# Find size of the largest ‘+’ formed by all ones in a binary matrix

Given a N X N binary matrix, find the size of the largest ‘+’ formed by all 1s.

Example:

For above matrix, largest ‘+’ would be formed by highlighted part of size 17.

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

The idea is to maintain four auxiliary matrices left[][], right[][], top[][], bottom[][] to store consecutive 1’s in every direction. For each cell (i, j) in the input matrix, we store below information in these four matrices –

```left(i, j) stores maximum number of
consecutive 1's to the left of cell (i, j)
including cell (i, j).

right(i, j) stores maximum number of
consecutive 1's to the right of cell (i, j)
including cell (i, j).

top(i, j) stores maximum number of
consecutive 1's at top of cell (i, j)
including cell (i, j).

bottom(i, j) stores maximum number of
consecutive 1's at bottom of cell (i, j)
including cell (i, j).
```

After computing value for each cell of above matrices, the largest + would be formed by a cell of input matrix that has maximum value by considering minimum of (left(i, j), right(i, j), top(i, j), bottom(i, j) )

We can use Dynamic Programming to compute the total amount of consecutive 1’s in every direction.

```if mat(i, j) == 1
left(i, j) = left(i, j - 1) + 1
else left(i, j) = 0

if mat(i, j) == 1
top(i, j) = top(i - 1, j) + 1;
else
top(i, j) = 0;

if mat(i, j) == 1
bottom(i, j) = bottom(i + 1, j) + 1;
else
bottom(i, j) = 0;

if mat(i, j) == 1
right(i, j) = right(i, j + 1) + 1;
else
right(i, j) = 0;
```

Below is the implementation of above idea –

 `// C++ program to find the size of the largest '+' ` `// formed by all 1's in given binary matrix ` `#include ` `using` `namespace` `std; ` ` `  `// size of binary square matrix ` `#define N 10 ` ` `  `// Function to find the size of the largest '+' ` `// formed by all 1's in given binary matrix ` `int` `findLargestPlus(``int` `mat[N][N]) ` `{ ` `    ``// left[j][j], right[i][j], top[i][j] and ` `    ``// bottom[i][j] store maximum number of ` `    ``// consecutive 1's present to the left, ` `    ``// right, top and bottom of mat[i][j] including ` `    ``// cell(i, j) respectively ` `    ``int` `left[N][N], right[N][N], top[N][N], ` `        ``bottom[N][N]; ` ` `  `    ``// initialize above four matrix ` `    ``for` `(``int` `i = 0; i < N; i++) ` `    ``{ ` `        ``// initialize first row of top ` `        ``top[i] = mat[i]; ` ` `  `        ``// initialize last row of bottom ` `        ``bottom[N - 1][i] = mat[N - 1][i]; ` ` `  `        ``// initialize first column of left ` `        ``left[i] = mat[i]; ` ` `  `        ``// initialize last column of right ` `        ``right[i][N - 1] = mat[i][N - 1]; ` `    ``} ` ` `  `    ``// fill all cells of above four matrix ` `    ``for` `(``int` `i = 0; i < N; i++) ` `    ``{ ` `        ``for` `(``int` `j = 1; j < N; j++) ` `        ``{ ` `            ``// calculate left matrix (filled left to right) ` `            ``if` `(mat[i][j] == 1) ` `                ``left[i][j] = left[i][j - 1] + 1; ` `            ``else` `                ``left[i][j] = 0; ` ` `  `            ``// calculate top matrix ` `            ``if` `(mat[j][i] == 1) ` `                ``top[j][i] = top[j - 1][i] + 1; ` `            ``else` `                ``top[j][i] = 0; ` ` `  `            ``// calculate new value of j to calculate ` `            ``// value of bottom(i, j) and right(i, j) ` `            ``j = N - 1 - j; ` ` `  `            ``// calculate bottom matrix ` `            ``if` `(mat[j][i] == 1) ` `                ``bottom[j][i] = bottom[j + 1][i] + 1; ` `            ``else` `                ``bottom[j][i] = 0; ` ` `  `            ``// calculate right matrix ` `            ``if` `(mat[i][j] == 1) ` `                ``right[i][j] = right[i][j + 1] + 1; ` `            ``else` `                ``right[i][j] = 0; ` ` `  `            ``// revert back to old j ` `            ``j = N - 1 - j; ` `        ``} ` `    ``} ` ` `  `    ``// n stores length of longest + found so far ` `    ``int` `n = 0; ` ` `  `    ``// compute longest + ` `    ``for` `(``int` `i = 0; i < N; i++) ` `    ``{ ` `        ``for` `(``int` `j = 0; j < N; j++) ` `        ``{ ` `            ``// find minimum of left(i, j), right(i, j), ` `            ``// top(i, j), bottom(i, j) ` `            ``int` `len = min(min(top[i][j], bottom[i][j]), ` `                          ``min(left[i][j], right[i][j])); ` ` `  `            ``// largest + would be formed by a cell that ` `            ``// has maximum value ` `            ``if``(len > n) ` `                ``n = len; ` `        ``} ` `    ``} ` ` `  `    ``// 4 directions of length n - 1 and 1 for middle cell ` `    ``if` `(n) ` `       ``return` `4 * (n - 1) + 1; ` ` `  `    ``// matrix contains all 0's ` `    ``return` `0; ` `} ` ` `  `/* Driver function to test above functions */` `int` `main() ` `{ ` `    ``// Binary Matrix of size N ` `    ``int` `mat[N][N] = ` `    ``{ ` `        ``{ 1, 0, 1, 1, 1, 1, 0, 1, 1, 1 }, ` `        ``{ 1, 0, 1, 0, 1, 1, 1, 0, 1, 1 }, ` `        ``{ 1, 1, 1, 0, 1, 1, 0, 1, 0, 1 }, ` `        ``{ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0 }, ` `        ``{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }, ` `        ``{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 }, ` `        ``{ 1, 0, 0, 0, 1, 0, 0, 1, 0, 1 }, ` `        ``{ 1, 0, 1, 1, 1, 1, 0, 0, 1, 1 }, ` `        ``{ 1, 1, 0, 0, 1, 0, 1, 0, 0, 1 }, ` `        ``{ 1, 0, 1, 1, 1, 1, 0, 1, 0, 0 } ` `    ``}; ` ` `  `    ``cout << findLargestPlus(mat); ` ` `  `    ``return` `0; ` `} `

 `// Java program to find the size of the largest '+' ` `// formed by all 1's in given binary matrix ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// size of binary square matrix ` `    ``static` `int` `N = ``10``; ` ` `  `    ``// Function to find the size of the largest '+' ` `    ``// formed by all 1's in given binary matrix ` `    ``static` `int` `findLargestPlus(``int` `mat[][]) ` `    ``{ ` `         `  `        ``// left[j][j], right[i][j], top[i][j] and ` `        ``// bottom[i][j] store maximum number of ` `        ``// consecutive 1's present to the left, ` `        ``// right, top and bottom of mat[i][j]  ` `        ``// including cell(i, j) respectively ` `        ``int` `left[][] = ``new` `int``[N][N]; ` `        ``int` `right[][] = ``new` `int``[N][N]; ` `        ``int` `top[][] = ``new` `int``[N][N]; ` `        ``int` `bottom[][] = ``new` `int``[N][N]; ` ` `  `        ``// initialize above four matrix ` `        ``for` `(``int` `i = ``0``; i < N; i++) { ` `             `  `            ``// initialize first row of top ` `            ``top[``0``][i] = mat[``0``][i]; ` ` `  `            ``// initialize last row of bottom ` `            ``bottom[N - ``1``][i] = mat[N - ``1``][i]; ` ` `  `            ``// initialize first column of left ` `            ``left[i][``0``] = mat[i][``0``]; ` ` `  `            ``// initialize last column of right ` `            ``right[i][N - ``1``] = mat[i][N - ``1``]; ` `        ``} ` ` `  `        ``// fill all cells of above four matrix ` `        ``for` `(``int` `i = ``0``; i < N; i++) { ` `            ``for` `(``int` `j = ``1``; j < N; j++) { ` `                 `  `                ``// calculate left matrix  ` `                ``// (filled left to right) ` `                ``if` `(mat[i][j] == ``1``) ` `                    ``left[i][j] = left[i][j - ``1``] + ``1``; ` `                ``else` `                    ``left[i][j] = ``0``; ` ` `  `                ``// calculate top matrix ` `                ``if` `(mat[j][i] == ``1``) ` `                    ``top[j][i] = top[j - ``1``][i] + ``1``; ` `                ``else` `                    ``top[j][i] = ``0``; ` ` `  `                ``// calculate new value of j to  ` `                ``// calculate value of bottom(i, j)  ` `                ``// and right(i, j) ` `                ``j = N - ``1` `- j; ` ` `  `                ``// calculate bottom matrix ` `                ``if` `(mat[j][i] == ``1``) ` `                    ``bottom[j][i] = bottom[j + ``1``][i] + ``1``; ` `                ``else` `                    ``bottom[j][i] = ``0``; ` ` `  `                ``// calculate right matrix ` `                ``if` `(mat[i][j] == ``1``) ` `                    ``right[i][j] = right[i][j + ``1``] + ``1``; ` `                ``else` `                    ``right[i][j] = ``0``; ` ` `  `                ``// revert back to old j ` `                ``j = N - ``1` `- j; ` `            ``} ` `        ``} ` ` `  `        ``// n stores length of longest + found so far ` `        ``int` `n = ``0``; ` ` `  `        ``// compute longest + ` `        ``for` `(``int` `i = ``0``; i < N; i++) { ` `            ``for` `(``int` `j = ``0``; j < N; j++) { ` `                ``// find minimum of left(i, j),  ` `                ``// right(i, j), top(i, j),  ` `                ``// bottom(i, j) ` `                ``int` `len = Math.min(Math.min(top[i][j],  ` `                    ``bottom[i][j]),Math.min(left[i][j],  ` `                                        ``right[i][j])); ` ` `  `                ``// largest + would be formed by a ` `                ``// cell that has maximum value ` `                ``if` `(len > n) ` `                    ``n = len; ` `            ``} ` `        ``} ` ` `  `        ``// 4 directions of length n - 1 and 1 for ` `        ``// middle cell ` `        ``if` `(n > ``0``) ` `            ``return` `4` `* (n - ``1``) + ``1``; ` ` `  `        ``// matrix contains all 0's ` `        ``return` `0``; ` `    ``} ` ` `  `    ``/* Driver function to test above functions */` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `         `  `        ``// Binary Matrix of size N ` `        ``int` `mat[][] = { ` `            ``{ ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``0``, ``1``, ``1``, ``1` `}, ` `            ``{ ``1``, ``0``, ``1``, ``0``, ``1``, ``1``, ``1``, ``0``, ``1``, ``1` `}, ` `            ``{ ``1``, ``1``, ``1``, ``0``, ``1``, ``1``, ``0``, ``1``, ``0``, ``1` `}, ` `            ``{ ``0``, ``0``, ``0``, ``0``, ``1``, ``0``, ``0``, ``1``, ``0``, ``0` `}, ` `            ``{ ``1``, ``1``, ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1` `}, ` `            ``{ ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``0` `}, ` `            ``{ ``1``, ``0``, ``0``, ``0``, ``1``, ``0``, ``0``, ``1``, ``0``, ``1` `}, ` `            ``{ ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``0``, ``0``, ``1``, ``1` `}, ` `            ``{ ``1``, ``1``, ``0``, ``0``, ``1``, ``0``, ``1``, ``0``, ``0``, ``1` `}, ` `            ``{ ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``0``, ``1``, ``0``, ``0` `} ` `        ``}; ` `        ``System.out.println(findLargestPlus(mat)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

 `# Python 3 program to find the size  ` `# of the largest '+' formed by all  ` `# 1's in given binary matrix ` ` `  `# size of binary square matrix ` `N ``=` `10` ` `  `# Function to find the size of the  ` `# largest '+' formed by all 1's in ` `# given binary matrix ` `def` `findLargestPlus(mat): ` ` `  `    ``# left[j][j], right[i][j], top[i][j] and ` `    ``# bottom[i][j] store maximum number of ` `    ``# consecutive 1's present to the left, ` `    ``# right, top and bottom of mat[i][j] including ` `    ``# cell(i, j) respectively ` `    ``left ``=` `[[``0` `for` `x ``in` `range``(N)]  ` `               ``for` `y ``in` `range``(N)] ` `    ``right ``=` `[[``0` `for` `x ``in` `range``(N)]  ` `                ``for` `y ``in` `range``(N)] ` `    ``top ``=` `[[``0` `for` `x ``in` `range``(N)]  ` `              ``for` `y ``in` `range``(N)] ` `    ``bottom ``=` `[[``0` `for` `x ``in` `range``(N)]  ` `                 ``for` `y ``in` `range``(N)] ` ` `  `    ``# initialize above four matrix ` `    ``for` `i ``in` `range``(N): ` `         `  `        ``# initialize first row of top ` `        ``top[``0``][i] ``=` `mat[``0``][i] ` ` `  `        ``# initialize last row of bottom ` `        ``bottom[N ``-` `1``][i] ``=` `mat[N ``-` `1``][i] ` ` `  `        ``# initialize first column of left ` `        ``left[i][``0``] ``=` `mat[i][``0``] ` ` `  `        ``# initialize last column of right ` `        ``right[i][N ``-` `1``] ``=` `mat[i][N ``-` `1``] ` ` `  `    ``# fill all cells of above four matrix ` `    ``for` `i ``in` `range``(N): ` `        ``for` `j ``in` `range``(``1``, N): ` `             `  `            ``# calculate left matrix (filled  ` `            ``# left to right) ` `            ``if` `(mat[i][j] ``=``=` `1``): ` `                ``left[i][j] ``=` `left[i][j ``-` `1``] ``+` `1` `            ``else``: ` `                ``left[i][j] ``=` `0` ` `  `            ``# calculate top matrix ` `            ``if` `(mat[j][i] ``=``=` `1``): ` `                ``top[j][i] ``=` `top[j ``-` `1``][i] ``+` `1` `            ``else``: ` `                ``top[j][i] ``=` `0` ` `  `            ``# calculate new value of j to calculate ` `            ``# value of bottom(i, j) and right(i, j) ` `            ``j ``=` `N ``-` `1` `-` `j ` ` `  `            ``# calculate bottom matrix ` `            ``if` `(mat[j][i] ``=``=` `1``): ` `                ``bottom[j][i] ``=` `bottom[j ``+` `1``][i] ``+` `1` `            ``else``: ` `                ``bottom[j][i] ``=` `0` ` `  `            ``# calculate right matrix ` `            ``if` `(mat[i][j] ``=``=` `1``): ` `                ``right[i][j] ``=` `right[i][j ``+` `1``] ``+` `1` `            ``else``: ` `                ``right[i][j] ``=` `0` ` `  `            ``# revert back to old j ` `            ``j ``=` `N ``-` `1` `-` `j ` ` `  `    ``# n stores length of longest '+'  ` `    ``# found so far ` `    ``n ``=` `0` ` `  `    ``# compute longest + ` `    ``for` `i ``in` `range``(N): ` `        ``for` `j ``in` `range``(N): ` `             `  `            ``# find minimum of left(i, j),  ` `            ``# right(i, j), top(i, j), bottom(i, j) ` `            ``l ``=` `min``(``min``(top[i][j], bottom[i][j]), ` `                    ``min``(left[i][j], right[i][j])) ` ` `  `            ``# largest + would be formed by  ` `            ``# a cell that has maximum value ` `            ``if``(l > n): ` `                ``n ``=` `l ` ` `  `    ``# 4 directions of length n - 1 and 1  ` `    ``# for middle cell ` `    ``if` `(n): ` `        ``return` `4` `*` `(n ``-` `1``) ``+` `1` ` `  `    ``# matrix contains all 0's ` `    ``return` `0` ` `  `# Driver Code ` `if` `__name__``=``=``"__main__"``: ` `     `  `    ``# Binary Matrix of size N ` `    ``mat ``=` `[ [ ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``0``, ``1``, ``1``, ``1` `], ` `            ``[ ``1``, ``0``, ``1``, ``0``, ``1``, ``1``, ``1``, ``0``, ``1``, ``1` `], ` `            ``[ ``1``, ``1``, ``1``, ``0``, ``1``, ``1``, ``0``, ``1``, ``0``, ``1` `], ` `            ``[ ``0``, ``0``, ``0``, ``0``, ``1``, ``0``, ``0``, ``1``, ``0``, ``0` `], ` `            ``[ ``1``, ``1``, ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1` `], ` `            ``[ ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``1``, ``0` `], ` `            ``[ ``1``, ``0``, ``0``, ``0``, ``1``, ``0``, ``0``, ``1``, ``0``, ``1` `], ` `            ``[ ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``0``, ``0``, ``1``, ``1` `], ` `            ``[ ``1``, ``1``, ``0``, ``0``, ``1``, ``0``, ``1``, ``0``, ``0``, ``1` `], ` `            ``[ ``1``, ``0``, ``1``, ``1``, ``1``, ``1``, ``0``, ``1``, ``0``, ``0` `]] ` ` `  `    ``print``(findLargestPlus(mat)) ` ` `  `# This code is contributed by ChitraNayal `

 `// C# program to find the size of the largest '+' ` `// formed by all 1's in given binary matrix ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// size of binary square matrix ` `    ``static` `int` `N = 10; ` ` `  `    ``// Function to find the size of the largest '+' ` `    ``// formed by all 1's in given binary matrix ` `    ``static` `int` `findLargestPlus(``int` `[,] mat) ` `    ``{ ` `         `  `        ``// left[j][j], right[i][j], top[i][j] and ` `        ``// bottom[i][j] store maximum number of ` `        ``// consecutive 1's present to the left, ` `        ``// right, top and bottom of mat[i][j]  ` `        ``// including cell(i, j) respectively ` `        ``int` `[,] left = ``new` `int``[N,N]; ` `        ``int` `[,] right = ``new` `int``[N,N]; ` `        ``int` `[,] top = ``new` `int``[N,N]; ` `        ``int` `[,] bottom = ``new` `int``[N,N]; ` ` `  `        ``// initialize above four matrix ` `        ``for` `(``int` `i = 0; i < N; i++) { ` `             `  `            ``// initialize first row of top ` `            ``top[0,i] = mat[0,i]; ` ` `  `            ``// initialize last row of bottom ` `            ``bottom[N - 1,i] = mat[N - 1,i]; ` ` `  `            ``// initialize first column of left ` `            ``left[i,0] = mat[i,0]; ` ` `  `            ``// initialize last column of right ` `            ``right[i,N - 1] = mat[i,N - 1]; ` `        ``} ` ` `  `        ``// fill all cells of above four matrix ` `        ``for` `(``int` `i = 0; i < N; i++) { ` `            ``for` `(``int` `j = 1; j < N; j++) { ` `                 `  `                ``// calculate left matrix  ` `                ``// (filled left to right) ` `                ``if` `(mat[i,j] == 1) ` `                    ``left[i,j] = left[i,j - 1] + 1; ` `                ``else` `                    ``left[i,j] = 0; ` ` `  `                ``// calculate top matrix ` `                ``if` `(mat[j,i] == 1) ` `                    ``top[j,i] = top[j - 1,i] + 1; ` `                ``else` `                    ``top[j,i] = 0; ` ` `  `                ``// calculate new value of j to  ` `                ``// calculate value of bottom(i, j)  ` `                ``// and right(i, j) ` `                ``j = N - 1 - j; ` ` `  `                ``// calculate bottom matrix ` `                ``if` `(mat[j,i] == 1) ` `                    ``bottom[j,i] = bottom[j + 1,i] + 1; ` `                ``else` `                    ``bottom[j,i] = 0; ` ` `  `                ``// calculate right matrix ` `                ``if` `(mat[i,j] == 1) ` `                    ``right[i,j] = right[i,j + 1] + 1; ` `                ``else` `                    ``right[i,j] = 0; ` ` `  `                ``// revert back to old j ` `                ``j = N - 1 - j; ` `            ``} ` `        ``} ` ` `  `        ``// n stores length of longest + found so far ` `        ``int` `n = 0; ` ` `  `        ``// compute longest + ` `        ``for` `(``int` `i = 0; i < N; i++) { ` `            ``for` `(``int` `j = 0; j < N; j++) { ` ` `  `                ``// find minimum of left(i, j),  ` `                ``// right(i, j), top(i, j),  ` `                ``// bottom(i, j) ` `                ``int` `len = Math.Min(Math.Min(top[i,j],  ` `                    ``bottom[i,j]),Math.Min(left[i,j],  ` `                                        ``right[i,j])); ` ` `  `                ``// largest + would be formed by a ` `                ``// cell that has maximum value ` `                ``if` `(len > n) ` `                    ``n = len; ` `            ``} ` `        ``} ` ` `  `        ``// 4 directions of length n - 1 and 1 for ` `        ``// middle cell ` `        ``if` `(n > 0) ` `            ``return` `4 * (n - 1) + 1; ` ` `  `        ``// matrix contains all 0's ` `        ``return` `0; ` `    ``} ` ` `  `    ``/* Driver function to test above functions */` `    ``public` `static` `void` `Main() ` `    ``{ ` `         `  `        ``// Binary Matrix of size N ` `        ``int` `[,]mat = { ` `            ``{ 1, 0, 1, 1, 1, 1, 0, 1, 1, 1 }, ` `            ``{ 1, 0, 1, 0, 1, 1, 1, 0, 1, 1 }, ` `            ``{ 1, 1, 1, 0, 1, 1, 0, 1, 0, 1 }, ` `            ``{ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0 }, ` `            ``{ 1, 1, 1, 0, 1, 1, 1, 1, 1, 1 }, ` `            ``{ 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 }, ` `            ``{ 1, 0, 0, 0, 1, 0, 0, 1, 0, 1 }, ` `            ``{ 1, 0, 1, 1, 1, 1, 0, 0, 1, 1 }, ` `            ``{ 1, 1, 0, 0, 1, 0, 1, 0, 0, 1 }, ` `            ``{ 1, 0, 1, 1, 1, 1, 0, 1, 0, 0 } ` `        ``}; ` ` `  `        ``Console.Write(findLargestPlus(mat)); ` `    ``} ` `} ` ` `  `// This code is contributed by KRV. `

 ` ``\$n``) ` `                ``\$n` `= ``\$len``; ` `        ``} ` `    ``} ` ` `  `    ``// 4 directions of length n - 1 and 1 ` `    ``// for middle cell ` `    ``if` `(``\$n``) ` `    ``return` `4 * (``\$n` `- 1) + 1; ` ` `  `    ``// matrix contains all 0's ` `    ``return` `0; ` `} ` ` `  `// Driver Code ` ` `  `// Binary Matrix of size N ` `\$mat` `= ``array``(``array``(1, 0, 1, 1, 1, 1, 0, 1, 1, 1), ` `             ``array``(1, 0, 1, 0, 1, 1, 1, 0, 1, 1), ` `             ``array``(1, 1, 1, 0, 1, 1, 0, 1, 0, 1), ` `             ``array``(0, 0, 0, 0, 1, 0, 0, 1, 0, 0), ` `             ``array``(1, 1, 1, 0, 1, 1, 1, 1, 1, 1), ` `             ``array``(1, 1, 1, 1, 1, 1, 1, 1, 1, 0), ` `             ``array``(1, 0, 0, 0, 1, 0, 0, 1, 0, 1), ` `             ``array``(1, 0, 1, 1, 1, 1, 0, 0, 1, 1), ` `             ``array``(1, 1, 0, 0, 1, 0, 1, 0, 0, 1), ` `             ``array``(1, 0, 1, 1, 1, 1, 0, 1, 0, 0)); ` ` `  `echo` `findLargestPlus(``\$mat``); ` ` `  `// This code is contributed by Sach_Code ` `?> `

Output:
```17
```

Time complexity of above solution is O(n2).

Auxiliary space used by the program is O(n2).