Find the minimum number of moves needed to move from one cell of matrix to another


Given a N X N matrix (M) filled with 1 , 0 , 2 , 3 . Find the minimum numbers of moves needed to move from source to destination (sink) . while traversing through blank cells only. You can traverse up, down, right and left.
A value of cell 1 means Source.
A value of cell 2 means Destination.
A value of cell 3 means Blank cell.
A value of cell 0 means Blank Wall.
Note : there is only single source and single destination.they may be more than one path from source to destination(sink).each move in matrix we consider as ‘1’

Examples:

Input : M[3][3] = {{ 0 , 3 , 2 },
                   { 3 , 3 , 0 },
                   { 1 , 3 , 0 }};
Output : 4 

Input : M[4][4] = {{ 3 , 3 , 1 , 0 },
                   { 3 , 0 , 3 , 3 },
                   { 2 , 3 , 0 , 3 },
                   { 0 , 3 , 3 , 3 }};
Output : 4

Asked in: Adobe Interview
.minimum_move



The idea is to use Level graph ( Breadth First Traversal ). Consider each cell as a node and each boundary between any two adjacent cells be an edge . so total number of Node is N*N. 

 1. Create an empty Graph having N*N node ( Vertex ).
 2. Push all node into graph.
 3. Note down source and sink vertices.
 4. Now Apply  level graph concept ( that we achieve using BFS  ) .
    In which we find level of every node from source vertex.
    After that we return  'Level[d]' ( d is destination ).
    (which is the minimum move from source to sink )

Below is implementation of above idea.

C++

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// C++ program to find the minimum numbers
// of moves needed to move from source to
// destination .
#include<bits/stdc++.h>
using namespace std;
#define N 4
  
class Graph
{
    int V ;
    list < int > *adj;
public :
    Graph( int V )
    {
        this->V = V ;
        adj = new list<int>[V];
    }
    void addEdge( int s , int d ) ;
    int BFS ( int s , int d) ;
};
  
// add edge to graph
void Graph :: addEdge ( int s , int d )
{
    adj[s].push_back(d);
    adj[d].push_back(s);
}
  
// Level  BFS function to find minimum path
// from source to sink
int Graph :: BFS(int s, int d)
{
    // Base case
    if (s == d)
        return 0;
  
    // make initial distance of all vertex -1
    // from source
    int *level = new int[V];
    for (int i = 0; i < V; i++)
        level[i] = -1  ;
  
    // Create a queue for BFS
    list<int> queue;
  
    // Mark the source node level[s] = '0'
    level[s] = 0 ;
    queue.push_back(s);
  
    // it will be used to get all adjacent
    // vertices of a vertex
    list<int>::iterator i;
  
    while (!queue.empty())
    {
        // Dequeue a vertex from queue
        s = queue.front();
        queue.pop_front();
  
        // Get all adjacent vertices of the
        // dequeued vertex s. If a adjacent has
        // not been visited ( level[i] < '0') ,
        // then update level[i] == parent_level[s] + 1
        // and enqueue it
        for (i = adj[s].begin(); i != adj[s].end(); ++i)
        {
            // Else, continue to do BFS
            if (level[*i] < 0 || level[*i] > level[s] + 1 )
            {
                level[*i] = level[s] + 1 ;
                queue.push_back(*i);
            }
        }
  
    }
  
    // return minimum moves from source to sink
    return level[d] ;
}
  
bool isSafe(int i, int j, int M[][N])
{
    if ((i < 0 || i >= N) ||
            (j < 0 || j >= N ) || M[i][j] == 0)
        return false;
    return true;
}
  
// Returns minimum numbers of  moves  from a source (a
// cell with value 1) to a destination (a cell with
// value 2)
int MinimumPath(int M[][N])
{
    int s , d ; // source and destination
    int V = N*N+2;
    Graph g(V);
  
    // create graph with n*n node
    // each cell consider as node
    int k = 1 ; // Number of current vertex
    for (int i =0 ; i < N ; i++)
    {
        for (int j = 0 ; j < N; j++)
        {
            if (M[i][j] != 0)
            {
                // connect all 4 adjacent cell to
                // current cell
                if ( isSafe ( i , j+1 , M ) )
                    g.addEdge ( k , k+1 );
                if ( isSafe ( i , j-1 , M ) )
                    g.addEdge ( k , k-1 );
                if (j< N-1 && isSafe ( i+1 , j , M ) )
                    g.addEdge ( k , k+N );
                if ( i > 0 && isSafe ( i-1 , j , M ) )
                    g.addEdge ( k , k-N );
            }
  
            // source index
            if( M[i][j] == 1 )
                s = k ;
  
            // destination index
            if (M[i][j] == 2)
                d = k;
            k++;
        }
    }
  
    // find minimum moves
    return g.BFS (s, d) ;
}
  
// driver program to check above function
int main()
{
    int M[N][N] = {{ 3 , 3 , 1 , 0 },
        { 3 , 0 , 3 , 3 },
        { 2 , 3 , 0 , 3 },
        { 0 , 3 , 3 , 3 }
    };
  
    cout << MinimumPath(M) << endl;
  
    return 0;
}

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# Python3 program to find the minimum numbers  


# of moves needed to move from source to  


# destination .  


  


class Graph: 


    def __init__(self, V): 


        self.V = V  


        self.adj = [[] for i in range(V)] 


  


    # add edge to graph  


    def addEdge (self, s , d ): 


        self.adj[s].append(d)  


        self.adj[d].append(s) 


      


    # Level BFS function to find minimum  


    # path from source to sink  


    def BFS(self, s, d): 


          


        # Base case  


        if (s == d):  


            return 0


      


        # make initial distance of all  


        # vertex -1 from source  


        level = [-1] * self.V 


      


        # Create a queue for BFS  


        queue = [] 


      


        # Mark the source node level[s] = '0'  


        level[s] = 0


        queue.append(s)  


      


        # it will be used to get all adjacent  


        # vertices of a vertex  


      


        while (len(queue) != 0): 


              


            # Dequeue a vertex from queue  


            s = queue.pop()  


      


            # Get all adjacent vertices of the  


            # dequeued vertex s. If a adjacent has  


            # not been visited ( level[i] < '0') ,  


            # then update level[i] == parent_level[s] + 1  


            # and enqueue it  


            i = 0


            while i < len(self.adj[s]): 


                  


                # Else, continue to do BFS  


                if (level[self.adj[s][i]] < 0 or 


                    level[self.adj[s][i]] > level[s] + 1 ): 


                    level[self.adj[s][i]] = level[s] + 1


                    queue.append(self.adj[s][i]) 


                i += 1


      


        # return minimum moves from source 


        # to sink  


        return level[d] 


  


def isSafe(i, j, M): 


    global N 


    if ((i < 0 or i >= N) or


        (j < 0 or j >= N ) or M[i][j] == 0):  


        return False


    return True


  


# Returns minimum numbers of moves from a  


# source (a cell with value 1) to a destination  


# (a cell with value 2)  


def MinimumPath(M): 


    global N 


    s , d = None, None # source and destination  


    V = N * N + 2


    g = Graph(V)  


  


    # create graph with n*n node  


    # each cell consider as node  


    k = 1 # Number of current vertex 


    for i in range(N): 


        for j in range(N): 


            if (M[i][j] != 0): 


                  


                # connect all 4 adjacent cell to  


                # current cell  


                if (isSafe (i , j + 1 , M)):  


                    g.addEdge (k , k + 1) 


                if (isSafe (i , j - 1 , M)): 


                    g.addEdge (k , k - 1)  


                if (j < N - 1 and isSafe (i + 1 , j , M)):  


                    g.addEdge (k , k + N)  


                if (i > 0 and isSafe (i - 1 , j , M)):  


                    g.addEdge (k , k - N) 


  


            # source index  


            if(M[i][j] == 1): 


                s = k  


  


            # destination index  


            if (M[i][j] == 2):  


                d = k  


            k += 1


  


    # find minimum moves  


    return g.BFS (s, d) 


  


# Driver Code 


N = 4


M = [[3 , 3 , 1 , 0 ], [3 , 0 , 3 , 3 ],  


     [2 , 3 , 0 , 3 ], [0 , 3 , 3 , 3]] 


  


print(MinimumPath(M)) 


  


# This code is contributed by PranchalK 



















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Output:


4 



This article is contributed by Nishant Singh . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


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