Questions tagged [greedy-algorithms]

Questions about algorithms that make at each step the locally optimal choice.

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Finding an optimal solution for the following problem

This is an intriguing question given by my friend for which I want to find an optimal solution: Each week, you can choose to work ONLINE $(ON)$ or in person $(WR)$ in your department's office. If you ...
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Minimum Number of Refueling Stops with Dynamic Programming

This is a question from Leetcode and I wanted to solve it with Dynamic Programming. upon seeing the solution, I am not able to get the intuition behind the logic. I was able to understand the solution ...
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Time to form a complete graph from n vertices given that only k vertices can be used at a time [closed]

I know this problem is related to the greedy algorithm and max edges incomplete graph but can't come up with a solution. Problem You are given two numbers n and k: n >= k n is the total # of ...
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How to prove the my greedy algorithm for placing guards?

Given $n$ images placed in indexes $x_1 < x_2 < ... < x_n$ and an endless number of guards, where each guard if placed in index $y$ can protect $[y-0.5,y+1]$. I want to protect all images ...
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Filling Two Knapsacks with greedy algorithm

I've got the next problem, where I have two, instead of one, knapsacks. Formally, we have items $1, \ldots , n$ and each item $i$ has a positive integer weight $w_i \in \mathbb{N}$ and a positive ...
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Greedy Algorithm: Optimal Substructure

I don't have a CS degree but I have recently taken up studying algorithms very seriously. I have been studying greedy and dynamic programming for days and I come across the below definition a lot, ...
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Is correctness implied by an optimality proof?

New to proofs (in the context of analysis of algorithms). I'm wondering, if I were to prove a greedy algorithm is the optimal solution, does this imply its correctness as well? (partial correctness + ...
25 views

Proof of Correctness Request for Greedy Algorithm that solves “The Weight Job Scheduling” problem

Today, in my self-lead studies, I found out about greedy algorithms, more specifically, a greedy approach to solve The Weighted Job Scheduling Problem. I understand how the solution is implemented but,...
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Which algorithms exhibits Greedy Choice Property but not Optimal Substructure Property

After a few courses using CLRS, I still have not been able to find a satisfying answer to the title question. This answer suggests Hoffman trees. But here the greedy choice is the two subtrees with ...
76 views

Proof of Correctness : Arranging the sheep

I've come across a question in Codeforces contest 719(Div - 3). The problem goes like this : I was able to solve the problem by using another approach but had to use 4*n auxiliary space, where n is ...
27 views

maximal independent set on grid-based graph proof of approximation ratio

We have a G = (V, E, w), in form of a grid graph with a single diagonal line in each grid in form of below. Where w is the V weight. We use a greedy algorithm that takes in each step maximum weighted ...
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Optimize stacking time series by offsetting start times (feels like a backpack problem?)

Given a time-series of data collected from a single running process that takes 8 hours to complete: Minute GB of Disk Space Used 0 0 1 8 2 15 3 22 ...Etc. It is sampled every minute, for 8 ...
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maximum sum of diameter of tree + leaf removal

Problem: A tree of n nodes is given. Have a sum variable. Choose the leaves furthest from one and other and add their distance(the number of edges between them) to the sum variable. Now remove one of ...
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Find the minimum cost of adding the elements of a set (greedy algorithm)

I'm VERY stuck with this problem: Given a set (with possible repeated elements), the cost of adding two elements $x, y$ is $x + y$. For example, the possible costs of the next set $\{1,2,5 \}$ are: ...
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How to (Efficiently) Sort a List of Items with Parent/Child Relationship

I have a list of items that have a parent/child/grandchild/etc. type of relationship. Each item has a list of descendants, and an _.isDescendentOf(other) member ...
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Maximum Independent Set of special Directed Graph

I was given this special type of Directed Graph and was asked to find it's Maximum Independent Set. Graph Properties : Graph has $N$ vertices and $N$ edges There can be no edge from a vertex $v$ to ...
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Greedy algorithm for subset sum on powers of 2

I have some $n$ numbers which are powers of $2$, say $a_1,a_2,a_3,\ldots,a_n$ which are not necessarily all distinct. I have option to give them any sign. I have to find if I can make their sum after ...
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Rearrange string k distance Apart

The question statement is as follows: Given a non-empty string s and an integer k, rearrange the string such that the same characters are at least distance k from each other. All input strings are ...
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Greedy Best-First Search Performance for Tree and Graph Space

I am currently reviewing the GBFS algorithm and when looking at its completeness I am confused between the difference of it being not optimal in Tree Search for Finite and Infinite Spaces that it is ...
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Spanning hypertree which connects the vertices as slowly as possible

I want to find a reference for the following problem or a similar problem for my paper. I found a greedy algorithm for this problem, but writing such an algorithm in a paper is not common in my area, ...
52 views

Highest Product of X Items

🧩 How do you find the highest product of X items? This should optimize for runtime complexity and protect from overflows from large products. Inputs An array of both positive and negative Ints ...
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2-Approximation algorithm for for messages across a cyclic network

Question There are $n$ computers arranged in a cycle ($1,2,3..,n,1$), with undirected edges between adjacent computers. There are $m$ messages that need to be delivered. Message $i$ ($1 \le i \le m$) ...
33 views

Modified topological sort

I recently asked a related question at the theoretical CS stack exchange, but I have modification to the problem that I think is a bit tougher. This seems like a better place anyways. Let's define a &...
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Does the existence of a matroid structure imply that the greedy algorithm is optimal?

I was going through the topic of matroid structures for the problems like Activity selection ,minimum spanning tree. I also came to know how to solve if a problem exhibits matroid structure. The ...
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Greedy Proof: For coin denomination systems, faster proof to ensure greedy solution yields the optimal solution

I have reasons to believe that there is a faster way to confirm, that for coin denomination systems if the greedy solution yields the optimal solution or not. I believe that if you check that for all ...
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How to understand the solution to Task Scheduler problem on LeetCode?

LeetCode Task Scheduler problem is the following: Given a characters array tasks, representing the tasks a CPU needs to do, where each letter represents a different task. Tasks could be done in any ...
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Serving $k$ customers with bounded time window

A person provides a service and he/she can serve $k$ clients each minute. Now, client number $i$ comes at the beginning of minute $a_{i}$ and waits $w_{i}$ minutes to receive the service and if they ...
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Ordering the tasks to minimize penalties

So I just started learning greedy algorithms and I have a problem that I want to solve. The statement is as follows: In your calendar you have an $L$ list of all the tasks you need to complete today. ...
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Correctness proof of a greedy approximation algorithm

How do I prove the correctness of this algorithm?
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Maximize the minimum gap while scheduling within intervals?

Problem There are N intervals in which a particular integer can be chosen. What is the maximum possible minimum gap between each integer if one integer is chosen for each of those intervals? For ...
Problem Statement: Say you have an array prices for which the $i^{th}$ element is the price of a given stock on day $i$. Design an algorithm to find the maximum profit. You may complete as many ...