Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

All Questions

0
votes
0answers
37 views

Greedy algorithm correctness

I'm trying to solve the following problem: CEO is checking on it's employees at a constant times every day (for an example the number of minutes after a shift started> {5, 35, 120..}). ...
0
votes
1answer
297 views

Is my proof of my greedy algorithm to find subsequence correct?

Credit to KleinBerg and Taros Book Some of your friends have gotten into the burgeoning field of time-series data mining, in which one looks for patterns in sequences of events that occur over time. ...
0
votes
1answer
241 views

How this proof of fractional knapsack works?

I don't understand a step in my book proving the fractional knapsack problem: Let value of items $v_1\ge v_2\ge \dots\ge v_n$, and assume $X=\langle x_1, \dots,x_n\rangle$ are the solution by ...
1
vote
1answer
163 views

Correctness proof for greedy algorithm based on ratio

I've an issue stated as follows: We have 10000 jobs to do, each with some length $l_i$ and weight (importance) $w_i$. Our goal is to arrange the schedule of doing these jobs (in other words, ...
1
vote
1answer
325 views

Proof of a greedy algorithm concerning “Buy and Resell Problem”

"Buy and Resell Problem" can be described in the following way: There are $n$ cities. For each city, the price of products in this city is given (a positive number). Now a person will travel from ...
0
votes
1answer
487 views

proof of correctness for greedy knapsack algorithm

I don't really understand why is statement 1 ≥ statement 2 in the attached picture. From what I understand the negative term in statement 2 must be greater than or equal the negative term in statement ...
1
vote
1answer
35 views

Check if possible to perform n tasks, each between moment b(i) and e(i) and taking 1 time unit

I have such a task at university: we have n tasks, i-th of them can be done between moment b(i) and e(i). If we decide to perform a task in moment x, we finish performing it in moment x+1. We can ...
1
vote
2answers
55 views

Element wise product sum of two arrays

I have two arrays, namely $a$ and $b$. Both have the same length $n$. I have to find the maximum value of $\sum a_i b_j$, in which every element can be used at most one time. My algorithm for solving ...
1
vote
0answers
77 views

how to prove correctness of this greedy algorithm? [duplicate]

I did exercise problem from Pittsburgh university cs department. homework. Question 8 is somewhat exciting. Q8 is solved using greedy algorithm but I have no idea how to prove. Below is Question. ...
4
votes
1answer
904 views

Greedy algorithms: Minimum sum number pairing

Given $n$ real numbers (where $n$ is even) find a pairing which minimizes the maximum sum of a pair. I think the optimal pairing is obtained by sorting the original set, pairing the first element ...
3
votes
1answer
724 views

How to prove a greedy algorithm that uses the longest increasing subsequence?

Here is the thing, I am solving an problem, and I think, say, I am pretty sure that I have the correct algorithm but I haven't been able to prove it because of my lack of practice prooving greedy ...
1
vote
0answers
279 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 ...
0
votes
1answer
155 views

Cards shuffling. Greedy algorithm

We have n deck of cards. To shuffle i-th deck we need a(i) seconds. Our task is to give a greedy algorithm, which will merge two decks until we have one deck. My idea is to create a priority queue. ...
0
votes
0answers
137 views

Greedy algorithm correctness proof (UVA 10716)

Given an input string, not necessarily a palindrome, compute the number of swaps necessary to transform the string into a palindrome. By swap we mean reversing the order of two adjacent symbols (UVA ...
25
votes
2answers
22k 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
5answers
471 views

Correctness of the greedy algorithm

I am trying to solve the following problem: Given a matrix which consists of only 0's and 1's. Considering the matrix as a metal sheet, we need to "cut-out" square blocks of sizes 2x2 consisting of ...
4
votes
1answer
402 views

Greedy algorithm correctness proof for “Elegant Permuted Sum” (UVa 11158)

Given a sequence of $2 \leq n \leq 50$ numbers $s = (s_1,s_2,...,s_n)$, find a permutation $a = (a_1,a_2,...,a_n)$ of $s$ such that $$\sum_{i=1}^{n-1} |a_i - a_{i+1}|$$ is maximized. I found many ...
1
vote
1answer
2k views

People crossing a bridge (a proof for a greedy algorithm)

The problem Some people are crossing a bridge. Each one takes a different time to pass. Assume the people are sorted by their passing time increasingly. These are the conditions of crossing the ...
1
vote
0answers
53 views

Conjecture about a matrix column swapping challenge problem

So here is the challenge problem statement: https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=1512 Basically, given a 0/1 matrix, you ...
1
vote
3answers
4k views

Correctness proof of greedy algorithm for 0-1 knapsack problem

We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an ...
-1
votes
2answers
2k views

Proof of Correctness of Prim's algorithm [duplicate]

what is the reason for the correctness proof of Prim's Algorithm for the undirected case cannot carry over to the directed case? Is it because of after any number of steps, $S$ might not be in a sub ...
2
votes
1answer
11k views

Proving greedy choice property of fractional knapsack

A typical way of proving the greedy choice property of the fractional knapsack problem is as follows: From Slide 5 of this link: Given: A set of items $I = \{I_1,I_2..I_n\}$ with weights $\{w_1,w_2 ....