysis on an unsuccessful search.
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