3
votes
2answers
144 views

How to solve this recurrence Relation - Varying Coefficient

Sir,I have two questions related to this recurrence relation. It has been messing with me for long. Because of this I couldn't proceed my work for some time .This contains a polynomial term n+2 in ...
0
votes
0answers
15 views

Question about set and series notation in the GSP Algorithm

I tried this in programming forums with no luck and since my primary issue is with the notation, I'm asking here: I have the definition of the GSP Algorithm: Definition However I don't understand ...
0
votes
0answers
16 views

Produce a list of the most-similar units, given various correlations/relationships

I have a database full of units (U1 - U50, U51...) where every unit has the same standard attributes (A1 - A10) and where a % of each attribute defines the amount of that attribute for that particular ...
2
votes
0answers
76 views

Building Minimum warehouses

A big international retailer is setting up shop in India and plans to open stores in N towns (3 ≤ N ≤ 1000), denoted by 1, 2, . . . , N. There are direct routes connecting M pairs among these towns. ...
1
vote
1answer
48 views

How to prove a very basic algorithm by induction

I just studied proofs by induction on a math book here and everything is neat and funny: the general strategy is to assume the LHS to be true, and use it to prove the RHS (for the inductive step). Now ...
2
votes
1answer
63 views

Algorithm - iterative method

I'm stuck on an exercise on algorithms, can you help me with this exercise? Solve this recursion using iterative method. $$T(n) = \begin{cases}1 & n=1;\\ 2, & n=2;\\ T(n-2) + n/2,& ...
2
votes
0answers
35 views

Dynamic Programming: Stock Exercise

I'm having a trouble dealing with this problem: Since future market prices, and the effect of large sales on these prices, are very hard to predict, brokerage firms use models of the market to ...
0
votes
1answer
36 views

Number Triangle pattern

I have a number triangle as follows: $$\begin{array}{|c|c|c|} \hline 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ \hline 0 & 0 & 1 & 1 & 1 & 0 & 0 \\ \hline 0 ...
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
1answer
38 views

N balls of k colors on a cirlce, no two neighboring balls have same color - recursive algorithm

Suppose we have N balls of k different colors. What is the number of arrangements of these N balls on a circle with no two neighboring balls having the same color? Actually, the task is to make up a ...
2
votes
2answers
46 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: ...
4
votes
1answer
43 views

Problem understanding Master theorem

I'm studying the Master theorem (for the analysis of recursive algorithms) and I perfectly understand why a binary search is of order $\log_2(n)$. I also understand that if we formulate it as $T(n) ≤ ...
7
votes
6answers
616 views

Non-literal applications of “Shortest Path” algorithm?

It's obvious that it's used in stuff like Google Maps, but what are some more metaphorical applications where you're minimizing the path between nodes (which can represent anything)
1
vote
1answer
141 views

Solving the recurrence relation $T(n) = T(n-\sqrt n) + 1$

I have an algorithm that at each step can discard $\lceil\sqrt(n)\rceil$ possibilities at a cost $1$. The solution to the recurrence relation below is related to the question of complexity of such ...
2
votes
0answers
26 views

Verify that this recurrence relation is in O(log n)

For the recurrence $T(n)=2*\lceil\frac{n+1}{2}\rceil+c$ is in $\Theta(lg n)$ My attempt at a solution (mostly just wanting to verify its correct). Lower Bound: $T(n)=2*\lceil\frac{n+1}{2}\rceil+c$ ...
0
votes
0answers
24 views

How to prove that in optimal strategie of tower of Hanoi none of the disks can't be placed on a disk of same parity

How to prove that in optimal strategie of tower of Hanoi none of the disks can't be placed on a disk of same parity if we have 3 rods. So for example disk 2 can't be placed on disk 4, or disk 1 can't ...
1
vote
1answer
68 views

Cyclic tower of hanoi problem [duplicate]

If I have 3 rods in a circle and it is allowed to move the disks only in the clockwise direction. How many moves is necessary to move n disks from first rod to the third rod?
1
vote
2answers
43 views

Calculate a recursive equation in terms of theta

I am struggling with the following equation for one week! Please help me solve it. $$T(n)=T(\frac{n}{2})+\frac{n}{logn}$$ So far, I have come to the equation $T(n)=\Sigma \frac{2^x}{x}$
2
votes
1answer
183 views

How to solve this recurrence relation with Sigma notation (f(n, m) = f(n - 1, m) + f(n, m- 1) + c?

This recurrence relation was inferred from the function $f(n, m) = f(n - 1, m) + f(n, m-1) + c$. After expanding the latter, I ended up with the following: $$f(n,m)=\begin{cases} 0,&\text{if ...
0
votes
1answer
25 views

Recursive Algorithm Analysis

$$T(n) = 2\cdot \sqrt{n} \cdot T(\sqrt{n}) + \Theta (\lg n)$$ I have been trying to solve this question but I could not find anything. My approach: $n = 2^k$ $S(k) = T(2^n)$ and $S(k/2) = ...
1
vote
1answer
22 views

What is the link between the quotient and the Bézout coefficients in the Extended Euclidean Algorithm?

Here is an image from the wikipedia page of the EEA for working out the Bézout coefficients for 240·sk + 46·tk = rk where rk = GCD(240,183): What I am trying to work out is what si and ti ...
0
votes
0answers
48 views

Why can I not generalize O(n^log5) for squaring matrice of size n

I have a question that is bugging me for around a 3 days, I first asked this question in stackoverflow but no one could answer it reasonably though they tried to help, so finally I found here as a ...
1
vote
1answer
29 views

Multiplication cannot be obtained from zero, successor, and identity by composition without recursion

The task is to show that multiplication cannot be obtained by zero, successor, or identity functions by composition without using recursion at least twice. I'm primarily confused because it doesn't ...
0
votes
1answer
93 views

Show that $gcd(x,y)$ and $z = lcm(x,y)$ is primitive recursive

For the $gcd(x,y)$ we note: $gcd(x,0) = x$ $gcd(x,succ(y)) = gcd(succ(y),mod(x,succ(y)))$ $succ(x)$ and $mod(x,y)$ are both primitive recursive, so $gcd(x,y)$ must be as well. $z = lcm(x,y)$ if ...
1
vote
1answer
65 views

Find coefficients of polynomial that has zeros at certain points

Given a list of values z0, z1, ..., zn-1 (possibly with repetitions), show how to find the coefficients of a polynomial P(x) of degree-bound n + 1 that has zeros only at z0, z1, ..., zn-1 (possibly ...
1
vote
0answers
18 views

Determining the optimally scoring move on a probabilistically represented 2D grid in real time

I'm posting this to StackOverflow, cstheory.stackexchange.com, and math.stackexchange.com because I'm not really sure where it fits best. I hope that's OK. I have a 2D grid (size varies per map, ...
1
vote
3answers
148 views

Recurrence relations (Big-O notation)

Say I'm given a recursive function such as: function(n) { if (n <= 1) return; int i; for(i = 0; i < n; i++) { function(0.8n) } } ...
0
votes
0answers
134 views

Find all possible paths in a Matrix

I'm looking for algorithms to find all paths in a 4 x 4 matrix. The rules are as follows You can move in any direction (up, down, left, right, and diagonally) The next square in the path must be a ...
2
votes
1answer
75 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
89 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
3answers
92 views

Can I use the master theorem for this?

this is a HW question so please don't just give me the answer right away. Basically, I'm working on solving the running time of this recurrence method: $$T(n) = 4T(n/3) + n \log \log n$$ I want to ...
1
vote
1answer
123 views

Proving by induction that a palindrome contains an even number of $b$s and $c$s

Suppose we want to construct palindromes that contain an $aa$ in the middle if the length is even and an $a$ in the middle if the length is odd. I'm trying to prove by induction that all of these ...
0
votes
1answer
42 views

A recursive definition of palidrome over {a,b}

Can someone please explain how this recursive definition produces palindromes over $\{a,b\}$? For example, how can we get the string $abaaaba$ as a valid string? Rule 1: $\epsilon$, $a$, and $b$ are ...
1
vote
1answer
40 views

A Shifted Sorted Array - finding the shift

I was given a problem concerning a sorted array that is shifted by some "number of spaces", k. For example, take the sorted array $1, 2, 3, 4, 5 ,6$ It is shifted 2 spaces, we get: $5, 6, 1, 2, 3 ...
1
vote
1answer
28 views

Correctness of complexity analysis of recursive algorithm

Given following recursive equation: $$T(n) = T(n-3) + \Theta(1)$$ Is it correct that this equation is O(1)?
0
votes
0answers
339 views

Algorithm to Generate Number with 0 and 9 [duplicate]

You are given an integer N. Can you find the least positive integer X made up of only 9’s and 0’s such that X is a multiple of N? Is there any Algorithm to generate the least number. Thank you.
0
votes
1answer
183 views

how to prove the convergence of fixed point iteration algorithm

Please refer to the below algorithm: Above two steps can be rewritten as, \begin{equation} x(k+1)=\arccos\bigg( -\frac{1}{2(Dr^{\frac {|\sin(2x(k)+\theta)|}{M\sin ...
2
votes
2answers
105 views

Tiny Planet Algorithm?

So I've recently been looking at the Tiny Planet images. I've been googling a few things to try and find out how images are converted from normal to a tiny planet. Some phone apps, as well as ...
0
votes
0answers
76 views

Strassen's Matrix Multiplication Example Problem

How to multiply two matrices using strassen's matrix multiplication.I have only learned the theory part but i cannot find any examples on the net. Could some one explain with two 2X2 Matrices.
1
vote
0answers
114 views

Sequential Algorithm to generate Fractal (Koch's snowflake)

As part of an assignment I had developed a sequential algorithm to generate a Koch's snowflake. Algorithm I have encountered so far have been recursive and iterations generate closer approximations. ...
5
votes
1answer
91 views

Flip all to zero

I have a square grid of size $N$, with rows numbered from $0$ to $N - 1$ starting from the top and columns numbered from $0$ to $N - 1$ starting from the left. A cell $(u, v)$ refers to the cell that ...
3
votes
1answer
38 views

Finding a recursive definition and computing $B(10)$

For $n \geq 1$, let $B(n)$ be the number of ways to express $n$ as the sum of $1$s and $2$s, taking order into account. Thus $B(4) = 5$ because $4 = 1 + 1 + 1 + 1 = 1 + 1 + 2 = 1 + 2 + 1 = 2 + 1 + 1 = ...
2
votes
1answer
84 views

number of derangements

In the normal derangement problem we have to count the number of derangement when each counter has just one correct house,what if some counters have shared houses. A derangement of n numbers is a ...
1
vote
0answers
131 views

Help with find recurrence relation running time.

Write a recurrence relation describing the worst case running time of each of the following algorithms, and determine the asymptotic complexity of the function defined by the recurrence relation. ...
3
votes
2answers
140 views

Google Question: Number of ways to select sets such that n is pure

Consider a subset $S$ of positive integers. A number in $S$ is considered pure with respect to $S$ if, starting from it, you can continue taking its rank in $S$, and get a number that is also in $S$, ...
0
votes
1answer
111 views

Recurrence Relation for Optimal Card Game Score

I have the following problem where Alice and Bob decide to play a simple card game. At the beginning of the game, $n$ cards are dealt face up in a long row. Each card is worth a different number of ...
0
votes
1answer
59 views

Give a randomized algorithm to find the median that has an expected number of comparisons = 2n + o(n)

Any help would be very much appreciated. I'm aware of 2 types of algorithms: "Median of the medians" and one using guards like here: http://www.cs.nthu.edu.tw/~wkhon/random12/lecture/lecture9.pdf ...
1
vote
2answers
67 views

How does my textbook solve this summation equation for the answer?

Summations have always been my weakness in mathematics, and it's showing here as I'm very confused how my textbook, Introduction to Algorithms, goes from basically the second half of the following ...
2
votes
1answer
88 views

What is the bound of: $T(n) = T(n-2) + (n)log(n)$?

I am given the following recurrence relationship: $\ T(n) = T(n-2) + nlog(n)\\ T(1) = T(0) = constant$, I need to find the order for the recurrence. So, using the iterative methodology, what I ...
1
vote
1answer
54 views

How does my textbook come up with this statement? I don't believe it to be true.

My textbook (Introduction to Algorithms) states the following: When polynomially comparing $n^\epsilon$ and $lgn$, it states that $n^\epsilon$ is polynomially greater for any positive $\epsilon$. ...