Program for Conway’s Game Of Life | Set 2

Given a binary grid[ ][ ] of size N*M, with each cell containing either 0 or 1, where 1 represents an alive cell and the 0 represents a dead cell. The task is to generate the next generation of cells based on the following rules:  

1. Any live cell with fewer than two live neighbors dies due to under-population.
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies due to overpopulation.
4. Any dead cell with exactly three live neighbors becomes a live cell by reproduction.

Here, the neighbor of a cell includes its adjacent cells as well as diagonal ones, so for each cell, a total of 8 neighbors are there.
Examples:

Input: N = 5, M = 10 
0000000000 
0001100000 
0000100000 
0000000000 
0000000000 
Output:
0000000000 
0001100000 
0001100000 
0000000000 
0000000000 
Explanation:
The cells at (1, 3), (1, 4) and (2, 4) are alive and have 2 neighbors, 
So, according to Rule 2, they live on to the next generation. 
The cell at (2, 3) is dead and has exactly 3 neighbors, 
So, according to Rule 4, it becomes a live cell.
Input: N = 4, M = 5 
00000 
01100 
00010 
00000 
Output:
00000 
00100 
00100 
00000 
Explanation:
The cells at (1, 1) and (2, 3) have only 1 neighbor, 
So, according to Rule 1, they die. 
The cell at (1, 2) is alive and has 2 neighbors, 
So, according to Rule 2, it lives on to the next generation. 
The cell at (2, 2) is dead and has exactly 3 neighbors, 
So, according to Rule 4, it becomes a live cell.

Naive Approach:
We have already discussed an approach to this problem in Program for Conway’s Game Of Life | Set 1. In this approach, an extra grid future[ ][ ] of size N*M is created to store the next generation of cells. 
Time complexity: O(N*M)
Auxiliary Space: O(N*M)
Efficient Approach:
A space-optimized approach is possible for this problem, which uses no extra space. For every alive cell, increment its value by 1 each time we encounter an alive neighbor for it. And, for every dead cell, decrement its value by 1 each time we encounter an alive neighbor for it. Now, if the value in a cell is smaller than 0, it means it is a dead cell and if the value is greater than 0, it is an alive cell, also the magnitude of value in a cell will represent the number of its alive neighbors. In this way, an extra grid will not be required and a space-optimized solution is obtained. Detailed steps of this approach are as follows:
For the present grid position, we will look at all the neighbors.  

1. Traverse the whole grid.
2. If the value of the neighbor is >= 1(i.e. initial value of the neighbor was 1)
   • If, the current cell is >= 1, just increment the current cell value by 1. 
     Now, grid [ i ][ j ] > 0 will imply that initial grid [ i ][ j ] == 1.
   • Else, the current cell is <= 0, just decrement the current cell value by 1. 
     Now, grid [ i ][ j ] <= 0 will imply that initial grid [ i ][ j ] == 0.
3. Now, generate the required new generation grid using the modified grid. 
   • If the current cell value is > 0, there are 3 possible cases: 
     • If the value is < 3 then change it to 0.
     • Else if the value is <= 4 then change it to 1.
     • Else change the value to 0.
   • Else, the current cell value is <= 0. 
     • If the value is 3 then change it to 1.
     • Else change it to 0.

Below is the implementation of the above approach:

C++

// C++ implementation of
// the above approach

#include <bits/stdc++.h>
using namespace std;

void print(vector<vector<int>> grid)
{
    int p = grid.size(),
    q = grid[0].size();

    for (int i = 0; i < p; i++) {
      for (int j = 0; j < q; j++) {

        cout << grid[i][j];
     }
    cout << endl;
    }
}
// Function to check if
// index are not out of grid
static bool save(vector<vector<int> > grid,int row, int col)
{
    return (grid.size() > row && grid[0].size() > col && row >= 0 && col >= 0);
}
    // Function to get New Generation
void solve(vector<vector<int> >& grid)
{
      int p = grid.size(),
        q = grid[0].size();
      int u[] = { 1, -1, 0, 1, -1, 0, 1, -1 };
      int v[] = { 0, 0, -1, -1, -1, 1, 1, 1 };
     for (int i = 0; i < p; i++)
     {
      for (int j = 0; j < q; j++)
      {
      // IF the initial value
      // of the grid(i, j) is 1
      if (grid[i][j] > 0)
      {
        for (int k = 0; k < 8; k++)
        {
          if (save(grid, i + u[k],
                   j + v[k]) &&
                   grid[i + u[k]][j + v[k]] > 0)
          {
            // If initial value > 0,
            // just increment it by 1
            grid[i][j]++;
          }
        }
      }

      // IF the initial value
      // of the grid(i, j) is 0
      else
      {
         for (int k = 0; k < 8; k++)
         {
           if (save(grid, i + u[k],
                   j + v[k]) &&
                   grid[i + u[k]][j + v[k]] > 0)
              {
                // If initial value <= 0
                // just decrement it by 1
                grid[i][j]--;
              }
           }
        }
      }
    }

    // Generating new Generation.
    // Now the magnitude of the
    // grid will represent number
    // of neighbours
    for (int i = 0; i < p; i++)
      {
          for (int j = 0; j < q; j++)
         {
        // If initial value was 1.
        if (grid[i][j] > 0)
        {
            // Since Any live cell with
          // < 2 live neighbors dies
           if (grid[i][j] < 3)
              grid[i][j] = 0;

             // Since Any live cell with
            // 2 or 3 live neighbors live
           else if (grid[i][j] <= 4)
            grid[i][j] = 1;

            // Since Any live cell with
             // > 3 live neighbors dies
            else if (grid[i][j] > 4)
              grid[i][j] = 0;
        }
       else
        {
        // Since Any dead cell with
        // exactly 3 live neighbors
        // becomes a live cell
         if (grid[i][j] == -3)
              grid[i][j] = 1;
         else
              grid[i][j] = 0;
            }
        }
     }
}
// Driver code
int main ()
{
  vector<vector<int>> grid = {{0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0},
                  {0, 0, 0, 1, 1,
                   0,0, 0, 0, 0},
                  {0, 0, 0, 0, 1,
                   0, 0, 0, 0, 0},
                  {0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0},
                  {0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0}};

  // Function to generate
  // New Generation inplace
  solve(grid);

  // Displaying the grid
  print(grid);
  return 0;
}

Java

// Java program for
// the above approach
import java.util.*;
import java.lang.*;
class GFG{

static void print(int[][] grid)
{
  int p = grid.length,
  q = grid[0].length;

  for (int i = 0; i < p; i++)
  {
    for (int j = 0; j < q; j++)
    {
      System.out.print(grid[i][j]);
    }
    System.out.println();;
  }
}

static boolean save(int[][] grid,
                    int row, int col)
{
  return (grid.length > row &&
          grid[0].length > col &&
          row >= 0 && col >= 0);
}

static void solve(int[][] grid)
{
  int p = grid.length,
  q = grid[0].length;

  // Possible neighboring
  // indexes
  int u[] = {1, -1, 0, 1,
             -1, 0, 1, -1};
  int v[] = {0, 0, -1, -1,
             -1, 1, 1, 1};

  for (int i = 0; i < p; i++)
  {
    for (int j = 0; j < q; j++)
    {
      // IF the initial value
      // of the grid(i, j) is 1
      if (grid[i][j] > 0)
      {
        for (int k = 0; k < 8; k++)
        {
          if (save(grid, i + u[k],
                   j + v[k]) &&
                   grid[i + u[k]][j + v[k]] > 0)
          {
            // If initial value > 0,
            // just increment it by 1
            grid[i][j]++;
          }
        }
      }

      // IF the initial value
      // of the grid(i, j) is 0
      else
      {
        for (int k = 0; k < 8; k++)
        {
          if (save(grid, i + u[k],
                   j + v[k]) &&
                   grid[i + u[k]][j + v[k]] > 0)
          {
            // If initial value <= 0
            // just decrement it by 1
            grid[i][j]--;
          }
        }
      }
    }
  }

  // Generating new Generation.
  // Now the magnitude of the
  // grid will represent number
  // of neighbours
  for (int i = 0; i < p; i++)
  {
    for (int j = 0; j < q; j++)
    {
      // If initial value was 1.
      if (grid[i][j] > 0)
      {
        // Since Any live cell with
        // < 2 live neighbors dies
        if (grid[i][j] < 3)
          grid[i][j] = 0;

        // Since Any live cell with
        // 2 or 3 live neighbors live
        else if (grid[i][j] <= 4)
          grid[i][j] = 1;

        // Since Any live cell with
        // > 3 live neighbors dies
        else if (grid[i][j] > 4)
          grid[i][j] = 0;
      }
      else
      {
        // Since Any dead cell with
        // exactly 3 live neighbors
        // becomes a live cell
        if (grid[i][j] == -3)
          grid[i][j] = 1;
        else
          grid[i][j] = 0;
      }
    }
  }
}

// Driver code
public static void main (String[] args)
{
  int[][] grid = {{0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0},
                  {0, 0, 0, 1, 1,
                   0,0, 0, 0, 0},
                  {0, 0, 0, 0, 1,
                   0, 0, 0, 0, 0},
                  {0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0},
                  {0, 0, 0, 0, 0,
                   0, 0, 0, 0, 0}};

  // Function to generate
  // New Generation inplace
  solve(grid);

  // Displaying the grid
  print(grid);
}
}

// This code is contributed by offbeat

Python3

# Python3 implementation of
# the above approach

def print2dArr(grid):
    p = len(grid)
    q = len(grid[0])

    for i in range(p):
        for j in range(q):
            print(grid[i][j], end='')

        print()


# Function to check if
# index are not out of grid
def save(grid, row, col):
    return (len(grid) > row and len(grid[0]) > col and row >= 0 and col >= 0)

# Function to get New Generation


def solve(grid):
    p = len(grid)
    q = len(grid[0])
    u = [1, -1, 0, 1, -1, 0, 1, -1]
    v = [0, 0, -1, -1, -1, 1, 1, 1]
    for i in range(p):
        for j in range(q):
            # IF the initial value
            # of the grid(i, j) is 1
            if (grid[i][j] > 0):
                for k in range(8):
                    if (save(grid, i + u[k], j + v[k]) and grid[i + u[k]][j + v[k]] > 0):
                        # If initial value > 0,
                        # just increment it by 1
                        grid[i][j] += 1

            # IF the initial value
            # of the grid(i, j) is 0
            else:
                for k in range(8):
                    if (save(grid, i + u[k], j + v[k]) and grid[i + u[k]][j + v[k]] > 0):
                        # If initial value <= 0
                        # just decrement it by 1
                        grid[i][j] -= 1
    # Generating new Generation.
    # Now the magnitude of the
    # grid will represent number
    # of neighbours
    for i in range(p):
        for j in range(q):
            # If initial value was 1.
            if (grid[i][j] > 0):
                # Since Any live cell with
                # < 2 live neighbors dies
                if (grid[i][j] < 3):
                    grid[i][j] = 0

                # Since Any live cell with
                # 2 or 3 live neighbors live
                elif (grid[i][j] <= 4):
                    grid[i][j] = 1

                # Since Any live cell with
                # > 3 live neighbors dies
                elif (grid[i][j] > 4):
                    grid[i][j] = 0

            else:
                # Since Any dead cell with
                # exactly 3 live neighbors
                # becomes a live cell
                if (grid[i][j] == -3):
                    grid[i][j] = 1
                else:
                    grid[i][j] = 0


# Driver code
if __name__ == '__main__':
    grid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ], ]

    # Function to generate
    # New Generation inplace
    solve(grid)

    # Displaying the grid
    print2dArr(grid)

C#

// C# program for
// the above approach
using System;
using System.Text;

public class GFG{

  static void print(int[,] grid)
  {
    int p = grid.GetLength(0), q = grid.GetLength(1);

    for (int i = 0; i < p; i++)
    {
      for (int j = 0; j < q; j++)
      {
        Console.Write(grid[i,j]);
      }
      Console.Write("\n");
    }
  }

  static bool save(int[,] grid,int row, int col)
  {
    return (grid.GetLength(0) > row && grid.GetLength(1) > col && row >= 0 && col >= 0);
  }

  static void solve(int[,] grid)
  {
    int p = grid.GetLength(0), q = grid.GetLength(1);

    // Possible neighboring
    // indexes
    int[] u = {1, -1, 0, 1, -1, 0, 1, -1};
    int[] v = {0, 0, -1, -1, -1, 1, 1, 1};

    for (int i = 0; i < p; i++)
    {
      for (int j = 0; j < q; j++)
      {
        // IF the initial value
        // of the grid(i, j) is 1
        if (grid[i,j] > 0)
        {
          for (int k = 0; k < 8; k++)
          {
            if (save(grid, i + u[k], j + v[k]) && grid[(i + u[k]),(j + v[k])] > 0)
            {
              // If initial value > 0,
              // just increment it by 1
              grid[i,j]++;
            }
          }
        }

        // IF the initial value
        // of the grid(i, j) is 0
        else
        {
          for (int k = 0; k < 8; k++)
          {
            if (save(grid, i + u[k], j + v[k]) && grid[(i + u[k]),(j + v[k])] > 0)
            {
              // If initial value <= 0
              // just decrement it by 1
              grid[i,j]--;
            }
          }
        }
      }
    }

    // Generating new Generation.
    // Now the magnitude of the
    // grid will represent number
    // of neighbours
    for (int i = 0; i < p; i++)
    {
      for (int j = 0; j < q; j++)
      {
        // If initial value was 1.
        if (grid[i,j] > 0)
        {
          // Since Any live cell with
          // < 2 live neighbors dies
          if (grid[i,j] < 3)
            grid[i,j] = 0;

          // Since Any live cell with
          // 2 or 3 live neighbors live
          else if (grid[i,j] <= 4)
            grid[i,j] = 1;

          // Since Any live cell with
          // > 3 live neighbors dies
          else if (grid[i,j] > 4)
            grid[i,j] = 0;
        }
        else
        {
          // Since Any dead cell with
          // exactly 3 live neighbors
          // becomes a live cell
          if (grid[i,j] == -3)
            grid[i,j] = 1;
          else
            grid[i,j] = 0;
        }
      }
    }
  }

  //Driver Code
  static public void Main (){

    int[,] grid = {{0, 0, 0, 0, 0,
                    0, 0, 0, 0, 0},
                   {0, 0, 0, 1, 1,
                    0,0, 0, 0, 0},
                   {0, 0, 0, 0, 1,
                    0, 0, 0, 0, 0},
                   {0, 0, 0, 0, 0,
                    0, 0, 0, 0, 0},
                   {0, 0, 0, 0, 0,
                    0, 0, 0, 0, 0}};

    // Function to generate
    // New Generation inplace
    solve(grid);

    // Displaying the grid
    print(grid);

  }
}

// This code is contributed by shruti456rawal

Javascript

<script>

// JavaScript implementation of
// the above approach

function print2dArr(grid){
    let p = grid.length
    let q = grid[0].length

    for(let i=0;i<p;i++){
        for(let j=0;j<q;j++){
            document.write(grid[i][j],'')
        }
        document.write("</br>")
    }
}


// Function to check if
// index are not out of grid
function save(grid, row, col){
    return grid.length > row && grid[0].length > col && row >= 0 && col >= 0
}

// Function to get New Generation


function solve(grid){
    let p = grid.length
    let q = grid[0].length
    let u = [1, -1, 0, 1, -1, 0, 1, -1]
    let v = [0, 0, -1, -1, -1, 1, 1, 1]
    for(let i = 0; i < p; i++)
    {
        for(let j = 0; j < q; j++)
        {

            // IF the initial value
            // of the grid(i, j) is 1
            if (grid[i][j] > 0)
            {
                for(let k = 0; k < 8; k++)
                {
                    if (save(grid, i + u[k], j + v[k]) && grid[i + u[k]][j + v[k]] > 0)

                        // If initial value > 0,
                        // just increment it by 1
                        grid[i][j] += 1
                }
            }

            // IF the initial value
            // of the grid(i, j) is 0
            else{
                for(let k = 0;k<8;k++){
                    if (save(grid, i + u[k], j + v[k]) && grid[i + u[k]][j + v[k]] > 0)
                        // If initial value <= 0
                        // just decrement it by 1
                        grid[i][j] -= 1
                }
            }
        }
    }

    // Generating new Generation.
    // Now the magnitude of the
    // grid will represent number
    // of neighbours
    for(let i = 0; i < p; i++)
    {
        for(let j = 0; j < q; j++)
        {

            // If initial value was 1.
            if (grid[i][j] > 0){
                // Since Any live cell with
                // < 2 live neighbors dies
                if (grid[i][j] < 3)
                    grid[i][j] = 0

                // Since Any live cell with
                // 2 or 3 live neighbors live
                else if(grid[i][j] <= 4)
                    grid[i][j] = 1

                // Since Any live cell with
                // > 3 live neighbors dies
                else if(grid[i][j] > 4)
                    grid[i][j] = 0
            }

            else{
                // Since Any dead cell with
                // exactly 3 live neighbors
                // becomes a live cell
                if (grid[i][j] == -3)
                    grid[i][j] = 1
                else
                    grid[i][j] = 0
            }
        }
    }
}


// Driver code

let    grid = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 1, 1, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ],
            [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ], ]

// Function to generate
// New Generation inplace
solve(grid)

// Displaying the grid
print2dArr(grid)


// This code is contributed by shinjanpatra

</script>

Output:

0000000000
0001100000
0001100000
0000000000
0000000000

Time complexity: O(N*M)
Auxiliary Space: O(1)