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Shine wOng
2019-05-15 09:16:42 +08:00
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thu_dsa/chp1/master theorem.md
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@@ -9,9 +9,9 @@ We all know that for `divide-and-conquer` algorithms, there are two way to analy
## Introduction
First we'll make some abstractions. Lets' consider an algorithm implemented in the form of a recursion. Generally, we can assume that to solve a problem of scale `n`, we can divide it into `a` subproblems, whose scale would be `n/b`, with $f(n)$ being the time to create the subproblems and combine their results in the above procedure.
First we'll make some abstractions. Let's consider an algorithm implemented in the form of a recursion. Generally, we can assume that to solve a problem of scale `n`, we can divide it into `a` subproblems, whose scales would be `n/b`, with $f(n)$ being the time to create the subproblems and combine their results in the above procedure.
The runtime of subck an algorithm on an input of size 'n', usually denoted $T(n)$, can be expressed by the recurrence relation
The runtime of an algorithm on an input of size 'n', usually denoted $T(n)$, can be expressed by the recurrence relation
$$
T(n) = aT(\frac{n}{b}) + f(n)