Check whether row or column swaps produce maximum size binary sub-matrix with all 1s - GeeksforGeeks

Check whether row or column swaps produce maximum size binary sub-matrix with all 1s - GeeksforGeeks
Given a binary matrix, the task is to find whether row swaps or column swaps give maximum size sub-matrix with all 1's. In a row swap, we are allowed to swap any two rows. In a column swap we are allowed to swap any two columns. Output "Row Swap" or "Column Swap" and the maximum size.

The idea is to find both row swap and column swap maximum size binary submatrix and compare.

To find the maximum sized binary sub-matrix with row swaps allowed, make a 2-D array, say dp[i][j]. Each value of dp[i][j] contains the number of consecutive 1s on right side of (i,j) in i-th row. Now, store each column in the 1-D temporary array one by one, say b[] and sort, and find maximum b[i] * (n – i), since b[i] is indicating the sub-matrix width and (n – i) is sub-matrix height.

Similarly, to find the maximum size binary sub-matrix with column swap allowed, find dp[i][j], where each value contains the number of consecutive 1 below the (i, j) in j-th column. Similarly, store each row in the 1-D temporary array one by one, say b[] and sort. Find maximum b[i] * (m – i), since b[i] is indicating the submatrix height and (n – i) is submatrix width.

// Precompute the number of consecutive 1 below the

// (i, j) in j-th column and the number of consecutive 1s

// on right side of (i, j) in i-th row.

void precompute(int mat[R][C], int ryt[][C + 2],

                               int dwn[R + 2][C + 2])

{

    // Travesing the 2d matrix from top-right.

    for (int j=C-1; j>=0; j--)

    {

        for (int i=0; i<R; ++i)

        {

            // If (i,j) contain 0, do nothing

            if (mat[i][j] == 0)

                ryt[i][j] = 0;

 

            // Counting consecutive 1 on right side

            else

                ryt[i][j] = ryt[i][j + 1] + 1;

        }

    }

 

 

    // Travesing the 2d matrix from bottom-left.

    for (int i = R - 1; i >= 0; i--)

    {

        for (int j = 0; j < C; ++j)

        {

            // If (i,j) contain 0, do nothing

            if (mat[i][j] == 0)

                dwn[i][j] = 0;

 

            // Counting consecutive 1 down to (i,j).

            else

                dwn[i][j] = dwn[i + 1][j] + 1;

        }

    }

}

 

// Return maximum size submatrix with row swap allowed.

int solveRowSwap(int ryt[R + 2][C + 2])

{

    int b[R] = { 0 }, ans = 0;

 

    for (int j=0; j<C; j++)

    {

        // Copying the column

        for (int i=0; i<R; i++)

            b[i] = ryt[i][j];

 

        // Sort the copied array

        sort(b, b + R);

 

        // Find maximum submatrix size.

        for (int i = 0; i < R; ++i)

            ans = max(ans, b[i] * (R - i));

    }

 

    return ans;

}

 

// Return maximum size submatrix with column

// swap allowed.

int solveColumnSwap(int dwn[R + 2][C + 2])

{

    int b[C] = { 0 }, ans = 0;

 

    for (int i = 0; i < R; ++i)

    {

        // Copying the row.

        for (int j = 0; j < C; ++j)

            b[j] = dwn[i][j];

 

        // Sort the copied array

        sort(b, b + C);

 

        // Find maximum submatrix size.

        for (int i = 0; i < C; ++i)

            ans = max(ans, b[i] * (C - i));

    }

 

    return ans;

}

 

void findMax1s(int mat[R][C])

{

    int ryt[R + 2][C + 2], dwn[R + 2][C + 2];

    memset(ryt, 0, sizeof ryt);

    memset(dwn, 0, sizeof dwn);

 

    precompute(mat, ryt, dwn);

 

    // Solving for row swap and column swap

    int rswap = solveRowSwap(ryt);

    int cswap = solveColumnSwap(dwn);

 

    // Comparing both.

    (rswap > cswap)? (cout << "Row Swap\n" << rswap << endl):

                     (cout << "Column Swap\n" << cswap << endl);

}

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