# Minimum product in a grid of adjacent elements

Given an N x M grid. The task is to find the minimum product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the matrix.

Examples:

```Input : mat[][] = {1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12}
Output : 700

2*5*7*10 gives output as 700 which is the smallest
product possible

Input :{7, 6, 7, 9
1, 2, 3, 4
1, 2, 3, 6,
5, 6, 7, 1}

Output: 36
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Traverse in the matrix apart from first row, last row, first column and last column. Compute the product of the four adjacent numbers which are at mat[i-1][j], mat[i+1][j], mat[i][j+1] and mat[i][j-1]. On each computation, if the product thus formed is less than the previous minimum found, then replace the minimum variable with the computed product.

Below is the implementation of the above approach:

## C++

 `// C++ program to find the minimum product ` `// of adjacent elements ` `#include ` `using` `namespace` `std; ` `const` `int` `N = 3; ` `const` `int` `M = 4; ` ` `  `// Function to return the minimum ` `// product of adjacent elements ` `int` `minimumProduct(``int` `mat[N][M]) ` `{ ` ` `  `    ``// initial minimum ` `    ``int` `minimum = INT_MAX; ` ` `  `    ``// Traverse in the matrix ` `    ``// except the first, last row ` `    ``// first and last coloumn ` `    ``for` `(``int` `i = 1; i < N - 1; i++) { ` `        ``for` `(``int` `j = 1; j < M - 1; j++) { ` `            ``// product the adjacent elements ` `            ``int` `p = mat[i - 1][j] * mat[i + 1][j] ` `                    ``* mat[i][j + 1] * mat[i][j - 1]; ` ` `  `            ``// if the product is less than ` `            ``// the previously computed minimum ` `            ``if` `(p < minimum) ` `                ``minimum = p; ` `        ``} ` `    ``} ` ` `  `    ``return` `minimum; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `mat[] = { { 1, 2, 3, 4 }, ` `                     ``{ 4, 5, 6, 7 }, ` `                     ``{ 7, 8, 9, 12 } }; ` ` `  `    ``cout << minimumProduct(mat); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find  ` `// the minimum product ` `// of adjacent elements ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` `static` `int` `N = ``3``; ` `static` `int` `M = ``4``; ` ` `  `// Function to return the  ` `// minimum product of  ` `// adjacent elements ` `static` `int` `minimumProduct(``int` `mat[][]) ` `{ ` ` `  `    ``// initial minimum ` `    ``int` `minimum = Integer.MAX_VALUE; ` ` `  `    ``// Traverse in the matrix ` `    ``// except the first, last row ` `    ``// first and last coloumn ` `    ``for` `(``int` `i = ``1``; i < N - ``1``; i++)  ` `    ``{ ` `        ``for` `(``int` `j = ``1``; j < M - ``1``; j++)  ` `        ``{ ` `            ``// product the  ` `            ``// adjacent elements ` `            ``int` `p = mat[i - ``1``][j] *  ` `                    ``mat[i + ``1``][j] * ` `                    ``mat[i][j + ``1``] *  ` `                    ``mat[i][j - ``1``]; ` ` `  `            ``// if the product is less  ` `            ``// than the previously  ` `            ``// computed minimum ` `            ``if` `(p < minimum) ` `                ``minimum = p; ` `        ``} ` `    ``} ` ` `  `    ``return` `minimum; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `mat[][] = {{``1``, ``2``, ``3``, ``4``}, ` `                   ``{``4``, ``5``, ``6``, ``7``}, ` `                   ``{``7``, ``8``, ``9``, ``12``}}; ` ` `  `    ``System.out.println(minimumProduct(mat)); ` `} ` `} ` ` `  `// This code is contributed ` `// by anuj_67. `

## Python3

 `# Python 3 program to find the minimum  ` `# product of adjacent elements ` `import` `sys ` ` `  `N ``=` `3` `M ``=` `4` ` `  `# Function to return the minimum ` `# product of adjacent elements ` `def` `minimumProduct(mat): ` `     `  `    ``# initial minimum ` `    ``minimum ``=` `sys.maxsize ` ` `  `    ``# Traverse in the matrix except  ` `    ``# the first, last row first  ` `    ``# and last coloumn ` `    ``for` `i ``in` `range``(``1``, N ``-` `1``, ``1``): ` `        ``for` `j ``in` `range``(``1``, M ``-` `1``, ``1``): ` `             `  `            ``# product the adjacent elements ` `            ``p ``=` `(mat[i ``-` `1``][j] ``*` `mat[i ``+` `1``][j] ``*` `                 ``mat[i][j ``+` `1``] ``*` `mat[i][j ``-` `1``]) ` ` `  `            ``# if the product is less than ` `            ``# the previously computed minimum ` `            ``if` `(p < minimum): ` `                ``minimum ``=` `p ` `     `  `    ``return` `minimum ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``mat ``=` `[[``1``, ``2``, ``3``, ``4``],     ` `           ``[``4``, ``5``, ``6``, ``7``], ` `           ``[``7``, ``8``, ``9``, ``12``]] ` ` `  `    ``print``(minimumProduct(mat)) ` `     `  `# This code is contributed by ` `# Shashank_Sharma `

## C#

 `// C# program to find  ` `// the minimum product ` `// of adjacent elements ` `using` `System; ` ` `  `class` `GFG ` `{ ` `static` `int` `N = 3; ` `static` `int` `M = 4; ` ` `  `// Function to return the  ` `// minimum product of  ` `// adjacent elements ` `static` `int` `minimumProduct(``int` `[,]mat) ` `{ ` ` `  `    ``// initial minimum ` `    ``int` `minimum = ``int``.MaxValue; ` ` `  `    ``// Traverse in the matrix ` `    ``// except the first, last row ` `    ``// first and last coloumn ` `    ``for` `(``int` `i = 1;  ` `             ``i < N - 1; i++)  ` `    ``{ ` `        ``for` `(``int` `j = 1;  ` `                 ``j < M - 1; j++)  ` `        ``{ ` `            ``// product the  ` `            ``// adjacent elements ` `            ``int` `p = mat[i - 1, j] *  ` `                    ``mat[i + 1, j] * ` `                    ``mat[i, j + 1] *  ` `                    ``mat[i, j - 1]; ` ` `  `            ``// if the product is less  ` `            ``// than the previously  ` `            ``// computed minimum ` `            ``if` `(p < minimum) ` `                ``minimum = p; ` `        ``} ` `    ``} ` ` `  `    ``return` `minimum; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main () ` `{ ` `    ``int` `[,]mat = {{1, 2, 3, 4}, ` `                  ``{4, 5, 6, 7}, ` `                  ``{7, 8, 9, 12}}; ` ` `  `    ``Console.WriteLine(minimumProduct(mat)); ` `} ` `} ` ` `  `// This code is contributed ` `// by anuj_67. `

## PHP

 ` `

Output:

```384
```

Time Complexity: O(N*M)

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