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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