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Analysis of Algorithms

The theoretical study of computer program?performance?and?resource?usage.

Performance: time

Resource: communication, RAM memory or disk memory and so on.

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What's more important than performance?

Correctness, Simplicity, Maintainability, Robustness, Features, Functionality, Modularity, Security, User-friendliness.

Why study algorithm and performance?

They are the fundamental thing for above.

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Problem: sorting

Input:?sequence <a1, a2, ..., an> of numbers

Output:?permutation <a1’, a2’, ..., an’>, s.t. a1’?<= a2’?<= ... <= an’

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Insertion Sort:

Insertion-Sort(A,n) //Sorts A[1...n]

for j <- 2 to n

? ? do key <- A[j]

? ? ? ? i <- j - 1

? ? ? ? while i > 0 and A[i] > key

? ? ? ? ? ? do A[i+1] <- A[i]

? ? ? ? ? ? ? ? i <- i - 1

? ? ? ? A[i+1] <- key

?

?

Running time:

-Depends on input (eg. Already sorted)

-Depends on input size (6 elem. VS 6*10**9)

? ? -parameterize in input size

-Want upper bounds

? ? -guarantee to the user

?

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Kinds of analysis

Worst-case?(usually): T(n) = max time on any input of size n.

Average-case?(sometimes): T(n) = expected time over all inputs of size n.

(Need assumption of statistic of distribution: uniform distribution)

Best-case?(bogus) cheat

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What is insertion sort's worst-case time?

Depends on computer

-relative speed (on same machine)

-absolute speed (on different machine)

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BIG IDEA! ?Asymptotic analysis

1.?Ignore machine dependent constants;

2.?Look at?growth?of T(n) as n ->?infinity.

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轉(zhuǎn)載于:https://my.oschina.net/kuailechengxuyuan/blog/1926433

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