Questions tagged [backtracking]

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Problem with the algorithm

I am trying to execute the following algorithm shown in the image from my course slide. I am trying to get the table shown in the image: 1st Iteration L2: 1:CS=A, SL = A, NSL = A L3: while NSL!=[]: ...
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35 views

Choosing a method for algorithmic problems - is it an art or science?

I've been doing lot of programming challenges lately (such as on leetcode.com) and often find myself in a situation when I cannot pick a method for solving a problem. I stuck with questions like - ...
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20 views

Extending a solution in backtracking

Steven Skiena's "Algorithm Design Manual" has the following code for the backtracking algorithm: ...
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2answers
61 views

Does DFS have better constants/complexity than Backtracking on a Graph?

I came to know through some examples that DFS and Backtracking aren't exactly the same ( A misconception I had since a long time). So now my question is, since Backtracking visits nodes backwards step ...
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40 views

The class of grammars recognizable by backtracking recursive-descent parsers

It is easy to show that there exists a grammar that can be parsed by a recursive-descent parser with backtracking but is not an $\text{LL}(k)$ grammar (consider any grammar with a production featuring ...
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93 views

Can the algorithm be optimized?

I am new to backtracking and recursion. I have seen numerous explanations on how on to find the minimum number of coins needed to make a particular amount. This involves a top down dynamic approach ...
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6 views

Backtracking - How do explicit constraints depend on problem instance in backtracking?

I was reading the Chapter on Backtracking in Fundamentals of Computer Algorithms by Horowitz and Sahani, and I read the following line. The explicit constraints depend on the particular instance I ...
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512 views

Backtracking vs Branch-and-Bound

I'm getting a bit confused about the three terms and their differences: Depth-First-Search (DFS), Backtracking, and Branch-and-Bound. What confuses me: Stack Overflow: Difference between '...
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1answer
41 views

Why N-Queens Problem is not used as experiment in CSP thesis?

I am studying CSP for my master thesis. I found that many thesis based on CSP described N-Queens as an introductory and they actually do experiment on random CSP problems. If so,when I do master ...
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2answers
64 views

Need recursive version of Conflict based backjumping

I am implementing conflict directed Backjumping algorithm of prosser in java. But, the algorithm is iterative approach. How can it be built with recursive approach? In AIMA they give the recursive ...
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203 views

Does Warnsdorff’s algorithm for Knight’s tour problem always gives complete tour

I have implemented the basic algorithm. easily available but I am not getting the complete tour. The visited square never equals N * N;
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74 views

Line-search does not guarantee convergence so how to use it?

Line-search/backtracking in gradient descent methods essentially boils down to picking the current estimate $\theta_n$ (which depends on the stepsize $\gamma$ and the prior estimate $\theta_{n-1}$) by ...
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713 views

How to generate all combinations given an array of elements using backtracking?

Given an array, generate all combinations For example: Input: {1,2,3} Output: {1}, {2}, {3}, {1,2}, {2,1}, {1,3}, {3,1}, {2,3}, {3,2}, {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1} I am ...
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How to approach backtracking when using immutable types (Python)? [closed]

In Python when we are building a recursive algorithm that uses backtracking a mutable type such as a list is great to use. It can be modified at each call in our recursion tree, then returned back to ...
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23 views

How to rule bactrack research on alphametric puzzles?

I have a funny aphametic problem: I A + I A ----- P B I have to find which are the values of the letters. I know I can try backtrack with forward research, MRV ...
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1answer
36 views

Cracking code with clues

I am trying to solve this code cracking problem. The solution is either the code or all possible solutions if you can't narrow the possibilities. We have a 5 character code that is consisting of ...
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2answers
72 views

Maximize number of museums visited in a day

Given a list of museums, their opening hours and time needed to visit each, make a schedule such that a tourist visits maximal number of museums in a given day. Suppose that no time is needed in ...
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2answers
154 views

Why run -time of N-Queens using backtracking algorithm fluctuates?

I have tested and measured the running time of a backtracking algorithm for solving the $N$-Queens problem. When $N=7$, the run time is $0.773$, but for $N=8$, the run time is $0.492$. I think the ...
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1answer
129 views

Help with graph search problem

For the next problem I can not think of how to find a solution with graph searches (I thought it was backtracking but my college professor told me that I should use graph searches, which I do not know ...
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1answer
30 views

Is there any advantage of using an Integer Linear Program over Backtracking in a combinatorial optimization problem?

Is there any advantage of using an Integer Linear Program over Backtracking in a combinatorial optimization problem? I saw this Gurobi post that uses Integer Linear Programming to solve the traveling ...
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1answer
63 views

How to count the combinations not greater than a given volume in a knapsack problem?

You are given a certain set of items with weight wi and the volume of the bag. Case: ...
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1answer
373 views

Can memoization be applied to any recursive algorithm?

I am new to the concepts of recursion, backtracking and dynamic programming. I am having a hard time understanding if at all I can apply memoization to a particular recursive algorithm and if there ...
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1answer
249 views

Recursively edit 2-D array using backtracking

I have a 2-D array which contain 3 types of elements: C (Contaminant) R (Rock) W (Water) The rule is that: contaminant can seep through water but not through rocks. Let's say I have the ...
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1answer
2k views

Checking the validity of a pyramid of dominoes

I came across this question in a coding interview and couldn't figure out a good solution. You are given 6 dominoes. A domino has 2 halves each with a number of spots. You are building a 3-level ...
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115 views

N-Queens problem - maximum number of function calls

N-Queens problem - maximum number of function calls. We say, that a backtracking algorithm (code below) 'checks' a setup of N queens, when the function isFree(n-1, y) is called for $0\leq y < n$ ...
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1answer
62 views

Interpretation of Backtracking Algorithm Problem - weighted matching

I am attempting to resolve the following problem using Backtracking: Suppose that you have $n$ men and $n$ women and two matrices P y Q (n x n); such that $P_{ij}$ is the preference of the man $i$ ...
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897 views

How can I write this backtracking algorithm using dynamic programming?

Problem: There are $n$ points on a map, $p_1,..p_n$. There are two officers located initially at $(0,0)$ coordinate. They want to patrol all of these points with a minimum traveling (each officer ...
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1answer
241 views

Algorithm to organize a tournament where the team componentes change each round

So, I was tasked with creating an app that generates the schedule of a doubles tennis tournament (i.e., teams of two) in a way that, by the end of it, everyone would have played against the rest of ...
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1answer
89 views

Is any State Space Tree always Binary Tree?

A backtracking algorithm generates, explicitly or implicitly, a state-space tree. Introduction to the design & analysis of algorithms / Anany Levitin I wonder that whether the saying always holds....
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409 views

understanding constraint satisfaction problem: map coloring algorithm

I am trying to implement this recursive-backtracking function for a constraint satisfaction problem from the given algorithm: ...
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1answer
2k views

Aren’t most constraining variable and least constraining value the exact opposite?

So aren’t MCV and LCV the exact opposite?MCV tries to choose the variable with the most constraints on remaining variables but LCV is opposite: it tries to rule out as least values for other variables ...
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1answer
323 views

SAT Solving + Turing Machines

I have a couple of questions based on how SAT solvers work. I understand that SAT solvers may employ any/all of the following techniques: Randomness Heuristics Backtracking SAT is just one example ...
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1answer
816 views

Divide an array into two sub arrays such that their sums are equal and possibly maximum

Given an array A, we should partition A into two subarrays whose sums are equal, and that maximizes this sum. We are free to omit items from the subarrays. For example, ...
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1answer
587 views

Optimal way to find maximal sum (with constraints) of array elements

Problem: Find the maximum sum of the elements in an array, with the following constraints: all the elements of the array are non-negative integers each element can either be left out completely from ...
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1answer
195 views

Print all subsets of a set ($a$) of $n$ positive integers, such that the product of their elements equals $p$

I have the following problem: Given a set a of n positive integers, write a backtracking C function that prints out all the subsets of a such that the product of their elements is p. Use an array ...
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32 views

Filling a board with maximum number of fixed size tiles

You are given a rectangular board of known size, e.g. 20x20 cm. Some 1x1 cm pieces are missing. Your task is to cover this board with a maximum number of 2x2 cm tiles (an example is attached below), ...
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1answer
138 views

Neural Network: Why can't we calculate derivatives during forward prop itself?

I have been studying Andrew Ng's Coursera course about Deep Learning. In that he mentions that we calculate the activation functions during the forward pass, and the derivatives $\dfrac{dL}{dz} \ $, $\...
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1answer
77 views

Filling a 3x3 board with connected tiles

long story short: I want to list all possible combinations of n tiles on a 3x3 board with the restriction that at least 6 tiles are part of a connected chain. Tiles are connected if the pattern ...
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2answers
11k views

Using backtracking to find all possible permutations in a string

I came across this algorithm in a book, and have been struggling to understand the basic idea. The books says it uses backtracking to print all possible permutations of the characters in a string. In ...
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2answers
3k views

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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186 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 ...
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1answer
425 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
945 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 ...
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70 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 ...
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1answer
170 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 , ...
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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 ...
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1answer
593 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 ...
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1answer
15k 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 ...
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838 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 $\phi$. ...
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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 ...