|
摘要：
指示器随机变量简单的说就是，事件发生 为1， 不发生则为0.比如，为事件q申请一个指示器随机变量Xq，此时如果q发生，则Xq = 1 ，否则等于0。一个重要的定理是： E(Xq) = q事件发生的概率 。从该定理中可以知道指示器可能是用来找期望的，实际上确实如此。下面来看如何理解指示器：假设RES为结果集，现在有事件A,B,C,D,E,F ，其发生概率为Pa , Pb ....先为其每一个事件设置指示器随即变量为 Xa Xb Xc ....那么现在RES可以很好的表示为RES = Xa*A + Xb*B + Xc*C ..... 此时 结果集包含了所有发生了的事件这个很好理解，A发生了则 Xa 阅读全文
摘要：
假设被排序数为 n 个， 找pivot的随机办法对每一个数的概率严格为 1/n .步骤一： 建模。假设将第 K 个数选为pivot ， 则子问题规模为 k-1 和 n-k ， 并且该分割的running time 为Θ(n)所以容易得到： T(n) = T(k-1) + T(n-k) +Θ(n)步骤二：用喊有指示随机变量 Xk 来表达T(n)。设Xk 为指示随机变量 （当第k个数被选为pivot ，则 Xk = 1 ，相反则等于0），则有：T(n) = X1(T(0) + T(n)+Θ(n)) + X2(T(1) + T(n)+Θ(n)) + ...... + Xn(T(n) + T(n)+Θ 阅读全文
摘要：
What is it?If a binary tree who's node's value in left child tree is all smaller than root and the node's value in right child tree is all greater than root , and it also holds for any subtree in this tree, then this is a binary search tree.If we perform an inorder tree walk of T , which 阅读全文
摘要：
Order Statistic:The ith smallest of n elements.(i from 1 to n).Median:The [n/2]th smallest of n elements.Here we all talk about value , not key.How to find the ith smallest number in a part of a array?Steps:1) Call the function partition which I have written down in quick sort chapter.Get the positi 阅读全文
摘要：
Hash function:Solution: Use a hash function h(k) to map theuniverse U of all keys into continuous storage spaces{0, 1, ..., m–1}.Collision: When a record to be inserted maps to an alreadyoccupied slot in T.Resolving collisions:At first we assume that each key k ∈ K of keys is equally likely tobe has 阅读全文
摘要：
Why comparison sort has a lower bound at least nlgn,which means T(n)=Ω(nlgn)?Decision-tree can easily tell why. A decision-tree is always a full binary tree. In camparison sort (like merge sort), every step is actually a comparison between 2 elements.And decision-tree list all these comparison cases 阅读全文
摘要：
How it worksDivide: Partition the array into two subarrays around a pivot x such that elements in lower subarray ≤ x ≤ elements in upper subarray.Conquer: Recursively sort the two subarrays.Combine: Trivial.How to divide(Assume the array is start at p and end at q)1. First gives two pointer i j , i 阅读全文
摘要：
Steps:Divide the problem (instance) into subproblems.Conquer the subproblems by solving them recursively.Combine subproblem solutions.A typical algorithm solved by D&V is merge sort. Frist we partitions the array into two sorted array recursivly, that is the Dvide part.Then we combine the two so 阅读全文
摘要：
There are 3 methods to work out a Recurrence.Substitution method.Steps:Guess the result.Prove it by induction.Ex: T(n) = 4T(n/2) + n[Assume that T(1) = Θ(1)]Guess O(n3) . (Prove O and Ω separately.)Assume that T(k) ≤ ck3 for k < n .Prove T(n) ≤ cn3 by induction.T (n) = 4T (n / 2) + n ≤ 4c ( n / 2 阅读全文
|
