Which dynamic programming approach is used to solve the Coin Change problem?

Which dynamic programming approach is used to solve the Coin Change problem?

Step 1: Understand the Coin Change problem. It involves finding the number of ways to make a certain amount of money using different denominations of coins.
Step 2: Identify the smaller subproblems. For example, how many ways can you make change for smaller amounts using the available coins.
Step 3: Create a table (array) to store the number of ways to make change for each amount from 0 up to the target amount.
Step 4: Initialize the table. Set the number of ways to make change for 0 amount to 1 (there's one way to make 0 amount: use no coins).
Step 5: Loop through each coin denomination. For each coin, update the table for all amounts that can be formed using that coin.
Step 6: For each amount, add the number of ways to make change without the current coin to the number of ways to make change with the current coin.
Step 7: Continue this process until you fill the table for all amounts up to the target amount.
Step 8: The final value in the table for the target amount will give you the total number of ways to make change.

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