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

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

Options:

  1. Top-down
  2. Bottom-up
  3. Greedy
  4. Brute force

Correct Answer: Bottom-up

Solution: 

The Coin Change problem can be solved using a bottom-up dynamic programming approach, where solutions to smaller subproblems are built up to solve larger problems.

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

Practice Questions

Q1
Which dynamic programming approach is used to solve the Coin Change problem?
  1. Top-down
  2. Bottom-up
  3. Greedy
  4. Brute force

Questions & Step-by-Step Solutions

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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