What is the result of applying dynamic programming to the Coin Change problem?

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Question: What is the result of applying dynamic programming to the Coin Change problem?

Options:

Correct Answer: Finding the minimum number of coins

Solution:

Dynamic programming can be used to find the minimum number of coins needed to make a certain amount in the Coin Change problem.

What is the result of applying dynamic programming to the Coin Change problem?

What is the result of applying dynamic programming to the Coin Change problem?

Step 1: Understand the Coin Change problem. You need to make a certain amount of money using the least number of coins from given denominations.
Step 2: Identify the denominations of coins you have. For example, you might have coins of 1 cent, 5 cents, and 10 cents.
Step 3: Define the target amount you want to make. For example, let's say you want to make 12 cents.
Step 4: Create an array (or list) to store the minimum number of coins needed for each amount from 0 to the target amount.
Step 5: Initialize the array. Set the value for 0 cents to 0 (because you need 0 coins to make 0 cents) and all other values to a large number (like infinity) to start.
Step 6: Loop through each coin denomination. For each coin, update the array for all amounts that can be made using that coin.
Step 7: For each amount, check if using the current coin reduces the number of coins needed. If it does, update the array with the new minimum.
Step 8: After processing all coins, the value in the array at the index of the target amount will give you the minimum number of coins needed.

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