Questions tagged [greedy-algorithms]
Questions about algorithms that make at each step the locally optimal choice.
353
questions
0
votes
1answer
26 views
Greedy approach behind SPOJ Aggressive Cows problem
My doubt is related to the given SPOJ problem
I was able to come up with idea of using Binary Search but struggled with the positioning of the cows. After watching some solutions like this one , ...
0
votes
0answers
39 views
Gas Station problem proof
I'm trying to prove the solution for the problem Gas Station (LeetCode 134)
Let's define $d_i$ to be the difference $g_i - c_i$.
Basically it's a greedy solution where you look for the first $k$ s.t.
$...
0
votes
0answers
48 views
Sequential Tasks with Greedy Algorithm
We have N tasks that need to be scheduled for processing. Each task consists of two parts that need to executed in order. The first one is guarded by a mutex and therefore only one task can be ...
0
votes
0answers
23 views
A Variant to "Boats to Save People"
This question is a variant of LeetCode 881. Boats to Save People by removing the restriction of "each boat carries at most two people at the same time" from the original question.
Problem ...
3
votes
4answers
9k views
Fractional Knapsack in linear time
How to solve fractional knapsack in linear time? I found this on Google but don't really understand it.
Choose element $r$ at random from $R$ (set of profit/weight ratios)
Determine
$R_1 = \{ p_i / ...
2
votes
1answer
464 views
Task Distribution Algorithm
Different machine has different efficiency on different tasks, like:
...
-1
votes
1answer
29 views
Proving correctness for greedy algorithm in string removal problem
Problem Statement:
You are given a string s and two integers x and y. You can perform two types of operations any number of times.
Remove substring "ab" and gain x points.
For example, when ...
4
votes
1answer
333 views
An algorithm for a minimization problem, How to minimize the wasted length of combination of multiple items with different length and number
Suppose there is an unlimited number of pipes, each has length $x$ meters.
There is a list of requirements of pipes with shorter length than $x$. The number of these items are also given.
For example ...
0
votes
0answers
32 views
Sum optimization and greedy approach
I've came across the optimization bellow
$\phi=argmin_{\theta} \displaystyle\sum_{i=1}^{N}f(x_i,\theta)$
Can i say that minimizing this summation by minimizing each term $\left(\displaystyle\frac{df(...
0
votes
1answer
102 views
How to determine the approximation factor for greedy vertex cover algorithm?
The algorithm iteratively picks the vertex with maximum degree and removes it and every incident edge of the vertex, until only vertices with degree of $0$ are left.
Formally:
$\text{GreedyVertexCover}...
5
votes
0answers
54 views
Optimality of DSATUR on interval graphs
The DSATUR algorithm is a greedy graph coloring algorithm. It consists of applying the usual greedy coloring algorithm, considering vertices in reverse lexicographic order of (number of different ...
3
votes
1answer
127 views
Partition of a $k$-partite graph to minimal number of connected sets
Let $G$ be a $k$-partite directed acyclic graph where the edges are only between two adjacent sets of vertices.
I'm trying to partition the graph to the minimal number of connected sets.
Sets $A_0, ...
1
vote
1answer
26 views
Minimal number of intervals that covers $\{1,...,k\}$
Let $F$ be a family of sets of consecutive integers in $\{1,…,k\}$ that is closed under taking subintervals, i.e. for any $a≤b≤c≤d$, if $\{a,…,d\} \in F$, then $\{b,…,c\} \in F$ also. Find a minimum ...
3
votes
0answers
30 views
Equalizing level of water in glasses problem
I have a problem on my hands, and would like help matching it to the existing, studied problems. I explain it like so:
I have a sequence of $n$ equal-sized glasses of water. Each has a different ...
-1
votes
1answer
34 views
Fitting arrays into RAM algorithm question
We'll consider the RAM as a sequence of cells that can contain data. Some cells already contain some data, some are empty. The empty cells form the so-called memory clusters. Thus, a memory cluster is ...
37
votes
3answers
37k views
How to prove greedy algorithm is correct
I have a greedy algorithm that I suspect might be correct, but I'm not sure. How do I check whether it is correct? What are the techniques to use for proving a greedy algorithm correct? Are there ...
1
vote
0answers
46 views
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 ...
0
votes
0answers
160 views
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 ...
1
vote
0answers
20 views
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 ...
1
vote
1answer
86 views
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 ...
0
votes
1answer
61 views
What Makes an Algorthim Greedy [Graph Coloring Algorithm]
I have a simple graph G = (V,E) and each vertex has a range [a,b].Every two vertices are connected only if [a_1,b_1] and [a_2,b_2] have a common subrange.
Each range of vertex is rV1 = [0,5] rV2 = [1,...
0
votes
0answers
39 views
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 ...
1
vote
3answers
46 views
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, ...
0
votes
0answers
27 views
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 + ...
0
votes
0answers
29 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,...
2
votes
0answers
37 views
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 ...
-1
votes
1answer
156 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 ...
0
votes
0answers
33 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 ...
2
votes
1answer
24 views
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 ...
2
votes
2answers
441 views
FInding the combination with the least number of elements from and array of integers, given an integer sum
I'm doing and assignment where the problem is to find the combination with the least number of elements form an array of integers, given an integer sum. I have solved this using a gready algorithm ...
1
vote
1answer
433 views
Proof that the length of the largest ascending subsequence is the number of decreasing subsequences
Given a sequence of numbers, I have to prove that the number of decreasing subsequences (non-strictly), so that every number is included in one subsequence and the number of subsequences is minimum is ...
1
vote
1answer
43 views
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:
...
3
votes
1answer
45 views
Expected behavior of an algorithm to minimize rankings
Suppose $n$ students have preferences over $n$ different notebooks. Their preferences can be represented with a square matrix of size $n$ where each column is a different permutation of the vector $[1:...
2
votes
1answer
46 views
k-center problem: proof for Gon algorithm gives a 2-approximation
The $k$-center problem is where we a given a graph $G(V,E)$, an integer $k$, a distance metric $d$ and we want to find a subset $C\subseteq V$ (such that $|C|\leq k$) which minimizes the following ...
1
vote
1answer
25 views
Greedy approach suggestions for assigning objects
Suppose there are three categories of people.
Type X, Type Y, Type Z.
In each type, there are two objects of subtype Type 'a' and type 'b'.
For example.
X: a1 , a2 , b1 , b2
Y: a3 , a4 , b3 , b4
Z: a5 ...
1
vote
1answer
87 views
Find minimum number of points which intersect overlapping arcs
Say I have a circle of a fixed radius, with overlapping arc intervals along its edge. I want to return a minimum set of Points which intersects all arcs in $n^2$ time.
I'm having some trouble proving ...
1
vote
1answer
37 views
Does any graph based optimization problem, which have a greedy algorithm, has guarantee that there exist an order which give the optimum
There exist greedy algorithms for vertex coloring like optimization problems. We know that for graph coloring, there is an order of vertices for which greedy coloring produces the optimum results. Is ...
0
votes
1answer
33 views
A problem about Huffman codeword
Under Huffman Encoding, what circumstances codeword length of each character
be equal?(suppose number of character is power of 2)
I think if all frequency of characters is same then codeword length ...
1
vote
1answer
65 views
Greedy algorithm for maintaining drugs
Given $n$ drugs such that each drug $d_i$ should maintain in interval
$[c_i,h_i]$.We want to minimize number of containers to maintain
medicines in compatible interval.
My answer is as follows:
I use ...
2
votes
1answer
13 views
Scheduling algorithm for a student's study times given assignments, expected time, due dates, and class times
I would like to create an algorithm that advises a student when they should work on certain assignments given the expected time each assignment will take, and the due date of each assignment.
Say that ...
4
votes
1answer
139 views
Hamiltonian path greedy and anti-greedy algorithms
I had this question on a problem set recently, but I wasn't sure how to solve it.
Given a complete weighted undirected graph $G$, here are two "algorithms" to find a Hamiltonian path:
...
0
votes
0answers
89 views
Finding name of a specific problem
Input : $x \in \mathbb Z$ and $a_1,a_2,\dots,a_n \in \mathbb N$.
Output : $b_1,b_2,\dots,b_n \in \mathbb Z$ such that $\sum_{i} a_i b_i=x$ and $\sum_{i}|b_i|$ is minimized.
Main question is, can we ...
0
votes
0answers
55 views
Need help with a very specific Greedy Algorithm. Are there fast solutions?
i need help for a specific problem i have at work.
You have N number of rows in an array, each with some distribution of Numbers that range from 0 to N.Given an array of size 1000:
Row 1 might look ...
0
votes
0answers
29 views
Minimum cost bin assignment
I've been trying to solve the below problem the entire day but couldn't come up with a solution. I have the suspicion that it could by solved by a graph algorithm (or maybe some greedy approach?) but ...
1
vote
1answer
36 views
Must an optimization problem with a greedy algorithm belong to P?
If it is known that for some optimization problem there is a greedy algorithm that solves it and the solution includes sorting of input at the preliminary stage, is it necessarily true that the ...
1
vote
2answers
79 views
Best approach to resource allocation problem
Problem
The enemy army has taken $n$ of our cities. In each city $i$ the enemy has placed $e_i$ soldiers. We have $n$ teams, each team $j$ with $d_j$ soldiers. If we place more soldiers in a city ...
0
votes
1answer
27 views
Algorithm of split graph $G=(V,E)$ to 2 groups that at least half of the edges are between the groups [duplicate]
Can someone remind me the algorithm that split vertex of graph to 2 groups that at least half of the edges are external, I mean between the groups. As I remember it was a greedy algorithm, each time ...
2
votes
2answers
91 views
Maximize number of subsets
Given a list of subsets $S_1, \ldots, S_n$ of the universal set $U = \{e_1,\ldots, e_m\}$, find a subset $S \subset U$ of size $k$ that contains the maximum number of subsets $S_i$. In another words,
$...
4
votes
1answer
61 views
Is the following Greedy algorithm to generate Gray Codes always correct?
I recently solved the basic problem of generating a n-bit Gray Code. The solution I used involved building larger-bit Gray Codes from smaller ones recursively (the solution I've seen on most websites)....
2
votes
1answer
348 views
Going deeper with pseudo-polynomial time algorithm for set partitioning
If I have a set of (edit) positive integers, and I'm sure that the pseudo-polynomial time algorithm for partitioning the problem will not give me an answer - what would I do next?
To illustrate this ...
