backtracking

Solving Sudoku using Backtracking

Introduction This post is the continuation of the backtracking series. Sudoku can be solved using multiple algorithms based on Neural Networks and Genetic Algorithms by doing exhaustive searches in the solution space. However, here we are focusing on solving Sudoku using backtracking algorithm. For people who are unaware of the Sudoku puzzle, please check out Wikipedia for details. For a brief description read below: A Sudoku puzzle is a 9 * 9 grid. Few cells in the grid contain random numbers between 1 and 9 (both inclusive) A fully solved Sudoku must contain numbers through 1-...
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Print all paths of robot through the grid

Introduction This is a supplement to the previous post where we were interested in just one path of a robot from top left corner to the bottom right corner. In this post we will print all paths of robot moving through a given grid containing few blocked cells. The algorithm for this solution remains the same, we just need few tricks to get that right. Here, I will explain the idea behind printing all paths of robot through the grid. Approach Here, let us discuss what different we need to do to print all the paths. As we can recall from the previous post, the moment we reached the destina...
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Find Path through grid – constrained motion

Introduction This is another addition to the backtracking series of problems. The problem is asked in many interviews in many different forms. Here are few of them: Given a grid where few of the cells are blocked. You have a robot placed at the top left corner of the grid. Find path through grid such that the robot starts from the top left corner and moves to the bottom right corner. Another form just asks for all possible paths from one cell to another into a grid. Of course there are constraints on the movement of the robot, else you would end up going in circles and the paths wo...
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Knight’s Tour Problem Simply Explained

Introduction This post is a continuation of the back tracking series. You can refer to other similar posts here. In this post we will be discussing the Knight's Tour Problem. The problem states that, given a N * M chessboard, a Knight's Tour is defined as the sequence of moves of a Knight, such that the Knight visits every square only once. Does this sound similar? Yes it is similar to finding the Hamiltonian Path as defined in this post. Approach for solving the Knight's Tour problem Here I define the backtracking approach to solve this problem. Let the Knight start from any location...
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Solving the N Queen Problem

Introduction The N Queen Problem is one of the best problem used to teach backtracking and of course recursion. Backtracking is a general algorithm which finds all complete solutions to a problem by building over partial solutions. In this process, the problem might reach to a partial solution which may not result into a complete solution. Such partial solutions are effectively rejected by the backtracking algorithm. To know more about backtracking please visit the Wikipedia article. The classic case of N Queen problem In this problem, you are given an empty chess board of dimensions N *...
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