Find maximum length Snake sequence in Python

Suppose we have a grid of numbers; we have to find a snake sequence and return it. If there are multiple snake sequence, then return only one. As we know a snake sequence is made using adjacent numbers in the grid so for each number, the number on the right-hand side or the number below it is either +1 or -1 its value. So, if current value is in grid cell (a, b), we can either move right (a, b+1) if that number is ± 1 or move below (a+1, b) if that number is ± 1.

So, if the input is like

then the output will be 6, sequence − 10 (0, 0) to 9 (1, 0) to 8 (1, 1) to 7 (1, 2) to 6 (1, 3) to 7 (2, 3) to 8 (3, 3)

To solve this, we will follow these steps −

• Define a function get_path() . This will take grid, mat, i, j

• path := a new list

• pt := a point [i, j]

• insert pt at the end of path

• while grid[i, j] is not 0, do

  • if i > 0 and grid[i, j]-1 is same as grid[i-1, j], then

    • pt := [i-1, j]

    • insert pt at the end of path

    • i := i - 1

  • otherwise when j > 0 and grid[i, j]-1 is same as grid[i, j-1], then

    • pt := [i, j-1]

    • insert pt at the end of path

    • j := j - 1

• return path

• From the main method, do the following −

• lookup := make a grid of size M x N and fill with 0

• length_max := 0, max_row := 0, max_col := 0

• for i in range 0 to M, do

  • for j in range 0 to N, do

    • if i or j is non-zero, then

      • if (i > 0 an and |grid[i-1, j] - grid[i, j]| is 1, then

        • lookup[i,j] = maximum of lookup[i,j],lookup[i-1,j] + 1)

        • if length_max < lookup[i,j], then

          • length_max := lookup[i, j]

          • max_row := i

          • max_col := j

      • if (j > 0 and |grid[i, j-1] - grid[i, j]| is 1, then

        • if length_max < lookup[i][j] is non-zero, then

        • lookup[i,j] = maximum of lookup[i,j],lookup[i,j-1] + 1)

          • length_max := lookup[i, j]

          • max_row := i

          • max_col := j

• display length_max

• path := get_path(lookup, grid, max_row, max_col)

• print all elements in path in reverse order

Example

Let us see the following implementation to get better understanding &mius;

 Live Demo

M = 4
N = 4
def get_path(grid, mat, i, j):
   path = list()
   pt = [i, j]
   path.append(pt)
   while (grid[i][j] != 0):
      if (i > 0 and grid[i][j]-1 == grid[i-1][j]):
         pt = [i-1, j]
         path.append(pt)
         i -= 1
      elif (j > 0 and grid[i][j]-1 == grid[i][j-1]):
         pt = [i, j-1]
         path.append(pt)
         j -= 1
   return path
def get_sequence(grid):
   lookup = [[0 for i in range(N)] for j in range(M)]
   length_max = 0
   max_row = 0
   max_col = 0
   for i in range(M):
      for j in range(N):
         if (i or j):
            if (i > 0 and
               abs(grid[i-1][j] - grid[i][j]) == 1):
                  lookup[i][j] = max(lookup[i][j],lookup[i-1][j] + 1)
                  if (length_max < lookup[i][j]):
                     length_max = lookup[i][j]
                     max_row = i
                     max_col = j
                  if (j > 0 and
                     abs(grid[i][j-1] - grid[i][j]) == 1):
                     lookup[i][j] = max(lookup[i][j],lookup[i][j-1] + 1)
                     if (length_max < lookup[i][j]):
                        length_max = lookup[i][j]
                        max_row = i
                        max_col = j
   print("Maximum length:", length_max)
   path = get_path(lookup, grid, max_row, max_col)
   print("Sequence is:")
   for ele in reversed(path):
   print(grid[ele[0]][ele[1]], " [", ele[0], ", ", ele[1], "]", sep = "")
grid = [
   [10, 7, 6, 3],
   [9, 8, 7, 6],
   [8, 4, 2, 7],
   [2, 2, 2, 8]]
get_sequence(grid)

Input

[[10, 7, 6, 3],
[9, 8, 7, 6],
[8, 4, 2, 7],
[2, 2, 2, 8]]

Output

Maximum length: 6
Sequence is:
10 [0, 0]
9 [1, 0]
8 [1, 1]
7 [1, 2]
6 [1, 3]
7 [2, 3]
8 [3, 3]