Find paths from corner cell to middle cell in maze

Given a square maze containing positive numbers, find all paths from a corner cell (any of the extreme four corners) to the middle cell. We can move exactly n steps from a cell in 4 directions i.e. North, East, West and South where n is value of the cell,

We can move to mat[i+n][j], mat[i-n][j], mat[i][j+n], and mat[i][j-n] from a cell mat[i][j] where n is value of mat[i][j].

Example

Input:  9 x 9 maze
[ 3, 5, 4, 4, 7, 3, 4, 6, 3 ]
[ 6, 7, 5, 6, 6, 2, 6, 6, 2 ]
[ 3, 3, 4, 3, 2, 5, 4, 7, 2 ]
[ 6, 5, 5, 1, 2, 3, 6, 5, 6 ]
[ 3, 3, 4, 3, 0, 1, 4, 3, 4 ]
[ 3, 5, 4, 3, 2, 2, 3, 3, 5 ]
[ 3, 5, 4, 3, 2, 6, 4, 4, 3 ]
[ 3, 5, 1, 3, 7, 5, 3, 6, 4 ]
[ 6, 2, 4, 3, 4, 5, 4, 5, 1 ]

Output:
(0, 0) -> (0, 3) -> (0, 7) -> 
(6, 7) -> (6, 3) -> (3, 3) -> 
(3, 4) -> (5, 4) -> (5, 2) -> 
(1, 2) -> (1, 7) -> (7, 7) ->
(7, 1) -> (2, 1) -> (2, 4) -> 
(4, 4) -> MID

http://www.geeksforgeeks.org/find-paths-from-corner-cell-to-middle-cell-in-maze/

Backtracking — Search a Word In a Matrix

 Given a 2D matrix of char­ac­ters. Check whether the word exist in the matrix or not. If it exists then print its path. All move­ments are allowed (right, left, up, down and diagonally).

http://algorithms.tutorialhorizon.com/backtracking-search-a-word-in-a-matrix/

Backtracking — Knight’s Tour Problem

A knight’s tour is a sequence of moves of a knight on a chess­board such that the knight vis­its every square only once. If the knight ends on a square that is one knight’s move from the begin­ning square (so that it could tour the board again imme­di­ately, fol­low­ing the same path), the tour is closed, oth­er­wise it is open. (Source : http://en.wikipedia.org/wiki/Knight%27s_tour)

http://algorithms.tutorialhorizon.com/backtracking-knights-tour-problem/

Backtracking — N Queens Problem

Backtracking — N Queens Problem

In chess, a queen can move as far as she pleases, hor­i­zon­tally, ver­ti­cally, or diag­o­nally. A chess board has 8 rows and 8 columns. The stan­dard 8 by 8 Queen’s prob­lem asks how to place 8 queens on an ordi­nary chess board so that none of them can hit any other in one move.(Source: http://www.math.utah.edu/~alfeld/queens/queens.html)

Here we are solv­ing it for N queens in NxN chess board.

http://algorithms.tutorialhorizon.com/backtracking-n-queens-problem/

Backtracking — SUDOKU Solver

The objec­tive is to fill a 9×9 grid with dig­its so that each col­umn, each row, and each of the nine 3×3 sub-grids that com­pose the grid (also called “boxes”, “blocks”, “regions”, or “sub-squares”) con­tains all of the dig­its from 1 to 9. The puz­zle set­ter pro­vides a par­tially com­pleted grid, which for a well-posed puz­zle has a unique solu­tion. (Source: Wiki — http://en.wikipedia.org/wiki/Sudoku)

http://algorithms.tutorialhorizon.com/backtracking-sudoku-solver/

Rat in a maze algorithm

A mouse is at one corner of a maze and he has to reach the corner diagonally opposite to him. Write an algorithm to find the path through the maze. The maze is represented by a matrix of '0's and '1's where '1' denotes a path and '0' denotes a wall.

http://algorithms.tutorialhorizon.com/backtracking-rat-in-a-maze-puzzle/
http://www.geeksforgeeks.org/backttracking-set-2-rat-in-a-maze/

Code:BackTracking

#include<stdio.h>
#include<stdlib.h>

#define N 4

void printMaze(int maze[N][N])
{
    int i, j;

    for(i=0; i < N; i++)
    {
        for(j=0; j < N; j++)
            printf("%d ", maze[i][j]);
        printf("\n");
    }
}

void move(int maze[N][N], int sol[N][N], int x, int y)
{
    if((x == N-1) && (y == N-1))
    {
        sol[x][y] = 1;
        printMaze(sol);
        return;
    }

    if(x != N-1)
    {
        if(maze[x+1][y])
        {
            sol[x][y] = 1;
            move(maze, sol, x+1, y);
            sol[x][y] = 0;
        }
    }

    if(y != N-1)
    {
        if(maze[x][y+1])
        {
            sol[x][y] = 1;
            move(maze, sol, x, y+1);
            sol[x][y] = 0;
        }
    }
}

int main()
{
    int maze[N][N] =
    {
        {1, 0, 0, 0},
        {1, 1, 0, 1},
        {0, 1, 0, 0},
        {0, 1, 1, 1}
    };

    int sol[N][N] = {0,};

    move(maze, sol, 0, 0);
    return 0;
}

Backtracking

Disucuss Backtracking and relevent method to solve algorithmic problems