Assistant System Engineer

The problem is solved using a dynamic programming approach where:

DP Array Initialization:
Create an array dp of size amount + 1, where dp[i] represents the minimum number of coins needed to make the amount i. Initialize each element to amount + 1 (a value larger than any possible number of coins required) to signify that the amount isn't achievable initially, except for dp[0], which is 0 (zero coins are needed to make the amount 0).

Fill DP Array:
For each sub-amount i from 1 to amount, iterate through each coin:
If the coin value is less than or equal to i, update dp[i] to be the minimum of its current value or dp[i - coin] + 1.

Final Check:
After filling the dp array, dp[amount] gives the minimum number of coins needed for the amount. If dp[amount] is still greater than amount, it means the amount isn't achievable with the given coins, so return -1.

Tip 1: Answer all the questions positively.
Tip 2: Improve your English communication skills and avoid making mistakes while speaking.