# Maximum neighbor element in a matrix within distance K

Given a matrix mat[][] and an integer K, the task is to find the maximum neighbor within an absolute distance of K for each element of the matrix.

In other words for each Matrix[i][j] find maximum Matrix[p][q] such that abs (i-p) + abs (j-q) ≤ K.

Examples:

Input: mat[][] = {{1, 2}, {4, 5}}, K = 1
Output: {{4, 5}, {5, 5}}
Explanation:
Maximum neighbour to the element mat = 4 (Distance = 1)
Maximum neighbour to the element mat = 5 (Distance = 1)
Maximum neighbour to the element mat = 5 (Distance = 1)
Maximum neighbour to the element mat = 5 (Distance = 0)

Input: mat[][] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}, K = 2
Output: {{7, 8, 9}, {8, 9, 9}, {9, 9, 9}}

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

Approach: The idea is to iterate over a loop from 1 to K, to choose the element from neighbors with distance less than or equal to K. Each time, Iterate over the matrix to find the maximum adjacent element for each element of the matrix.

Below is the implementation of the above approach:

 `// C++ implmentation to find the  ` `// maximum neighbor element within ` `// the distance of less than K ` ` `  `#include ` ` `  `using` `namespace` `std; ` ` `  `// Function to print the matrix ` `void` `printMatrix(vector > A) ` `{ ` `    ``// Loop to iterate over the matrix ` `    ``for` `(``int` `i = 0; i < A.size(); i++) { ` `        ``for` `(``int` `j = 0; j < A.size(); j++) ` `            ``cout << A[i][j] << ``' '``; ` `        ``cout << ``'\n'``; ` `    ``} ` `} ` ` `  `// Function to find the maximum ` `// neighbor within the distance ` `// of less than equal to K ` `vector > getMaxNeighbour( ` `        ``vector >& A, ``int` `K) ` `{ ` `    ``vector > ans = A; ` `     `  `    ``// Loop to find the maximum ` `    ``// element within the distance ` `    ``// of less than K ` `    ``for` `(``int` `q = 1; q <= K; q++) { ` `        ``for` `(``int` `i = 0; i < A.size(); i++) { ` `            ``for` `(``int` `j = 0; j < A.size(); j++) { ` `                ``int` `maxi = ans[i][j]; ` `                ``if` `(i > 0) ` `                    ``maxi = max( ` `                        ``maxi, ans[i - 1][j]); ` `                ``if` `(j > 0) ` `                    ``maxi = max( ` `                        ``maxi, ans[i][j - 1]); ` `                ``if` `(i < A.size() - 1) ` `                    ``maxi = max( ` `                        ``maxi, ans[i + 1][j]); ` `                ``if` `(j < A.size() - 1) ` `                    ``maxi = max( ` `                        ``maxi, ans[i][j + 1]); ` `                ``A[i][j] = maxi; ` `            ``} ` `        ``} ` `        ``ans = A; ` `    ``} ` `    ``return` `ans; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``vector > B = { { 1, 2, 3 },  ` `                  ``{ 4, 5, 6 }, { 7, 8, 9 } }; ` `    ``printMatrix(getMaxNeighbour(B, 2)); ` `    ``return` `0; ` `} `

Output:
```7 8 9
8 9 9
9 9 9
```

Time Complexity: O(M*N*K)
Space Complexity: O(M*N)

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