Find Maximum Coins from Disappearing Coins Matrix in Python

Suppose we have a 2D matrix where each cell matrix[r, c] represents the number of coins present in that cell. When we pick up coins from matrix[r, c], all the coins on row (r - 1) and (r + 1) will disappear, as well as the coins at the two cells matrix[r, c + 1] and matrix[r, c - 1]. We have to find the maximum number of coins we can collect.

So, if the input is like

then the output will be 26 because we can pick cells with the coins 8, 6, and 9 and 3, so total is 26.

To solve this, we will follow these steps −

• Define a function getmax() . This will take arr
• prev_max := 0
• curr_max := 0
• res := 0
• for each num in arr, do
  • temp := curr_max
  • curr_max := num + prev_max
  • prev_max := maximum of temp and prev_max
  • res := maximum of res and curr_max
• return res
• From the main method do the following −
• if matrix is empty, then
  • return 0
• m := row count of matrix
• n := column count of matrix
• row_sum := an array of size m and fill with 0
• for i in range 0 to m - 1, do
  • row_sum[i] := getmax(matrix[i])
• return getmax(row_sum)

Example

Let us see the following implementation to get better understanding −

def getmax(arr):
   prev_max, curr_max = 0, 0
   res = 0
   for num in arr:
      temp = curr_max
      curr_max = num + prev_max
      prev_max = max(temp, prev_max)
      res = max(res, curr_max)
   return res

def solve(matrix):
   if not matrix:
      return 0
   m, n = len(matrix), len(matrix[0])
   row_sum = [0 for _ in range(m)]
   for i in range(m):
      row_sum[i] = getmax(matrix[i])
   return getmax(row_sum)

matrix = [
   [2, 8, 7, 6],
   [10, 10, 4, 2],
   [5, 9, 2, 3]
]
print(solve(matrix))

Input

[
[2, 8, 7, 6],
[10, 10, 4, 2],
[5, 9, 2, 3]
]

Output

26