Find Land with Longest Distance from Water in Python

Suppose we have a binary matrix where, 0 represents water and 1 represents land. Now we have to find the land which has the longest Manhattan distance from water and finally return the distance.

So, if the input is like

then the output will be 3, as [0,0] cell has Manhattan distance of 3 from water.

To solve this, we will follow these steps −

• if A is empty, then
  • return 0
• R := row count of matrix, C := column count of matrix
• distance := a matrix of order R x C and fill with 0
• q := a double ended queue with some pairs (r, c) where r and c are row and column index of matrix where matrix[r, c] is 0
• if size of q is wither 0 or R * C, then
  • return -1
• while q is not empty, do
  • (r, c) := left element of q, then remove from q
  • for each pair (x, y) in [(r - 1, c) ,(r + 1, c) ,(r, c + 1) ,(r, c - 1) ], do
    • if x and y are in range of matrix and A[x, y] is 1, then
      • A[x, y] := 0
      • distance[x, y] := distance[r, c] + 1
      • insert (x, y) at the end of q
• res := a list of containing maximum element of each rows
• return maximum of res

Example (Python)

Let us see the following implementation to get better understanding −

 Live Demo

from collections import deque
class Solution:
   def solve(self, A):
      if not A:
         return 0
      R, C = len(A), len(A[0])
      distance = [[0] * C for _ in range(R)]
      q = deque((r, c) for r in range(R) for c in range(C) if not A[r][c])
      if len(q) in (0, R * C):
         return -1
      while q:
         r, c = q.popleft()
         for x, y in [(r - 1, c), (r + 1, c), (r, c + 1), (r, c - 1)]:
            if 0 <= x < R and 0 <= y < C and A[x][y]:
               A[x][y] = 0
               distance[x][y] = distance[r][c] + 1
               q.append((x, y))
      return max(max(row) for row in distance)
ob = Solution()
matrix = [
   [1, 1, 1, 1],
   [1, 1, 0, 1],
   [1, 1, 1, 1],
   [0, 0, 1, 1]
]
print(ob.solve(matrix))

Input

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

Output

3