Find Largest Rectangle of 1's with Column Swapping in Python

Suppose we have a binary matrix, we have to find the largest rectangle of all 1's in that given matrix. The rectangle can be built by swapping or exchanging any pair of columns of that matrix.

So, if the input is like

then the output will be the 6 in this case. The rectangle can be generating by exchanging column 1 with 3. The matrix after exchanging will be −

To solve this, we will follow these steps −

• row := size of mat

• col := size of mat[0]

• temp := a matrix of order (row + 1) x (col + 1), and fill with 0

• for i in range 0 to col, do

  • temp[0, i] := mat[0, i]

  • for j in range 1 to row, do

    • if mat[j, i] is same as 0, then

      • temp[j, i] := 0

    • otherwise,

      • temp[j, i] := temp[j - 1, i] + 1

• for i in range 0 to row, do

  • cnt := an array of size (row + 1), and filled with 0

  • for j in range 0 to col, increase by 1, do

    • cnt[temp[i, j]] := cnt[temp[i, j]] + 1

  • col_no := 0

  • j := row

  • while j >= 0, do

    • if cnt[j] > 0, then

      • for k in range 0 to cnt[j], do

        • temp[i, col_no] := j

        • col_no := col_no + 1

    • j := j - 1

• area_maximum := 0

• for i in range 0 to row, do

  • for j in range 0 to col, do

    • area_current :=(j + 1) * temp[i, j]

    • if area_current > area_maximum, then

      • area_maximum := area_current

• return area_maximum

Example 

Let us see the following implementation to get better understanding −

 Live Demo

def maxArea(mat):
   row = len(mat)
   col = len(mat[0])
   temp = [[0 for i in range(col + 1)] for i in range(row + 1)]
   for i in range(0, col):
      temp[0][i] = mat[0][i]
   for j in range(1, row):
      if ((mat[j][i] == 0)):
         temp[j][i] = 0
      else:
         temp[j][i] = temp[j - 1][i] + 1
   for i in range(0, row):
      cnt = [0 for i in range(row + 1)]
      for j in range(0, col, 1):
         cnt[temp[i][j]] += 1
      col_no = 0
      j = row
      while(j >= 0):
         if (cnt[j] > 0):
            for k in range(0, cnt[j]):
               temp[i][col_no] = j
               col_no += 1
         j -= 1
   area_maximum = 0
   for i in range(0, row):
      for j in range(0, col):
         area_current = (j + 1) * temp[i][j]
         if (area_current > area_maximum):
            area_maximum = area_current

   return area_maximum
mat = [
   [0, 0, 1, 1, 0],
   [0, 0, 1, 1, 1],
   [1, 0, 1, 1, 0]]
print("Area : ",maxArea(mat))

Input

[ [1, 0, 0, 1, 0],
[1, 0, 0, 1, 1],
[1, 1, 0, 1, 0]]

Output

Area : 2