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Questions tagged [backtracking]

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Minimum sum of distance from entrance gate

Assumes we have N position, and 3 entrance gate. For example 10 position: 1--2--3--4--5--6--7--8--9--10 For each entrance gate, there is some people waiting to enter and fill positions, first number ...
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0answers
219 views

How to systematically think about building implicit tree or a search space graph?

I often see DFS is used interchangeably with backtracking specially in many permutation, combinations and subset problems. But usually DFS has implicit tree and does backtracking at leaf nodes whereas ...
2
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1answer
493 views

Binarization of Constraints

I am trying to solve a Constraint Satisfaction Problem that involves lots of n-ary constraints. But the solver I have implemented only works with algorithms for binary constraints. I've been reading ...
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1answer
1k views

time complexity of word break algorithm

I found this question here but I don't think the answer is correct. Here is the original word break question: Given a string s and a dictionary of words dict, add spaces in s to construct a sentence ...
4
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0answers
72 views

(Historical perspective) CSP and SAT inter-fertilization

[Disclaimer: this is a rather specialized question] It is known that techniques like Conflict-Driven Clause Learning (CDCL) and back-jumping -- which improved the Satisfiability (SAT) strategies ...
7
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1answer
187 views

Branch and bound for minimum linear arrangement

I am trying to solve this branch and bound problem but I could not come up with any approximate cost function which is better than the cost. Let's say $G$ is a graph of $n$ nodes $\{1, 2, 3, \ldots , ...
2
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1answer
249 views

Finding all soldier wins

Consider the following game (see also this question): One day a castle is attacked at sunrise (by surprise) by n soldiers. Each soldier carries a canon and a rifle. The castle has strength s. On the ...
3
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1answer
634 views

Why doesn't the Needleman-Wunsch algorithm find solutions that begin with a gap?

I have implemented in C++ the Needleman-Wunsch algorithm for pairwise sequence alignment using the following scores: +1 for match (regardless of base), -1 gap penalty and -1 for a mismatch. Given two ...
3
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1answer
16k views

Time complexity of this solution to N-queens problem

I'm trying to figure out the time complexity of this implementation of classic N-queens problem on geeksforgeeks. The goal is to find just one such non-attacking solution(as opposed to finding all of ...
2
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0answers
1k views

DPLL time complexity analysis

Consider the most naïve backtracking for CNF-SAT. It only checks if an assignment satisfies the input formula $\phi$ when all the $n$ variables have values assigned. Let $m$ be the size of $\phi$. ...
4
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1answer
1k views

Is there a more efficient algorithm than backtracking/dynamic programming?

Consider the following game: One day a castle is attacked at sunrise (by surprise) by n soldiers. Each soldier carries a canon and a rifle. The castle has strength s. On the first day each ...
9
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1answer
1k views

Conflict Driven Clause Learning backtracking clarification

On the wikipedia page here it describes pretty well the CDCL algorithm (and it seems the pictures were taken from slides created by Sharad Malik at Princeton). However when describing how to backtrack ...
2
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1answer
493 views

Basic question about backjumping in SAT solvers

I am reading "Formalization and Implementation of Modern SAT Solvers", by Filip Marić. My question is about how backjumping is defined. In an example [1], there is a conflict clause C equal to [-1,-...
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2answers
2k views

How does one formulate a backtracking algorithm

I am new to learning algorithms. I was reading backtracking algorithm for generating all strings for n bits. If I dry run the program I know the program is giving right result. But I didn't understood ...
1
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2answers
739 views

Maximum non-intersecting subset of circles

We are given a set of circles, stored by their center points in an array $A$. In particular, the center of the $i$th circle is at coordinates $(A[i].x, A[i].y)$. All the circles have radius of $k$. ...
6
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2answers
6k views

Greedy and backtracking solutions to an arrangement problem with constraints

I'm revising for my finals. I have found a pattern in past papers in terms of a recurring question, reworded coming up every year. But I've no idea what the marker actually wants... I've asked class ...
0
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1answer
145 views

Devise a backtracking algorithm to allocate $p$ projects to $s$ students

There are $p$ projects and $s$ students where $p \le s$. Multiple students can work on the same project but the same student cannot work on multiple projects. All projects must be allocated and all ...
1
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1answer
130 views

Generating hard puzzles for a backtracking snake

Let $M$ be a matrix of height $h$ and width $w$. Each entry of $M$ is an integer. There is a snake that starts from the "left side" of $M$, and its goal is to reach the "right side" of $M$. To get ...
1
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1answer
136 views
0
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1answer
402 views

Find all non-decreasing sequences given lenght and size [closed]

I'm trying to find a solution for this exercise: Give the pseudocode of an algorithm which takes two positive integers n and k and prints all the non-decreasing sequences of length k (1,2,...,n)...
1
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1answer
1k views

Backtracking for listing k elements

Can someone give me a hand here, I am new to backtracking, and preparing for an interview. I couldn't even attempt this question, please help. Describe a back tracking algorithm for efficiently ...
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1answer
651 views

Why does backtracking work the way it does?

I just recently started learning in a CS context (as opposed to a programming context) about simple recursive functions, along with the combinatorial applications, and techniques such as Backtracking ...

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