**6.184 algorithms questions.**

I want to use a PRNG to generate random patterns. I would provide the PRNG with a hash value as a seed. Ideally, the seed size would be 64-bit or 128-bit and I would expect no collisions if the seeds ...

I am looking for some suggestions on what algorithm to be used for the below task assignment problem.
There are multiple projects. Each project has multiple tasks for each week. Duration of each task ...

The most common method of proving that some problem, P, is at least as difficult as some other problem, Q, is to demonstrate that Q can be solved in terms of P (with the usual caveats for the ...

We are given a network flow, as well as a max flow in the network. An edge would be called $increasing \space edge$ if increasing its capacity in an arbitrary positive number, would also increase the ...

I am given weighted undirected and non-planar graph G=(V,E). I don't understand much about complex graph and how to work with them. So any tips will help.
For example like this
I don't know how to ...

I am currently going over this paper, and in fact have already tried to implement it:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4634483/ [1]
Paper looks at the amplitude of the step and the time ...

For the purposes of this question, a maze is a spanning tree on a square grid (although the type of grid isn't super important).
There are many Maze generation algorithms, but they only work on a ...

Given a connected, undirected graph G, edge-weighted (positive), prove that
If G has a spanning tree T which, for each vertex r in G, is a shortest path tree from r, then G has a unique MST.
I know ...

I have a set of leaf-labeled trees. I want to concatenate them into a single leaf labelled tree in such a way that the height of the resulting tree is smallest possible.
Can somebody please help me to ...

We're given $T$ a minimal spanning tree (MST) of a non-directed, connected graph $G=(V,E)$ with non-negative weights for each edge $e \in E$. Let $e^* \in T$ be an edge in $T$ and let $G'=(V,E')$ be ...

I have just completed a dynamic programming exercise on LeetCode (Coin Change). I tried a top down approach, but it failed for the larger inputs, whereas the bottom up approach worked for all inputs. ...

I'm looking to solve this planning problem. Any pointers or ideas are much appreciated!
You have a number of i individuals i = { 1, 2, ..., n } that need to perform tasks. Tasks are performed in ...

Question is:
Calculate the minimum absolute difference between the maximum and minimum number from the triplet a, b, c such that a, b, c belongs arrays A, B, C respectively.
There is another ...

Suppose f is a constant-time function. Is it always possible to apply it n times in O(log(n))...

I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum.org but I'm still ...

Good evening! I'm actually doing an internship at the Archives Nationales of France and I encountered a situation I wanted to solve using graphs...
I. The dusty situation
We want to optimize the ...

I have a sequence. And now for each element in this sequence I would like to know how many subsequent elements are larger. Or, in other words, I have a sequence $a_1, \ldots, a_n$, and for each $1\leq ...

I need to store a list of sequential intervals.
So for example I would to say:{0-5} = a{6} = b...

The problem:
This is a reduced version of a problem I currently have. I have a list of edges as input. This list contains the names of 2 nodes (the edge connects these 2 nodes) and 2 x 2D coordinates (...

There are $n$ jobs where each job $i$ has an arrival time $r_i$, a deadline $d_i$, a cost $c_i$, and a flag $\,f_i$. The problem is to find a scheduling time $t_i$ (where $r_i\leq t_i\leq d_i$) for ...

I am attempting to implement IDAstar and so just need to double check my reasoning.
Suppose I am trying to solve the following pancake sorting problem using IDA-star assuming all operations have a ...

Given $T$, an MST of $G(V,E)$ connected and undirected.
Assume we add an edge $e'$ with weight $w(e')$.
Suggest an algorithm which takes $T$ as input, and outs $T'$ MST of $G'(V,E\cup\{e'\})$.So i ...

In the programming pearls book by Jon Bentley, there is a section about the problem of finding a random set of m integers from range 0 to n-1 integers. To do so they use Knuth's algorithm given by the ...

I'm trying to find a network, where Dinic's algorithm makes |V|^2*|E| steps. Clearly it cannot be a network with 3 or less vertices, but I am not able to come up ...

I want to prove that The hardness of the Steiner tree problem lies in determining the optimal subset of Steiner vertices that need to be included in the tree and I need to Show this by proving that if ...

I'm struggling with this problem: you are given an array $A$ of $n$ integers and a number $k \in \mathbb{N} : k \neq 0$. The problem asks to find an algorithm that runs in $\Theta(n)$ that returns the ...

I have a directed graph and and a set of nodes(set = [1,2,5,9,24...]). I want to find a path that contains all the set of nodes and this path dont contain back edges(cycles) and forward edges. For ...

I have an array of length $n$ representing a time series of data. I want to implement a moving (sliding) window of length $k < n$ and calculate things like sliding median, sliding quantile, sliding ...

I am using neural networks to learning and predict a navigation process. The question I'm facing now is how do I use real-time neural network for learning and predict process?

We start with a given finite directed graph. It could represent transitive relations such as:
data transfer paths in social networks,
transportation connections, etc.
Let us use the notation
A->B ...

I have some sources of data, and each one of this sources have a cost per request. I know wich data attributes each one of these sources have, and what are the best sources for each attribute.
Given ...

Given a cycle of $n$ vertices and each vertices of the input graph $G$ assigned a weight.
We want to find an independent set of cycle such that weight of the vertices taken in the independent set is ...

I haven't done much algorithm writing till now. I have a specific scenario and I am wondering which approach shall I take.
Scenario:
Let us suppose that
we have 4 guys (A,B,C,D)
We want to ...

So in this math exchange question I asked, it was proven that for $n>2$ dimensions, you can always find a curve that separates $k$ points in $n$-dimensional space into $2$ arbitrary sets that you ...

Consider the following problem:
Let $S = \{ s_1, s_2, ... s_n \} $ be a finite subset of the natural numbers.
Let $G = \{$ $gcd(s_i, s_j)$ | $s_i, s_j \in S,$ $ s_i \neq s_j \}$ where $gcd(x,y)$ is ...

Given an undirected, connected, weighted graph $G = (V,E,w)$ where $w$ is the weight function $w: E \to \mathbb{R}$ and a minimum spanning tree (MST) $T$ of $G$.
Now we decrease the weight by $k$ of ...

We're developing a mobile application where one of it's functions is tracking user driving route.
The app simply pushes GPS-coordinates to the server, which stores them into a route.
Then we need to ...

This is inspired by an interview question.
We are given an array of integers $a_1, \dots, a_n$ and have to determine if there are distinct $i \lt j \lt k$ such that
$a_k - a_j = a_j - a_i$
$k - j = ...

I've been implementing a Fibonacci Heap in C this past week and today I just hit a mental roadblock that I can't figure out.
Decrease Key is a function that almost all min heaps have (vice versa with ...

i have a question for the knapsack problem that i am totally not able to comprehend properly. I know how to knapsack works with the 0-1 approach and fractional. kindly can i be helped with this ...

I have been exploring Dikstra partitioning Algorithm. Below are my given:R = Red
W = White
B = BlueI have this unpartitioned array.
...

Edited: Suppose we have 4 sets $A, B, C, D $ which can can hold a maximum of two elements, each.
Now, elements ($E_i$) arrive serially with properties such as:
...

A binary indexed tree has very less or relatively no literature as compared to other data structures. The only place where it is taught is the topcoder tutorial. Although the tutorial is complete in ...

I have been reading up on algorithm for finding the strongly connected components in a directed graph $G=(V,E)$. It considers two DFS search and the second step is transposing the original graph $G^T$....

I have a set of numbers, and want to calculate the maximum subset such that the sum of any two of it's elements is not divisible by an integer $K$.
I tried to solve this problem, but I have found the ...

We are given an array A of size n and we have to rotate it in left direction by d positions. So e.g. if A = {1, 2, 3, 4, 5, 6, 7} then for d = 2, the resultant rotated array is {3, 4, 5, 6, 7, 1, 2}.
...

Let $T=(V,E)$ be tree and each edge has a positive scalar weight. I need to print all paths in the tree and then sort the weight of edges in each paths. it needs $O(n^3\log(n))$ time. To solve this ...

Given an interval tree $T$ and an interval $I$, I need to find an algorithm that returns all intervals in $T$ that contain $I$. The asymptotic running time should be $O(min(n,(k + 1) log n))$ where $k$...

Let $A$ be a collection of strings over the alphabet $\{0,\ldots,m-1\}$ that in total contain $n$ symbols.
Your task is to sort each of the strings internally, and then sort the resulting strings ...

Referring to this website : Toptal
This website is confusing me, on clicking on play all, website starts to play animations of all available algorithms sorting the given arrays, which shows shell ...

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- algorithm-analysis
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- graph-theory
- data-structures
- complexity-theory
- sorting
- time-complexity
- computational-geometry
- shortest-path
- search-algorithms
- dynamic-programming
- runtime-analysis
- trees
- strings
- reference-request
- arrays
- combinatorics
- approximation
- asymptotics
- efficiency
- randomized-algorithms
- terminology
- graph-traversal
- greedy-algorithms

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