Explain how you would modify the coin change problem to find the total number of possible combinations instead of the minimum number of coins.
- Adjust the objective to maximize the number of coins used.
- Change the coin denominations to larger values.
- Modify the base case to return the total number of combinations.
- No modification is needed; the original problem already provides this information.
To find the total number of possible combinations, modify the base case of the dynamic programming solution for the coin change problem. Instead of returning the minimum number of coins, adjust it to return the total number of combinations that make up the target amount.
Consider a scenario where you have to sort a large dataset of positive integers ranging from 1 to 1000. Which sorting algorithm would be most efficient in terms of time complexity, radix sort, or merge sort? Justify your answer.
- Insertion Sort
- Merge Sort
- Quick Sort
- Radix Sort
Radix sort would be more efficient for sorting positive integers within a limited range like 1 to 1000. Its time complexity is O(nk), where 'n' is the number of elements, and 'k' is the number of digits in the largest number. In this scenario, the range is small, leading to a more favorable time complexity than merge sort.
Recursive implementation of binary search involves breaking the problem into _______ subproblems until a solution is found.
- Five
- Four
- Three
- Two
Recursive implementation of binary search involves breaking the problem into two subproblems at each step, making it a logarithmic algorithm with a time complexity of O(log n), where 'n' is the number of elements.