Problem to Find Out the Maximum Number of Coins that Can be Collected in Python

Suppose, we have a 2D matrix in which the cells represent the number of coins in it. There are our two friends to collect coins, and they are placed at the top left corner and at the top right corner at the start. They follow these rules:

• From cell (i, j), a coin-collector can move to cell (i + 1, j - 1), (i + 1, j), or (i + 1, j + 1).

• Upon reaching a cell they collect all the coins available making the cell empty.

• The collectors may choose to stay at one cell, but the coins in any cell can be collected only once.

We have to find the maximum number of coins that can be collected.

So, if the input is like

then the output will be 17.

To solve this, we will follow these steps −

• A := the input matrix

• R := row count of A

• C := column count of A

• Define a function dp() . This will take r, c1, c2

  • if r is same as R, then

    • return 0

  • ans := A[r, c1] +(if c1 is not equal to c2, then 1 else 0) * A[r, c2]

  • base := ans

  • for each nc1 in [c1 − 1, c1, c1 + 1], do

    • for each nc2 in [c2 − 1, c2, c2 + 1], do

      • if 0 <= nc1 < C and 0 <= nc2 < C, then

        • ans := maximum of ans and (base + dp(r + 1, nc1, nc2))

  • return ans

• return dp(0, 0, C − 1)

Let us see the following implementation to get better understanding −

Example

 Live Demo

class Solution:
   def solve(self, A):
      R, C = len(A), len(A[0])
      def dp(r, c1, c2):
         if r == R:
            return 0
         ans = base = A[r][c1] + (c1 != c2) * A[r][c2]
         for nc1 in [c1 − 1, c1, c1 + 1]:
            for nc2 in [c2 − 1, c2, c2 + 1]:
               if 0 <= nc1 < C and 0 <= nc2 < C:
                  ans = max(ans, base + dp(r + 1, nc1, nc2))
         return ans
      return dp(0, 0, C − 1)
ob = Solution()
print(ob.solve([
   [0, 4, 1, 0],
   [3, 1, 4, 0],
   [2, 5, 1, 1],
   [3, 0, 0, 0]
]))

Input

[
   [0, 4, 1, 0],
   [3, 1, 4, 0],
   [2, 5, 1, 1],
   [3, 0, 0, 0]
]

Output

17

Arnab Chakraborty

Published on 26-Dec-2020 11:17:07

• Related Questions & Answers
• Program to find maximum number of coins we can collect in Python
• Program to find maximum number of coins we can get using Python
• Maximum Number of Events That Can Be Attended in C++
• Maximum number of candies that can be bought in C
• Find maximum number that can be formed using digits of a given number in C++
• Find out the minimum number of coins required to pay total amount in C++
• Python Program to find out the number of rooms in which a prize can be hidden
• Program to find maximum number of package that can be bought by buyers in C++
• Program to find number of coins needed to make the changes with given set of coins in Python
• Program to find maximum units that can be put on a truck in Python
• Maximum given sized rectangles that can be cut out of a sheet of paper in C
• Program to find number of coins needed to make the changes in Python
• Program to find out the number of boxes to be put into the godown in Python
• Maximum number of partitions that can be sorted individually to make sorted in C++
• Maximum number of people that can be killed with strength P in C++