13 docs tagged with "backtracking"

In this blog post, we'll explore the backtracking algorithm, a powerful technique for solving combinatorial problems by building solutions incrementally.

The Bron-Kerbosch algorithm is a backtracking algorithm used to find all maximal cliques in an undirected graph. Known for its efficiency, especially on sparse graphs, it is widely applied in social network analysis, bioinformatics, and computational chemistry. The algorithm can be optimized with pivoting to reduce recursive calls and improve performance.

The Generate Parentheses problem requires generating all combinations of well-formed parentheses given n pairs. The solution uses recursion and backtracking to ensure that each combination is valid.

Hamiltonian Path and Cycle problems are a classic graph theory problem where the task is to find a path or cycle that visits every vertex exactly once. These problems are NP-complete and are widely used in various applications such as route planning, logistics, and genome sequencing.

The Knight's Tour problem is a classic backtracking problem where the goal is to move a knight across an n×n chessboard such that it visits every square exactly once. The problem is often solved using backtracking and recursion.

The Letter Combinations of a Phone Number problem involves generating all possible letter combinations that a string of digits (2-9) can represent based on a standard telephone keypad. This problem is often solved using recursion and backtracking.

The M-Coloring problem is a backtracking algorithm where the task is to assign colors to vertices of a graph so that no two adjacent vertices share the same color. The goal is to find if it is possible to color the graph using at most M colors.

The N-Queen problem is a classic combinatorial problem in which the goal is to place N queens on an N×N chessboard such that no two queens threaten each other. This means that no two queens can share the same row, column, or diagonal. The problem is often solved using backtracking, a form of recursion.

Overview and implementation of the N-Queens problem using a backtracking algorithm.

The N-Queens problem is a classic backtracking problem where the objective is to place N queens on an N×N chessboard such that no two queens threaten each other.

The N-Queens Problem is a classic problem where the objective is to place `N` queens on an `N x N` chessboard such that no two queens can attack each other. A queen can attack any other piece in the same row, column, or diagonal, making it challenging to place all `N` queens without conflict.

The Sudoku problem is a popular puzzle where the objective is to fill a 9x9 grid with digits from 1 to 9 so that each column, each row, and each of the nine 3x3 subgrids contain all the digits from 1 to 9 without repetition.

Backtracking is a systematic algorithmic method for solving problems where you need to explore all possible configurations (solution candidates) and discard those that fail to satisfy the given constraints. It is widely used to solve constraint satisfaction problems such as puzzles, combinatorial optimization problems, and decision problems.