coin row problem calculator

Coin Row Problem Calculator

The coin row problem is a classic dynamic programming problem. The goal is to find the maximum amount of money that can be obtained by selecting a subset of coins from a row of coins, where no two adjacent coins can be selected. Here are the steps to solve the coin row problem:

  1. Understand the Problem:

  2. The first step is to understand the problem statement and the constraints. In the coin row problem, we are given a row of coins, and we need to find the maximum amount of money that can be obtained by selecting a subset of coins, ensuring that no two adjacent coins are selected.

  3. Identify the Recursive Structure:

  4. The next step is to identify the recursive structure of the problem. This involves understanding how the problem can be broken down into smaller subproblems. In the coin row problem, the maximum amount of money that can be obtained from the first i coins can be expressed in terms of the maximum amount of money that can be obtained from the first i-1 and i-2 coins.

  5. Define the Base Cases:

  6. After identifying the recursive structure, it's important to define the base cases. These are the simplest, most basic subproblems that can be solved directly. In the coin row problem, the base cases involve the first few coins where no further breakdown is possible.

  7. Implement the Dynamic Programming Algorithm:

  8. Once the recursive structure and base cases are defined, the dynamic programming algorithm can be implemented. This involves using an array or table to store the solutions to subproblems, which can then be used to solve larger subproblems until the final solution is obtained.

  9. Trace Back to Find the Solution:

  10. Finally, the solution to the original problem can be obtained by tracing back through the table or array of solutions to find the subset of coins that yield the maximum amount of money.

By following these steps, the coin row problem can be effectively solved using dynamic programming to find the maximum amount of money that can be obtained by selecting a subset of non-adjacent coins from a given row.

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