# Questions tagged [backtracking]

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### Given a sequence of strings how can you find the maximum number of strings so that if you concatenate them you have a dominant letter?

The naive approach, which is the first thing that came to my mind, is to use some sort of backtracking to generate all subsets of the given set of strings and then to find the subset with the maximum ...
1 vote
90 views

### Partition a set of n integers into m subsets in a way that the maximum subset sum is minimized

Let's say we have a set of n integers. I'm trying to find a way to partition this set into m subsets (empty subsets are not ...
1 vote
19 views

### Find optimal starting point of recursive search, with solution known

An Exact Cover problem is commonly denoted as a matrix of 0s and 1s. Columns denote requirements, rows denote possible choices. The problem is solved when a set of rows was found such that, using just ...
78 views

### Time Complexity - Palindrome Partition

I am solving an interview practice question: Partition s such that every substring of the partition is a palindrome. Return all possible palindrome partitioning of s. My solution is as below, and was ...
1 vote
788 views

### Minimum no of swaps to be done in an array such that, no two adjacent elements are same

Given an array of size n, find minimum number of swaps required, so that no two adjacent elements are equal. For ex- n = 6, a[] = {1, 1, 5, 2, 5, 5}, answer = 1, ( swap a with a or a ) n = 8,...
19 views

### How do I group elements of a list into windows of predefined sizes with minimum cost given longer windows are cost efficient?

You are given a list of days numbered 0 to 365 in the calendar year where you need to be in a hotel. You need to book in advance for the year and need not necessarily be there when you have a booking. ...
45 views

### Complexity of backtracking to find power set given random array of numbers

Given an array of elements which can contain duplicates, this is an algorithm that solves the problem. ...
321 views

### Longest sequence of dominoes

Given $k$, a $k$-domino is a non-ordered pair of integer values of $[\![0, k-1]\!]$, for example $\langle 0, 3\rangle$ or $\langle 1, 1\rangle$ are dominoes, the domino $\langle 3, 0\rangle$ being the ...
183 views

### recurrence relation for this n queen problem algorithm . and the time complexity

I am not able to understand how to write a recurrence relation for this n queen problem algorithm down below. Recurrence relation is for n*n board and the time complexity ...
47 views

### How to solve this combinatoric problem without bruteforce

I'm trying to solve the following problem : A tile results of a number and a color. a tile can be black, red, orange or blue. a tile number is >= 1 and <= 15. Given a random set a tiles (a ...
22 views

### I need good book about algorithms, which explains recursion, backtracking and depth first recursion for beginners [duplicate]

I'm learning programming, Python 3 in particular, and I have a good book "Beginning Python - From Novice to Professional" by Magnus Lie Hetland, but the book doesn't explain algorithms at ...
1 vote
148 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 ...
1 vote
197 views

### Why is backtracking a necessary step in the Maze problem?

The problem I am working on is specifically this: A Maze is given as N*N binary matrix of blocks where source block is the upper left most block i.e., maze and destination block is lower ...
39 views

### Maximize Possible Subset Sums of A Multiset

The following problem is a problem I faced in one of my coding competitions. Given two positive integers $N$, $M$. You can have $M$ distinct types of stones, for which different types of stones must ...
42 views

### Number of Hamilton paths in graphs

I am trying to find a fast algorithm that can compute the number of hamiltonian paths in an undirected graph. I saw this on the web, but it sounds like this finds all hamiltonian paths starting from ...
1 vote
48 views

### Does this LCS algo generate all the CS or only all the LCSs?

The Wikipedia article on LCS has an algorithm that backtracks all the LCS strings. This link redirects to the desired bulletin in the article. The C table in the backtrackAll function is pre-...
31 views

### 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!=[]: ...
41 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 - ...
60 views

### Extending a solution in backtracking

Steven Skiena's "Algorithm Design Manual" has the following code for the backtracking algorithm: ...
1 vote
747 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 ...
60 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 ...
1 vote
112 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 ...
1k 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 '...
51 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 ...
178 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 ...
483 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;
1 vote
424 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 ...
1k 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 vote
233 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 vote
26 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 ...
1 vote
39 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 ...
83 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 ...
437 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 ...
192 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
58 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
176 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: ...
677 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 ...
449 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 ...
3k 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 ...
166 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 $0\leq y < n$ ...
76 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 $i$ ...
1k 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
372 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 ...
161 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....
1 vote
444 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: ...
4k 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 ... 534 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 ...
1k 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, ...