Magnet Puzzle

The puzzle game Magnets involves placing a set of domino-shaped magnets (or electrets or other polarized objects) in a subset of slots on a board so as to satisfy a set of constraints. For example, the puzzle on the left has the solution shown on the right: Each slot contains either a blank entry (indicated by ‘x’s), or a “magnet” with a positive and negative end. The numbers along the left and top sides show the numbers of ‘+’ squares in particular rows or columns. Those along the right and bottom show the number of ‘-’ signs in particular rows or columns. Rows and columns without a number at one or both ends are unconstrained as to the number of ‘+’ or ‘-’ signs, depending on which number is not present. In addition to fulfilling these numerical constraints, a puzzle solution must also satisfy the constraint that no two orthogonally touching squares may have the same sign (diagonally joined squares are not constrained). You are given top[], bottom[], left[], right[] arrays indicates the count of + or – along the top(+), bottom(-), left(+) and right(-) edges respectively. Values of -1 indicate any number of + and – signs. Also given matrix rules[][] contain any one T, B, L or R characters. For a vertical slot in the board, T indicates its top end and B indicates the bottom end. For a horizontal slot in the board, L indicates left end and R indicates the right end. Examples:

Input : M = 5, N = 6
        top[] = { 1, -1, -1, 2, 1, -1 }
        bottom[] = { 2, -1, -1, 2, -1, 3 }
        left[] = { 2, 3, -1, -1, -1 }
        right[] = { -1, -1, -1, 1, -1 }
        rules[][] = { { L, R, L, R, T, T },
                      { L, R, L, R, B, B },
                      { T, T, T, T, L, R },
                      { B, B, B, B, T, T },
                      { L, R, L, R, B, B }};
Output : + - + - X - 
         - + - + X + 
         X X + - + - 
         X X - + X + 
         - + X X X - 

Input : M = 4, N = 3
        top[] = { 2, -1, -1 }
        bottom[] = { -1, -1, 2 }
        left[] = { -1, -1, 2, -1 }
        right[] = { 0, -1, -1, -1 }
        rules[][] = { { T, T, T },
                      { B, B, B },
                      { T, L, R },
                      { B, L, R } };
Output : + X +
         – X –
        + – +
        – + –

We can solve this problem using Backtracking. 

C++

// Write Python3 code here
#include<bits/stdc++.h>
using namespace std;

bool checkConstraints(vector<vector<char>> &rules){
  int M = 5;
  int N = 6;
  vector<int> top = { 1, -1, -1, 2, 1, -1 };
  vector<int> bottom = {2, -1, -1, 2, -1, 3 };
  vector<int> left = {2, 3, -1, -1, -1};
  vector<int> right = {-1, -1, -1, 1, -1};

  vector<int> pCountH(rules.size(), 0);
  vector<int> nCountH(rules.size(), 0);

  for(int row = 0; row < rules.size(); row++){
    for(int col = 0; col < rules[0].size(); col++){
      char ch = rules[row][col];
      if(ch == '+'){
        pCountH[row] += 1;
      }
      else if(ch == '-'){
        nCountH[row] += 1;
      }
    }
  }


  vector<int> pCountV(rules[0].size(), 0);
  vector<int> nCountV(rules[0].size(), 0);
  for(int col = 0; col < rules[0].size(); col++){
    for(int row = 0; row < rules.size(); row++){
      char ch = rules[row][col];
      if(ch == '+'){
        pCountV[col] += 1;
      }
      else if(ch == '-'){
        nCountV[col] += 1;
      }
    }
  }

  for(int row = 0; row < rules.size(); row++){
    if(left[row] != -1){
      if(pCountH[row] != left[row]){
        return false;
      }
    }

    if (right[row] != -1){
      if(nCountH[row] != right[row]){
        return false;
      }
    }

  }


  for(int col = 0; col < rules[0].size(); col++){
    if(top[col] != -1){
      if(pCountV[col] != top[col]){
        return false;
      }
    }

    if(bottom[col] != -1){
      if(nCountV[col] != bottom[col]){
        return false;
      }
    }
    // if (top[col] != -1 and pCountH[col] != top[col]) or (bottom[col] != -1 and nCountH[col] != bottom[col]) :
    // return False
  }


  return true;
}



bool canPutPatternHorizontally(vector<vector<char>> &rules,int i,int j, string pat){
  if( j-1>=0 and rules[i][j-1] == pat[0]){
    return false;
  }
  else if(i-1>=0 and rules[i-1][j] == pat[0]){
    return false;
  }
  else if(i-1>=0 and rules[i-1][j+1] == pat[1]){
    return false;
  }
  else if(j+2 < rules[0].size() and rules[i][j+2] == pat[1]){
    return false;
  }
  return true;
}





bool canPutPatternVertically(vector<vector<char>> &rules,int i,int j, string pat){
  if( j-1>=0 and rules[i][j-1] == pat[0]){
    return false;
  }
  else if(i-1>=0 and rules[i-1][j] == pat[0]){
    return false;
  }
  else if(j+1 < rules[0].size() and rules[i][j+1] == pat[0]){
    return false;
  }

  return true;
}




void solveMagnets(vector<vector<char>> &rules, int i,int j){

  // check the constraint before printing
  if( i == rules.size() and j == 0){
    if(checkConstraints(rules)){

      // Printing rules array.
      cout << "[";
      for(int indxi = 0; indxi < rules.size(); indxi++){
        cout << "[";
        for(int indxj = 0; indxj < rules[0].size(); indxj++){
          cout <<"'"<< rules[indxi][indxj] << "', ";
        }
        cout << "]";
      }
      cout << "]";
    }

  }
  else if(j >= rules[0].size()){
    solveMagnets(rules, i+1, 0);
  }
  // normal cases
  else{

    if (rules[i][j] == 'L'){

      // option 1 +-
      if(canPutPatternHorizontally(rules,i,j,"+-")){
        rules[i][j] = '+';
        rules[i][j+1] = '-';

        solveMagnets(rules,i,j+2);

        rules[i][j] = 'L';
        rules[i][j+1] = 'R';
      }

      // option 2 -+
      if(canPutPatternHorizontally(rules,i,j,"-+")){
        rules[i][j] = '-';
        rules[i][j+1] = '+';

        solveMagnets(rules,i,j+2);

        rules[i][j] = 'L';
        rules[i][j+1] = 'R';
      }

      // option 3 xx
      if((1 == 1) || canPutPatternHorizontally(rules,i,j,"xx")){
        rules[i][j] = 'x';
        rules[i][j+1] = 'x';

        solveMagnets(rules,i,j+2);

        rules[i][j] = 'L';
        rules[i][j+1] = 'R';
      }

    }
    // vertical check
    else if(rules[i][j] == 'T'){
      // option 1 +-
      if(canPutPatternVertically(rules,i,j,"+-")){
        rules[i][j] = '+';
        rules[i+1][j] = '-';

        solveMagnets(rules,i,j+1);

        rules[i][j] = 'T';
        rules[i+1][j] = 'B';
      }


      // option 2 -+
      if(canPutPatternVertically(rules,i,j,"-+")){
        rules[i][j] = '-';
        rules[i+1][j] = '+';

        solveMagnets(rules,i,j+1);

        rules[i][j] = 'T';
        rules[i+1][j] = 'B';
      }


      // option 3 xx

      if ((1 == 1) or canPutPatternVertically(rules,i,j,"xx")){
        rules[i][j] = 'x';
        rules[i+1][j] = 'x';

        solveMagnets(rules,i,j+1);

        rules[i][j] = 'T';
        rules[i+1][j] = 'B';
      }

    }
    else{
      solveMagnets(rules,i,j+1);
    }
  }
}


void doTheStuff(vector<vector<char>> &rules,int i,int j){

  if(rules[i][j] == 'L' || rules[i][j] == 'R'){
    // option 1 +-
    if (canPutPatternHorizontally(rules, i, j ,"+-")){
      rules[i][j] = '+';
      rules[i][j+1] = '-';

      solveMagnets(rules,i,j);
    }

    // option 2 -+

    // option 3 xx
  }
}

// Driver code
int main(){

  vector<vector<char>> rules = {
    {'L','R','L','R','T','T' },
    {'L','R','L','R','B','B' },
    {'T','T','T','T','L','R' },
    {'B','B','B','B','T','T' },
    {'L','R','L','R','B','B' }
  };
  solveMagnets(rules,0,0);

}

// The code is contributed by Gautam goel.

Java

// java  code implementation
import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.stream.*;

public class Main {

  public static boolean canPutPatternHorizontally(char[][] rules,int i,int j, char[] pat){
    if( j-1>=0 && rules[i][j-1] == pat[0]){
      return false;
    }
    else if(i-1>=0 && rules[i-1][j] == pat[0]){
      return false;
    }
    else if(i-1>=0 && rules[i-1][j+1] == pat[1]){
      return false;
    }
    else if(j+2 < rules[0].length && rules[i][j+2] == pat[1]){
      return false;
    }
    return true;
  }
  public static boolean checkConstraints(char[][] rules){
    int M = 5;
    int N = 6;
    int[] top = { 1, -1, -1, 2, 1, -1 };
    int[] bottom = {2, -1, -1, 2, -1, 3 };
    int[] left = {2, 3, -1, -1, -1};
    int[] right = {-1, -1, -1, 1, -1};

    int[] pCountH = new int[rules.length];
    for(int i= 0; i < rules.length; i++){
      pCountH[i] = 0;
    }

    int[] nCountH = new int[rules.length];
    for(int i = 0; i < rules.length; i++){
      nCountH[i] = 0;
    }

    for(int row = 0; row < rules.length; row++){
      for(int col = 0; col < rules[0].length; col++){
        char ch = rules[row][col];
        if(ch == '+'){
          pCountH[row] += 1;
        }
        else if(ch == '-'){
          nCountH[row] += 1;
        }
      }
    }



    int[] pCountV = new int[rules[0].length];
    for(int i= 0; i < rules[0].length; i++){
      pCountV[i] = 0;
    }

    int[] nCountV = new int[rules[0].length];
    for(int i = 0; i < rules[0].length; i++){
      nCountV[i] = 0;
    }


    for(int col = 0; col < rules[0].length; col++){
      for(int row = 0; row < rules.length; row++){
        char ch = rules[row][col];
        if(ch == '+'){
          pCountV[col] += 1;
        }
        else if(ch == '-'){
          nCountV[col] += 1;
        }
      }
    }

    for(int row = 0; row < rules.length; row++){
      if(left[row] != -1){
        if(pCountH[row] != left[row]){
          return false;
        }
      }

      if (right[row] != -1){
        if(nCountH[row] != right[row]){
          return false;
        }
      }

    }


    for(int col = 0; col < rules[0].length; col++){
      if(top[col] != -1){
        if(pCountV[col] != top[col]){
          return false;
        }
      }

      if(bottom[col] != -1){
        if(nCountV[col] != bottom[col]){
          return false;
        }
      }
      // if (top[col] != -1 and pCountH[col] != top[col]) or (bottom[col] != -1 and nCountH[col] != bottom[col]) :
      // return False
    }


    return true;
  }



  public static boolean canPutPatternVertically(char[][] rules,int i,int j, char[] pat){
    if( j-1>=0 && rules[i][j-1] == pat[0]){
      return false;
    }
    else if(i-1>=0 && rules[i-1][j] == pat[0]){
      return false;
    }
    else if(j+1 < rules[0].length && rules[i][j+1] == pat[0]){
      return false;
    }

    return true;
  }

  public static void solveMagnets(char[][] rules, int i,int j){

    // check the constraint before printing
    if( i == rules.length && j == 0){
      if(checkConstraints(rules)){

        // Printing rules array.
        System.out.print("[");
        for(int indxi = 0; indxi < rules.length; indxi++){
          System.out.print("[");
          for(int indxj = 0; indxj < rules[0].length; indxj++){
            System.out.print("'" + rules[indxi][indxj] + "', ");
          }
          System.out.print("]");
        }
        System.out.print("]");
      }

    }
    else if(j >= rules[0].length){
      solveMagnets(rules, i+1, 0);
    }
    // normal cases
    else{

      if (rules[i][j] == 'L'){

        // option 1 +-
        if(canPutPatternHorizontally(rules,i,j,"+-".toCharArray()) == true){
          rules[i][j] = '+';
          rules[i][j+1] = '-';

          solveMagnets(rules,i,j+2);

          rules[i][j] = 'L';
          rules[i][j+1] = 'R';
        }

        // option 2 -+
        if(canPutPatternHorizontally(rules,i,j,"-+".toCharArray()) == true){
          rules[i][j] = '-';
          rules[i][j+1] = '+';

          solveMagnets(rules,i,j+2);

          rules[i][j] = 'L';
          rules[i][j+1] = 'R';
        }

        // option 3 xx
        if((1 == 1) || canPutPatternHorizontally(rules,i,j,"xx".toCharArray()) == true){
          rules[i][j] = 'x';
          rules[i][j+1] = 'x';

          solveMagnets(rules,i,j+2);

          rules[i][j] = 'L';
          rules[i][j+1] = 'R';
        }

      }
      // vertical check
      else if(rules[i][j] == 'T'){
        // option 1 +-
        if(canPutPatternVertically(rules,i,j,"+-".toCharArray()) == true){
          rules[i][j] = '+';
          rules[i+1][j] = '-';

          solveMagnets(rules,i,j+1);

          rules[i][j] = 'T';
          rules[i+1][j] = 'B';
        }

        // option 2 -+
        if(canPutPatternVertically(rules,i,j,"-+".toCharArray()) == true){
          rules[i][j] = '-';
          rules[i+1][j] = '+';

          solveMagnets(rules,i,j+1);

          rules[i][j] = 'T';
          rules[i+1][j] = 'B';
        }


        // option 3 xx

        if ((1 == 1) || canPutPatternVertically(rules,i,j,"xx".toCharArray()) == true){
          rules[i][j] = 'x';
          rules[i+1][j] = 'x';

          solveMagnets(rules,i,j+1);

          rules[i][j] = 'T';
          rules[i+1][j] = 'B';
        }

      }
      else{
        solveMagnets(rules,i,j+1);
      }
    }
  }

  public static void doTheStuff(char[][] rules,int i,int j){

    if(rules[i][j] == 'L' || rules[i][j] == 'R'){
      // option 1 +-

      if (canPutPatternHorizontally(rules, i, j ,"+-".toCharArray()) == true){
        rules[i][j] = '+';
        rules[i][j+1] = '-';

        solveMagnets(rules,i,j);
      }

      // option 2 -+

      // option 3 xx
    }
  }

  public static void main(String[] args) {
    char[][] rules = {
      {'L','R','L','R','T','T' },
      {'L','R','L','R','B','B' },
      {'T','T','T','T','L','R' },
      {'B','B','B','B','T','T' },
      {'L','R','L','R','B','B' }
    };
    solveMagnets(rules,0,0);
  }
}

// The code is contributed by Nidhi goel.

Python3

# Write Python3 code here
M = 5
N = 6
top = [ 1, -1, -1, 2, 1, -1 ]
bottom = [ 2, -1, -1, 2, -1, 3 ]
left = [ 2, 3, -1, -1, -1 ]
right = [ -1, -1, -1, 1, -1 ]

rules = [["L","R","L","R","T","T" ],
                      [ "L","R","L","R","B","B" ],
                      [ "T","T","T","T","L","R" ],
                      [ "B","B","B","B","T","T" ],
                      [ "L","R","L","R","B","B" ]];



def canPutPatternHorizontally(rules,i,j,pat):

    if j-1>=0 and rules[i][j-1] == pat[0]:
        return False
    elif i-1>=0 and rules[i-1][j] == pat[0]:
        return False
    elif i-1>=0 and rules[i-1][j+1] == pat[1]:
        return False
    elif j+2 < len(rules[0]) and rules[i][j+2] == pat[1]:
        return False

    return True


def canPutPatternVertically(rules,i,j,pat):

    if j-1>=0 and rules[i][j-1] == pat[0]:
        return False
    elif i-1>=0 and rules[i-1][j] == pat[0]:
        return False
    elif j+1 < len(rules[0]) and rules[i][j+1] == pat[0]:
        return False

    return True

def doTheStuff(rules,i,j):

    if rules[i][j] == "L" or rules[i][j] == "R":

        #        option 1 +-
        if canPutPatternHorizontally(rules,i,j,"+-"):
            rules[i][j] = "+"
            rules[i][j+1] = "-"

            solveMagnets(rules,i,j)
        #        option 2 -+

        #        option 3 xx

def checkConstraints(rules):

    pCountH = [0 for i in range(len(rules))]
    nCountH = [0 for i in range(len(rules))]
    for row in range(len(rules)):
        for col in range(len(rules[0])):
            ch = rules[row][col]
            if ch == "+":
                pCountH[row] += 1
            elif ch == "-":
                nCountH[row] += 1


    pCountV = [0 for i in range(len(rules[0]))]
    nCountV = [0 for i in range(len(rules[0]))]
    for col in range(len(rules[0])):
        for row in range(len(rules)):
            ch = rules[row][col]
            if ch == "+":
                pCountV[col] += 1
            elif ch == "-":
                nCountV[col] += 1


    for row in range(len(rules)):
        if left[row] != -1:
            if pCountH[row] != left[row]:
                return False
        if right[row] != -1:
            if nCountH[row] != right[row]:
                return False



    for col in range(len(rules[0])):
        if top[col] != -1:
            if pCountV[col] != top[col]:
                return False
        if bottom[col] != -1:
            if nCountV[col] != bottom[col]:
                return False
        #
        #  if (top[col] != -1 and pCountH[col] != top[col]) or (bottom[col] != -1 and nCountH[col] != bottom[col]) :
        #      return False

    return True







def solveMagnets(rules,i,j):

    if i == len(rules) and j == 0:

        # check the constraint before printing
        if checkConstraints(rules):
            print(rules)
    elif j >= len(rules[0]):

        solveMagnets(rules,i+1,0)

    # normal cases
    else:

        if rules[i][j] == "L":

            #  option 1 +-
            if canPutPatternHorizontally(rules,i,j,"+-"):
                rules[i][j] = "+"
                rules[i][j+1] = "-"

                solveMagnets(rules,i,j+2)

                rules[i][j] = "L"
                rules[i][j+1] = "R"

            # option 2 -+
            if canPutPatternHorizontally(rules,i,j,"-+"):
                rules[i][j] = "-"
                rules[i][j+1] = "+"

                solveMagnets(rules,i,j+2)

                rules[i][j] = "L"
                rules[i][j+1] = "R"

            # option 3 xx
            if True or canPutPatternHorizontally(rules,i,j,"xx"):
                rules[i][j] = "x"
                rules[i][j+1] = "x"

                solveMagnets(rules,i,j+2)

                rules[i][j] = "L"
                rules[i][j+1] = "R"

        #        vertical check
        elif rules[i][j] == "T":

            #        option 1 +-
            if canPutPatternVertically(rules,i,j,"+-"):
                rules[i][j] = "+"
                rules[i+1][j] = "-"

                solveMagnets(rules,i,j+1)

                rules[i][j] = "T"
                rules[i+1][j] = "B"

            #        option 2 -+
            if canPutPatternVertically(rules,i,j,"-+"):
                rules[i][j] = "-"
                rules[i+1][j] = "+"

                solveMagnets(rules,i,j+1)

                rules[i][j] = "T"
                rules[i+1][j] = "B"

            #        option 3 xx

            if True or canPutPatternVertically(rules,i,j,"xx"):
                rules[i][j] = "x"
                rules[i+1][j] = "x"

                solveMagnets(rules,i,j+1)

                rules[i][j] = "T"
                rules[i+1][j] = "B"

        else:
            solveMagnets(rules,i,j+1)


# Driver code
solveMagnets(rules,0,0)

Javascript

<script>
// javascript code here


function checkConstraints(rules){
  let M = 5;
  let N = 6;
  let top = [ 1, -1, -1, 2, 1, -1 ];
  let bottom = [2, -1, -1, 2, -1, 3 ];
  let left = [2, 3, -1, -1, -1];
  let right = [-1, -1, -1, 1, -1];

  let pCountH = new Array(rules.length).fill(0);
  let nCountH = new Array(rules.length).fill(0);

  for(let row = 0; row < rules.length; row++){
    for(let col = 0; col < rules[0].length; col++){
      let ch = rules[row][col];
      if(ch == '+'){
        pCountH[row] += 1;
      }
      else if(ch == '-'){
        nCountH[row] += 1;
      }
    }
  }


  let pCountV = new Array(rules[0].length).fill(0);
  let nCountV = new Array(rules[0].length).fill(0);

  for(let col = 0; col < rules[0].length; col++){
    for(let row = 0; row < rules.length; row++){
      let ch = rules[row][col];
      if(ch == '+'){
        pCountV[col] += 1;
      }
      else if(ch == '-'){
        nCountV[col] += 1;
      }
    }
  }

  for(let row = 0; row < rules.length; row++){
    if(left[row] != -1){
      if(pCountH[row] != left[row]){
        return false;
      }
    }

    if (right[row] != -1){
      if(nCountH[row] != right[row]){
        return false;
      }
    }

  }


  for(let col = 0; col < rules[0].length; col++){
    if(top[col] != -1){
      if(pCountV[col] != top[col]){
        return false;
      }
    }

    if(bottom[col] != -1){
      if(nCountV[col] != bottom[col]){
        return false;
      }
    }
    // if (top[col] != -1 and pCountH[col] != top[col]) or (bottom[col] != -1 and nCountH[col] != bottom[col]) :
    // return False
  }


  return true;
}



function canPutPatternHorizontally(rules, i, j,  pat){
  if( j-1>=0 && rules[i][j-1] == pat[0]){
    return false;
  }
  else if(i-1>=0 && rules[i-1][j] == pat[0]){
    return false;
  }
  else if(i-1>=0 && rules[i-1][j+1] == pat[1]){
    return false;
  }
  else if(j+2 < rules[0].length && rules[i][j+2] == pat[1]){
    return false;
  }
  return true;
}





function canPutPatternVertically(rules,i,j, pat){
  if( j-1>=0 && rules[i][j-1] == pat[0]){
    return false;
  }
  else if(i-1>=0 && rules[i-1][j] == pat[0]){
    return false;
  }
  else if(j+1 < rules[0].length && rules[i][j+1] == pat[0]){
    return false;
  }

  return true;
}




function solveMagnets(rules, i,j){

  // check the constraint before printing
  if( i == rules.length && j == 0){
    if(checkConstraints(rules)){

      // Printing rules array.
      console.log(rules);
    }

  }
  else if(j >= rules[0].length){
    solveMagnets(rules, i+1, 0);
  }
  // normal cases
  else{

    if (rules[i][j] == 'L'){

      // option 1 +-
      if(canPutPatternHorizontally(rules,i,j,"+-")){
        rules[i][j] = '+';
        rules[i][j+1] = '-';

        solveMagnets(rules,i,j+2);

        rules[i][j] = 'L';
        rules[i][j+1] = 'R';
      }

      // option 2 -+
      if(canPutPatternHorizontally(rules,i,j,"-+")){
        rules[i][j] = '-';
        rules[i][j+1] = '+';

        solveMagnets(rules,i,j+2);

        rules[i][j] = 'L';
        rules[i][j+1] = 'R';
      }

      // option 3 xx
      if((1 == 1) || canPutPatternHorizontally(rules,i,j,"xx")){
        rules[i][j] = 'x';
        rules[i][j+1] = 'x';

        solveMagnets(rules,i,j+2);

        rules[i][j] = 'L';
        rules[i][j+1] = 'R';
      }

    }
    // vertical check
    else if(rules[i][j] == 'T'){
      // option 1 +-
      if(canPutPatternVertically(rules,i,j,"+-")){
        rules[i][j] = '+';
        rules[i+1][j] = '-';

        solveMagnets(rules,i,j+1);

        rules[i][j] = 'T';
        rules[i+1][j] = 'B';
      }


      // option 2 -+
      if(canPutPatternVertically(rules,i,j,"-+")){
        rules[i][j] = '-';
        rules[i+1][j] = '+';

        solveMagnets(rules,i,j+1);

        rules[i][j] = 'T';
        rules[i+1][j] = 'B';
      }


      // option 3 xx

      if ((1 == 1) || canPutPatternVertically(rules,i,j,"xx")){
        rules[i][j] = 'x';
        rules[i+1][j] = 'x';

        solveMagnets(rules,i,j+1);

        rules[i][j] = 'T';
        rules[i+1][j] = 'B';
      }

    }
    else{
      solveMagnets(rules,i,j+1);
    }
  }
}


function doTheStuff(rules, i, j){

  if(rules[i][j] == 'L' || rules[i][j] == 'R'){
    // option 1 +-
    if (canPutPatternHorizontally(rules, i, j ,"+-")){
      rules[i][j] = '+';
      rules[i][j+1] = '-';

      solveMagnets(rules,i,j);
    }

    // option 2 -+

    // option 3 xx
  }
}

// Driver code
let rules = [
    ['L','R','L','R','T','T'],
    ['L','R','L','R','B','B'],
    ['T','T','T','T','L','R'],
    ['B','B','B','B','T','T'],
    ['L','R','L','R','B','B']
];

solveMagnets(rules,0,0);


// The code is contributed by Nidhi goel.
</script>

Output: 
[['+', '-', '+', '-', 'x', '-', ]['-', '+', '-', '+', 'x', '+', ]['x', 'x', '+', '-', '+', '-', ]['x', 'x', '-', '+', 'x', '+', ]['-', '+', 'x', 'x', 'x', '-', ]]

Source :https://people.eecs.berkeley.edu/~hilfingr/programming-contest/f2012-contest.pdf This article is contributed by Anuj Chauhan (anuj0503). If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.