# Questions tagged [algorithm-design]

Questions related to general, high level, techniques for the design of algorithms.

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### Need an optimized way to handle combination of entities to improve performance

So, I am working on a feature in a web application. The problem is like this- I have four different entities. Let's say those are - Item1, ...
26 views

### design cache system using queuing theory

If we have data from a random population, a 3d histogram of throughput and current cache size of DRAM (intersection of a IOPS & a cache size will have a count). How can one use queuing theory to ...
852 views

### How to Match Socks

When I do my laundry I tend to make a pile of unmatched socks, putting new socks on the top of the pile and matching off pairs if two of the same sock are near the top of the stack. Since eventually ...
40 views

### Lexicographic permutation list

Does anyone have an algorithm for stepping through all permutations of n given arbitrary objects in lexicographic order? Thanks.
67 views

### Given an array of size n, create a sub array with given conditions using dynamic programming

We are given an array of integers of size n, which is not necessarily sorted, and we want to create a sub array. We are allowed to do one of 3 tasks below in each level: 1. skip the number in original ...
81 views

### Can a greedy algorithm have more than one subproblems to solve after making greedy choice?

For example: s = <s1 s2 s3> is my problem, I make greedy choice s2 and solve s1 and <...
106 views

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### Deformation of algorithms

Has there been any attempt at a general theory to describe how an algorithm can be "deformed" to solve the problem more efficiently? For example suppose we have an algorithm (say sorting a list of ...
198 views

### Implementing supplies in Coin change problem

I started an algorithm course in C two months ago, for the last weeks I've been trying to solve this problem , i ran out of time but I cannot find an acceptable solution. Basically It's a coin change ...
187 views

### A general algorithm for greedy algorithms

I have been refreshing on greedy algorithms as an algorithm design technique. I have read many sources for an explanation of what a greedy algorithm is, because I would like to put together a general ...
444 views

### Finding longest balanced parentheses using $n$ smaller strings

Given $n$ strings consisting only of '$($' and '$)$', how one can compute the length of the longest string that can be built by concatenating a subset of these strings in some order such that the ...
424 views

### Is there a formalization of a general version of the sweep line algorithm? If not is it easy to derive?

A well known algorithm in computational geometry is the sweep plane algorithm. I've been trying to find if there's a general version of the sweep plane algorithm in $\mathbb{R}^n$, I don't need to ...
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### Is it correct to say that there are similarities between CORDIC and digit recurrence algorithm for division?

I've been studying recently some variations of the CORDIC, and it seems to me that the logic behind at least the basic cordic or the redundant CORDIC is very similar to the logic used to design digit ...
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### 4 Neurons to Decide 10 Digits

I am trying to solve this algorithm exercises (http://neuralnetworksanddeeplearning.com/chap1.html#exercise_513527) in Michael Nielson's online book: Neural Networks and Deep Learning (http://...
21 views

### A comparison operation for lists, based on P(a > b)

Consider two lists $A$ and $B$, both containing $n$ numbers. A comparison operation can be defined based on the probability of uniformly selecting an element $a$ from list $A$ and an element $b$ from ...
777 views

### Josephus Problem - A faster Solution

I came through Josephus problem a little while ago. Problem is stated as follows : "People are standing in a circle waiting to be executed. Counting begins at a specified point in the circle and ...
50 views

### Counting permutations whose elements are not exactly their index ± 1

This is a special case of the question: Counting permutations whose elements are not exactly their index ± M The $M=0$ case has already been solved, but no one was sure how to work out the non-...
209 views

### Counting permutations whose elements are not exactly their index ± M

I was recently asked this problem in an algorithmic interview and failed to solve it. Given two values N and M, you have to count the number of permutations of length N (using numbers from 1 to N) ...
130 views

### improve the running time

How can I use divide and conquer to improve the running time of this algorithm? input: A sorted array of length n output: the # of elements such that abs(A[i]) <= k
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### Without sound synthesis, what is a good way of making a program that plays guitar notes from an array of stored sounds?

Without sound synthesis, what is a good way of making a program that plays guitar notes from an array of stored sounds? What I have in mind is to make note as a function of vibration speed such as N (...
600 views

### Find all rational roots of a polynomial equation

I'm going to try to design an algorithm to find all the rational roots of a polynomial equation in range [a, b]. Can someone please tell me which algorithm currently solves the problem with lowest ...
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### Beginner help with Arrays & Complexity

My goal is to create a method that gets an array that only has 1's and 0's in it, and then turns every number into the amount of 'steps' it is away from the closest 0, left or right. So for example [...
477 views

### Designing bidirectional search algorithm

Write down the algorithm for bidirectional search, in pseudo-code. Assume that each search will be a breadth-first search, and that the forward and backward searches takes turns expanding a node at a ...
67 views

### finding a & b in an array that a+b = x, for a given integer x [closed]

I want to get an algorithm with $\theta(nlogn)$ time complexity that search for two elements in an array of integers, which their sum is equal to $x$ such that x is an integer and $n$ is array size.
141 views

### Why does counting sort copy the input elements?

When I was reading about counting sort in Introduction to Algorithms for the first time, I stopped reading after the step where they calculate the number of each element in the input array. It's the ...
264 views

### Any algorithm better that O(N*logN) for a problem of finding student with largest average score in a list of N scores of the form StudentID, score

Question: Suppose you are a given a csv with N lines of the form StudentID, score. Multiple lines can have same student-ID. Find the student with maximum average score I can't think of any way to ...
538 views

### Algorithm and proof for combining a list of node connections into groups of nodes efficiently

My goal is to algorithmically take a list of relations between nodes (in other words, a list of undirected edges between nodes of a graph) and label each group of nodes such that all nodes that have a ...
120 views

### Why is reduction mostly associated with proving hardness?

Reduction is a powerful problem solving technique that is helpful in solving problems in terms of the solution to other problems, it can also be used for complexity analysis. Why does most of the ...
2k views

### Is there Any difference between dynamic programming vs branch-bound vs delayed column generation

I was reading about cutting stock problem https://en.wikipedia.org/wiki/Cutting_stock_problem , this is best solved using dynamic programming but wiki page mentions 2 other techniques names Branch-...
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### Why isnt node checked for nil value in start when transplanting binary tree

Whilst I was reading CLRS I came across this: When TRANSPLANT replaces the subtree rooted at node u with the subtree rooted at node v, node u’s parent becomes node v’s parent, and u’s parent ends ...
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### Data structure for efficient searching, when insertions and removals are only one-sided

I need a data structure for storing a number $n$ of elements, each of whom is associated with some different time $t_i$. $n$ varies and while it has a theoretical upper limit, this is many orders of ...
128 views

### How to give an approximation algorithm for this unusual bin packing problem?

The usual bin packing problem can be formulated as: \begin{align} & \underset{x,y}{\min} & & B = \sum_{i=1}^n y_i\\ & \text{subject to} & & B \geq 1,\\ & & & \...
362 views

### Schedule two trains whose tracks overlap so they don't crash

I've encountered scheduling problems in my algorithms class before like the type we use vertex cover to solve. Recently I was asked this question and did not even know what algorithmic technique to ...
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### What is dynamic programming about?

Sorry in advance if this question sounds dumb... As far as I know, building an algorithm using dynamic programming works this way: express the problem as a recurrence relation; implement the ...
323 views

### Hash-Table in Practice

I have a set of $n$ values,$v_i$ and want to insert them into a hash-table, $HT$, in a way that each bucket (or hash-table cell) has at most $d$ values. I set $k=\frac{n }{d}$, where $k$ is the number ...
Good evening! I tried to model the Binomial theorem, that allows to expand any power of x + y into a sum of the form: (x+y)^n = {n \choose 0}x^n y^0 + {n \choose 1}x^{n-1}y^1 + {n \choose 2}x^{n-2}...