2
votes
1answer
21 views

Need an Algorithm Such that $\sum_{k-i}^{j}{A[k]}$

I need an algorithm for real application. Suppose we have array A (positive & negative ) numbers. we want to find index i, j such that $\sum_{k-i}^{j}{A[k]}$ has the lowest difference to zero. ...
2
votes
0answers
31 views

Can we sort 6 numbers with at most 9 comparison? [duplicate]

i know there is an algorithm to sort 5 numbers with 7 comparison. Can we sort 6 numbers with at most 9 comparison? thanks to all.
4
votes
3answers
89 views

2000 Olympiad in Informatics Question on Box

I have an old Olympiad question on informatics. There are 31 boxes. In each box there is one number. We know the number if and only if we open the box. We want to calculate the minimum number of ...
2
votes
1answer
29 views

Recurrence relation from code

My Friends, Hi, I see an old book in mathematics for computer science. everyone could help me, for example how we calculate the order (Time complexity) of following code: ...
1
vote
2answers
45 views

Solving a recurrence relation with square root

I ran into a bad recurrence relation. Anyone would calculate T(n) or add some hint? $$T(n) = \begin{cases} n,\quad &\text{ if n=1 or n=0 }\\ \sqrt{1/2[T^2(n-1)+T^2(n-2)]+}n ,\quad ...
2
votes
1answer
47 views

Height of Recursion Tree for $T(n, k) = T(n/2, k) + T(n, k/4) + kn$

If we use a recursion tree for solving $$\begin{cases} T(*,1)=T(1,*)=a \\ T(n,k)=T(n/2,k)+T(n,k/4)+kn \end{cases}$$ What is the height of the recursion tree? Any idea or solution highly ...
0
votes
1answer
29 views

Why $T(n) = 2T(n-1) + O(1)$ is $\Omega(2^n)$?

I was told that the complexity of $T(n) = 2T(n-1) + O(1)$ is $\Omega(2^n)$; however, since I was not convinced, I searched in the Internet and all I found is that problem or very similar ones with ...
2
votes
2answers
53 views

Master theorem - why the log factor?

I think I finally managed to fully understand the master theorem but there's one thing left in the second clause (I'm following here: ...
0
votes
1answer
31 views

Time complexity of indirect recursion

How to find the complexity of an the given algorithm: Algorithm f(int n) { if(n==1)return(1); else { f(n-1)+g(n-1); } } Algorithm g(int n) { ...
2
votes
1answer
76 views

Solve the recurrence relation:$T(n)=\sqrt{n}T\left(\sqrt{n}\right)+\sqrt{n}$ [closed]

I have doubt in solving the following questions: $T(n)=2T(\sqrt{n})+n$ $T(n)=\sqrt{n}T(\sqrt{n})+c$ $T(n)=\sqrt{n}T(\sqrt{n})+\sqrt{n}$ T(2)=1 for all the problems Atleast give the final answer.
1
vote
1answer
96 views

Help with Recursive Algorithm

We are to determine a recurrence relation for a recursive algorithm. Let us use the Josephus Problem for this: Given n people standing in a circle, every kth person is killed until one person ...
2
votes
4answers
117 views

find $O$ and $\Omega$ bounds as tight as possible for $T(n)=n+T(\frac n 2)+T(\frac n 4)+T(\frac n 8)+…+T(\frac n {2^k})$

find $O$ and $\Omega$ bounds as tight as possible for $T(n)=n+T(\frac n 2)+T(\frac n 4)+T(\frac n 8)+...+T(\frac n {2^k})$ while k is some constant and for any $n\leq3$ $\ T(n)=c$ for k=1 ...
0
votes
2answers
76 views

Calculating a SQRT digit-by-digit?

I need to calculate the SQRT of $x$ to $y$ decimal places. I'm dealing with $128$-bit precision, giving a limit of $28$ decimal places. Obviously, if $\,y > 28$, the Babylonian method, which I'm ...
2
votes
1answer
95 views

Algorithm analysis

Consider a recursive Mergesort implementation that calls Insertion Sort on sublists smaller than some threshold. If there are n calls to Mergesort, how many calls will there be to Insertion Sort? ...
2
votes
2answers
110 views

Purchasing Order: An Analysis on A ($\textrm{C++}$)-Approached Recurrence Relation

Suppose that we have $n$ dollars and that each day we buy either tape at a dollar, paper at a dollar, pens at two dollars, pencils at two dollars, or binders at three dollars. If $R_n$ is the number ...
-1
votes
1answer
126 views

How to know when to use Dynamic Programming? [closed]

Given any problem, how do I know whether it is solvable using Dynamic Programming? For example: consider the rod cutting problem. Now, how do I know whether dynamic programming will give me an optimal ...
0
votes
1answer
70 views

EFA and recursive algorithm

1) Is EFA stronger than recursive algorithm? (This can be in term of proof theoretic ordinal, or whatsoever - to rephrase the question, are all problems that can be solved(and halt) by recursive ...
2
votes
1answer
289 views

To officially be recursion, must there be a base case?

In this Python code, the function f is defined, which then immediately calls itself: def f(): f() It's not very complicated, the first line defines the ...
2
votes
2answers
447 views

Analysis of algorithms and recurrence relations

Suppose that the function of the time of execution of some recursive algorithm is given by a recurrence relation of order $n$. Let $$p(x)=0,$$ with $p(x)$ a polynomial of degree $n$, the corresponding ...
8
votes
3answers
678 views

Karatsuba vs. Schönhage-Strassen for multiplication of polynomials

I am wondering how to most effectively multiply two polynomials with several 100's of coefficients, each coefficient having 1000-2000 decimal digits. I know Schönhage-Strassen begins to outperform ...