Maximum product of 4 adjacent elements in matrix

Given a square matrix, find the maximum product of four adjacent elements of matrix. The adjacent elements of matrix can be top, down, left, right, diagonal or anti diagonal. The four or more numbers should be adjacent to each other.
Note: n should be greater than or equal to 4 i.e n >= 4

Examples :

Input : n = 4
        {{6, 2, 3 4},
         {5, 4, 3, 1},
         {7, 4, 5, 6},
         {8, 3, 1, 0}}

Output : 1680 

Explanation:
Multiplication of 6 5 7 8 produces maximum
result and all element are adjacent to 
each other in one direction

Input : n = 5
        {{1, 2, 3, 4, 5},
         {6, 7, 8, 9, 1},
         {2, 3, 4, 5, 6},
         {7, 8, 9, 1, 0},
         {9, 6, 4, 2, 3}}


Output: 3024

Explanation:
Multiplication of 6 7 8 9 produces maximum 
result and all elements are adjacent to
each other in one direction.

Asked in : Tolexo

Approach:
1. Group 4 elements which are adjacent to each other in each row and calculate their maximum result.
2. Group 4 elements which are adjacent to each other in each column and calculate their maximum results.
3. Group 4 elements which are adjacent to each other in diagonal and calculate their maximum results.
4. Group 4 elements which are adjacent to each other in anti diagonal and calculate their maximum results.
5. Compare of all calculated maximum results.

Below is the implementation of above approach:



C++

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// C++ program to find out the maximum product
// in the matrix which four elements are 
// adjacent to each other in one direction
#include <bits/stdc++.h>
using namespace std;
  
const int n = 5;
  
// function to find max product
int FindMaxProduct(int arr[][n], int n)
{
    int max = 0, result;
  
    // iterate the rows.
    for (int i = 0; i < n; i++) 
    {
  
        // iterate the columns.
        for (int j = 0; j < n; j++) 
        {
  
            // check the maximum product 
            // in horizontal row.
            if ((j - 3) >= 0) 
            {
                result = arr[i][j] * arr[i][j - 1] *
                    arr[i][j - 2] * arr[i][j - 3];
                  
                if (max < result)
                    max = result;
            }
  
            // check the maximum product 
            // in vertical row.
            if ((i - 3) >= 0) 
            {
                result = arr[i][j] * arr[i - 1][j] *
                    arr[i - 2][j] * arr[i - 3][j];
                  
                if (max < result)
                    max = result;
            }
  
            // check the maximum product in
            // diagonal (going through down - right)
            if ((i - 3) >= 0 && (j - 3) >= 0) 
            {
                result = arr[i][j] * arr[i - 1][j - 1] *
                    arr[i - 2][j - 2] * arr[i - 3][j - 3];
                  
                if (max < result)
                    max = result;
            }
              
            // check the maximum product in
            // diagonal (going through up - right)
            if ((i - 3) >= 0 && (j - 1) <= 0)
            {
                result = arr[i][j] * arr[i - 1][j + 1] *
                    arr[i - 2][j + 2] * arr[i - 3][j + 3];
      
                if (max < result)
                    max = result;
            }
        }
    }
  
    return max;
}
  
// driver code
int main()
{
  
    /* int arr[][4] = {{6, 2, 3, 4}, 
                    {5, 4, 3, 1},
                    {7, 4, 5, 6},
                    {8, 3, 1, 0}};*/
    /* int arr[][5] = {{1, 2, 1, 3, 4},
                    {5, 6, 3, 9, 2},
                    {7, 8, 8, 1, 2},
                    {1, 0, 7, 9, 3},
                    {3, 0, 8, 4, 9}};*/
                          
    int arr[][5] = {{1, 2, 3, 4, 5},
                    {6, 7, 8, 9, 1},
                    {2, 3, 4, 5, 6},
                    {7, 8, 9, 1, 0},
                    {9, 6, 4, 2, 3}};
  
    cout << FindMaxProduct(arr, n);
    return 0;
}

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Java

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// Java program to find out the
// maximum product in the matrix
// which four elements are adjacent
// to each other in one direction
class GFG 
{
static final int n = 5;
  
// function to find max product
static int FindMaxProduct(int arr[][], int n) 
{
    int max = 0, result;
  
    // iterate the rows.
    for (int i = 0; i < n; i++) 
    {
    // iterate the columns.
    for (int j = 0; j < n; j++) 
    {
        // check the maximum product
        // in horizontal row.
        if ((j - 3) >= 0
        {
        result = arr[i][j] * arr[i][j - 1] * 
                arr[i][j - 2] * arr[i][j - 3];
        if (max < result)
            max = result;
        }
  
        // check the maximum product
        // in vertical row.
        if ((i - 3) >= 0
        {
        result = arr[i][j] * arr[i - 1][j] * 
                arr[i - 2][j] * arr[i - 3][j];
  
        if (max < result)
            max = result;
        }
  
        // check the maximum product in
        // diagonal (going through down - right)
        if ((i - 3) >= 0 && (j - 3) >= 0
        {
        result = arr[i][j] * arr[i - 1][j - 1] * 
                arr[i - 2][j - 2] * arr[i - 3][j - 3];
  
        if (max < result)
            max = result;
        }
   
        // check the maximum product in
        // diagonal (going through up - right)
        if ((i - 3) >= 0 && (j - 1) <= 0)
        {
        result = arr[i][j] * arr[i - 1][j + 1] *
               arr[i - 2][j + 2] * arr[i - 3][j + 3];
      
        if (max < result)
            max = result;
        }
    }
    }
  
    return max;
}
  
// Driver code
public static void main(String[] args) 
{
  
    /* int arr[][4] = {{6, 2, 3, 4},
                       {5, 4, 3, 1},
                       {7, 4, 5, 6},
                       {8, 3, 1, 0}};*/
    /* int arr[][5] = {{1, 2, 1, 3, 4},
                       {5, 6, 3, 9, 2},
                       {7, 8, 8, 1, 2},
                       {1, 0, 7, 9, 3},
                       {3, 0, 8, 4, 9}};*/
  
    int arr[][] = {{1, 2, 3, 4, 5},
                {6, 7, 8, 9, 1},
                {2, 3, 4, 5, 6},
                {7, 8, 9, 1, 0},
                    {9, 6, 4, 2, 3}};
  
    System.out.print(FindMaxProduct(arr, n));
}
}
  
// This code is contributed by Anant Agarwal.

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Python 3

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# Python 3 program to find out the maximum 
# product in the matrix which four elements 
# are adjacent to each other in one direction
n = 5
  
# function to find max product
def FindMaxProduct(arr, n):
  
    max = 0
  
    # iterate the rows.
    for i in range(n): 
  
        # iterate the columns.
        for j in range( n): 
  
            # check the maximum product 
            # in horizontal row.
            if ((j - 3) >= 0):
                result = (arr[i][j] * arr[i][j - 1] * 
                          arr[i][j - 2] * arr[i][j - 3])
                  
                if (max < result):
                    max = result
  
            # check the maximum product 
            # in vertical row.
            if ((i - 3) >= 0) :
                result = (arr[i][j] * arr[i - 1][j] *
                          arr[i - 2][j] * arr[i - 3][j])
                  
                if (max < result):
                    max = result
  
            # check the maximum product in
            # diagonal going through down - right 
            if ((i - 3) >= 0 and (j - 3) >= 0):
                result = (arr[i][j] * arr[i - 1][j - 1] *
                          arr[i - 2][j - 2] * arr[i - 3][j - 3])
                  
                if (max < result):
                    max = result
  
            # check the maximum product in
            # diagonal going through up - right
            if ((i - 3) >= 0 and (j - 1) <= 0):
                result = (arr[i][j] * arr[i - 1][j + 1] *
                          arr[i - 2][j + 2] * arr[i - 3][j + 3])
  
                if (max < result):
                    max = result
  
    return max
  
# Driver code
if __name__ == "__main__":
      
  
    # int arr[][4] = {{6, 2, 3, 4}, 
    #                  {5, 4, 3, 1},
    #                  {7, 4, 5, 6},
    #                  {8, 3, 1, 0}};
    # int arr[][5] = {{1, 2, 1, 3, 4},
    #                  {5, 6, 3, 9, 2},
    #                  {7, 8, 8, 1, 2},
    #                  {1, 0, 7, 9, 3},
    #                  {3, 0, 8, 4, 9}};
                          
    arr = [[1, 2, 3, 4, 5],
           [6, 7, 8, 9, 1],
           [2, 3, 4, 5, 6],
           [7, 8, 9, 1, 0],
            [9, 6, 4, 2, 3]]
  
    print(FindMaxProduct(arr, n))
  
# This code is contributed by ita_c

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C#

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// C# program to find out the
// maximum product in the matrix
// which four elements are adjacent
// to each other in one direction
using System;
  
public class GFG {
      
    static int n = 5;
  
// Function to find max product
static int FindMaxProduct(int[,] arr, int n) 
{
    int max = 0, result;
  
    // iterate the rows
    for (int i = 0; i < n; i++) {
          
    // iterate the columns
    for (int j = 0; j < n; j++) {
          
        // check the maximum product
        // in horizontal row.
        if ((j - 3) >= 0) {
              
        result = arr[i, j] * arr[i, j - 1] * 
                             arr[i, j - 2] *
                             arr[i, j - 3];
                  
        if (max < result)
            max = result;
        }
  
        // check the maximum product
        // in vertical row.
        if ((i - 3) >= 0) {
        result = arr[i, j] * arr[i - 1, j] * 
                             arr[i - 2, j] *
                             arr[i - 3, j];
  
        if (max < result)
            max = result;
        }
  
        // check the maximum product in
        // diagonal going through down - right
        if ((i - 3) >= 0 && (j - 3) >= 0) 
        {
        result = arr[i, j] * arr[i - 1, j - 1] * 
                             arr[i - 2, j - 2] * 
                             arr[i - 3, j - 3];
  
        if (max < result)
            max = result;
        }
          
        // check the maximum product in 
        // diagonal going through up - right
        if ((i - 3 ) >= 0 && (j - 1) <= 0)
        {
        result = arr[i, j] * arr[i - 1, j + 1] * 
                             arr[i - 2, j + 2] *
                             arr[i - 3, j + 3];
        
        if (max < result)
            max = result;
        }
    }
    }
  
    return max;
}
  
    // Driver Code
    static public void Main ()
    {
    int[,]arr = {{1, 2, 3, 4, 5},
                 {6, 7, 8, 9, 1},
                 {2, 3, 4, 5, 6},
                 {7, 8, 9, 1, 0},
                 {9, 6, 4, 2, 3}};
                  
    Console.Write(FindMaxProduct(arr, n));
    }
}
  
// This code is contributed by Shrikant13

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PHP

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<?php
// PHP program to find out the maximum product
// in the matrix which four elements are 
// adjacent to each other in one direction
$n = 5;
  
// function to find max product
function FindMaxProduct( $arr, $n)
{
    $max = 0; $result;
  
    // iterate the rows.
    for ( $i = 0; $i < $n; $i++) 
    {
  
        // iterate the columns.
        for ( $j = 0; $j < $n; $j++) 
        {
  
            // check the maximum product 
            // in horizontal row.
            if (($j - 3) >= 0) 
            {
                $result = $arr[$i][$j] * 
                          $arr[$i][$j - 1] *
                          $arr[$i][$j - 2] * 
                          $arr[$i][$j - 3];
                  
                if ($max < $result)
                    $max = $result;
            }
  
            // check the maximum product 
            // in vertical row.
            if (($i - 3) >= 0) 
            {
                $result = $arr[$i][$j] * 
                          $arr[$i - 1][$j] *
                          $arr[$i - 2][$j] * 
                          $arr[$i - 3][$j];
                  
                if ($max < $result)
                    $max = $result;
            }
  
            // check the maximum product in
            // diagonal going through down - right
            if (($i - 3) >= 0 and ($j - 3) >= 0) 
            {
                $result = $arr[$i][$j] * 
                          $arr[$i - 1][$j - 1] *
                          $arr[$i - 2][$j - 2] * 
                          $arr[$i - 3][$j - 3];
                  
                if ($max < $result)
                    $max = $result;
            }
              
            // check the maximum product in
            // diagonal going through up - right
            if (($i - 3) >= 0 and ($j - 1) <= 0) 
            {
                $result = $arr[$i][$j] * 
                          $arr[$i - 1][$j + 1] *
                          $arr[$i - 2][$j + 2] * 
                          $arr[$i - 3][$j + 3];
                  
                if ($max < $result)
                    $max = $result;
            }
              
        }
    }
  
    return $max;
}
      
    // Driver Code                        
    $arr = array(array(1, 2, 3, 4, 5),
                 array(6, 7, 8, 9, 1),
                 array(2, 3, 4, 5, 6),
                 array(7, 8, 9, 1, 0),
                 array(9, 6, 4, 2, 3));
   
    echo FindMaxProduct($arr, $n);
  
// This code is contributed by anuj_67.
?>

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Output:

3024

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