Questions tagged [backtracking]
The backtracking tag has no usage guidance.
52
questions
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1answer
17 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 ...
0
votes
2answers
87 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 ...
1
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0answers
46 views
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 ...
1
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0answers
22 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, ...
0
votes
0answers
19 views
How to apply AC-3(Arc-consistency 3) algorithm in N-Queen problem?
I am building N-Queen Solver with java.
I confused with AC-3 algorithm.
I heard that AC-3 can be applied with backtracking algorithm before processing and during the search.The latter is called MAC-3 ...
1
vote
1answer
35 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 ...
0
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0answers
16 views
How to calculate constraint check in BT of 4-Queens problem?
I have seen number of constraint check in paper of CSPs.
The constraint checking is counted as followed: when a value of a variable x is checked against a value of variable y, this is counted as ...
3
votes
2answers
59 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 ...
0
votes
2answers
99 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 ...
0
votes
1answer
61 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 ...
1
vote
1answer
22 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 ...
1
vote
1answer
51 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:
...
2
votes
1answer
176 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 ...
0
votes
1answer
85 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 ...
2
votes
1answer
459 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 ...
0
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0answers
76 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 $0\leq y < n$ ...
0
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1answer
53 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 $i$ ...
-1
votes
2answers
418 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 ...
1
vote
1answer
157 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 ...
0
votes
1answer
30 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 ...
1
vote
0answers
246 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:
...
0
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1answer
693 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 ...
2
votes
1answer
154 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 ...
0
votes
1answer
622 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, ...
2
votes
1answer
464 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 ...
1
vote
1answer
146 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 ...
2
votes
0answers
27 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), ...
6
votes
1answer
114 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} \ $, $\...
1
vote
1answer
69 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 ...
4
votes
2answers
8k 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 ...
0
votes
2answers
2k 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 ...
1
vote
0answers
136 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
votes
1answer
297 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 ...
2
votes
1answer
620 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 ...
4
votes
0answers
66 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
votes
1answer
146 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
votes
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 ...
2
votes
1answer
532 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
votes
1answer
13k 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
votes
0answers
600 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
votes
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
votes
1answer
892 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
396 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,-...
5
votes
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
vote
2answers
461 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 $k$.
...
5
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2answers
5k 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
89 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
vote
1answer
121 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
101 views
0
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1answer
352 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)...
