Re: [问题] Google Interview Question (4)

楼主: Leon (Achilles)   2013-03-08 15:36:22
※ 引述《Leon (Achilles)》之铭言:
: 嗯, 刚刚想了一下.
: 这个题目, 是 KMP 的变形.
:
: 难的地方在于, 你怎么想到正确的方向
: (听起来有点废话, 哈哈..)
:
: 这里我采用之前的定义.
:
: For a sentance, we are given the occurance index.
: Take above example, say, only 3 words {a, b, c}.
: The sentance is [b b a c b a].
:
: The the occurance index will be
: a = {3, 6}.
: b = {1, 2, 5}.
: c = {4 }.
:
:
: 在开始之前, 我们先看几个非常简单的作法.
:
: 1. Naive: Arbitary choose 2 position from [1, N],
: then check the condition.
:
: 2. Choose one position as the left boundary, then,
: use the max-min of the rest set the decide the right boundary.
:
: For example, if I choose 2 as my left boundary,
: then I need to choose the right boundary by the max of
: d(2,3) and d(2,4) which cover set {a} and set {c}
:
: The result window is [2, 4].
:
: And the complexity should be O(N* K).
:
: 接下来, 就是有趣的地方了.
:
: 3. Follow the previous algorithm, inspired by KMP.
: When we start from 3, actually we don't need to compare all K groups.
:
: Because from previous step, we know [2] covers {b} for sure.
: And [3,4] covers {a,c} for sure.
:
: In this case, we only need to check the condition for set {b} !
: which is d(3,5).
:
: Then the computational complexity is O(N).
: I'll leave the detail for you.
:
:
:
:
作者: scwg ( )   2013-03-08 16:26:00
Since you claimed that the complexity is O(N), the innerloop must be amortized O(1), that's why I was wonderingwhat kind of data structure are you maintaining throughout the loop to keep the lookup o(log K). (Small-o, notbig-O.)
楼主: Leon (Achilles)   2013-03-08 16:44:00
it's not me to claim O(lg K).. please check my articleand, my article do explain how to achieve O(1) in innerloop based on KMP concept..
作者: ledia (付出不需要理由)   2013-03-08 21:11:00
o(lg K) is different than O(lg K)you did claim o(lg K)
作者: stimim (qqaa)   2013-03-08 22:19:00
我想 leon 的意思是这样 http://ideone.com/p6STMv

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