DirkNow的专栏

O notation:      O(g(n))={f(n): there exists consts c>0 no>0 such taht 0no}      f(n)=O(g(n)) represents an anonymous function[f(n)] in that set[O(g(n))].      Ex1. f(n)=n^3+O(n^2) means there i

Table S holding n records.One record structure is like this:struct{Key;Satellite data;}X, as a pointer, which point to one record.Operations- Insert(S,x); //S- Delete(S,x); //S

Randomized-Select：Question：Given n elements in array, find the i-th smallest element.Navie Algorithm: Sort A and return A[i]. Best Time cost will be O(nlgn).Divide: Using the Quick Sort Rand

Bucket Sort:Bucket sort assumes that the input is generated by a random process that distributes elements uniformly and independently over the interval [0,1). That is to say, the input number shou

Input: A[1...n], each 0Output: B[1...n] = sorting of AAuxiliary: C[1...k]Restricts: 1. each element little than a const "k"2. the element should be integer3. the range of the elements

Divide and Conquer:  1. Divide: Partition array into 2 subarrays around pivot, such that elements in lower subarray little than  pivot, and upper subarray bigger than pivot.  2. Conquer: Recursive

Q:Input:     A=[a_ij] B=[b_ij]    i,d=1,2,3...nOutput:  C=[c_ij]=A*B Naive Algorithm:  Θ(n^3)Realization --- CPP:long int** NaiveMatrixMulitiple(long int** lhs,long int** rhs,long int size

Q: given number x, and n>=0 compute x^n. Naive Algorithm:                 x*x*x*......*x=x^n   Time:Θ(n)Divide and Conquer Algorithm:                X^n=(X^2)^(n/2)                if n is a

Merge Sort:1. Divide:     Divide the input array into two subarray(n/2 and n/2).2. Conquer: Recursively sort each subarray.3. Combine: Linear-Time merge. Running Time:  T(n)=2T(n/2)+Θ(n).

Definition:                     Fn = 0                               if n==0                     Fn = 1                               if n==1                     Fn = F_n-1  +  F_n-2        if n

There are three solutions to solve the recurrences. Substitution method:          1. Guess the form of the solution          2. Verify by induction          3. Slove for constsRecursion-tr

Two key ingredients:#1 Optimal Substructure:       If an optimal solution to the problem exhibits optimal solution to subproblems.       Some common pattern:              1. You show that a so