Dynamic Programming Questions
The Coin Change problem is a classic algorithmic problem that involves finding the minimum number of coins needed to make a certain amount of change. Given a set of coin denominations and a target amount, the goal is to determine the minimum number of coins required to make the target amount.
Dynamic Programming can be used to solve the Coin Change problem efficiently. The approach involves breaking down the problem into smaller subproblems and solving them iteratively.
The steps to solve the Coin Change problem using Dynamic Programming are as follows:
1. Create a table or an array to store the minimum number of coins required for each target amount from 0 to the given target amount.
2. Initialize the table with a maximum value for all target amounts except for 0, which is initialized as 0.
3. Iterate through each coin denomination and for each target amount, calculate the minimum number of coins required by considering two possibilities:
a. If the current coin denomination is greater than the target amount, skip it.
b. Otherwise, calculate the minimum between the current minimum number of coins required for the target amount and the minimum number of coins required for the remaining amount (target amount - current coin denomination) plus one.
4. Repeat step 3 for all coin denominations and target amounts.
5. Finally, the value in the table for the given target amount will represent the minimum number of coins required to make that amount of change.
By using Dynamic Programming, we avoid redundant calculations and solve the problem efficiently in a bottom-up manner. The time complexity of this approach is O(coins * target), where coins is the number of coin denominations and target is the given target amount.