Dynamic Programming Questions Medium
To solve the Maximum Subarray Sum Circular problem using Dynamic Programming, we can follow these steps:
1. First, we need to understand the problem. The Maximum Subarray Sum Circular problem asks us to find the maximum sum of a subarray within a circular array. In a circular array, the last element is connected to the first element.
2. We can start by solving the problem for a non-circular array. We can use Kadane's algorithm, which is a dynamic programming approach, to find the maximum sum of a subarray in a linear array. This algorithm keeps track of the maximum sum found so far and updates it whenever a new maximum sum is found.
3. Now, to handle the circular array, we need to consider two cases: one where the maximum subarray is entirely within the array, and another where it wraps around the circular array.
4. To handle the first case, we can use Kadane's algorithm to find the maximum subarray sum in the linear array.
5. To handle the second case, we can use the fact that the maximum subarray sum that wraps around the circular array is equal to the total sum of the array minus the minimum subarray sum within the array. We can find the minimum subarray sum using a modified version of Kadane's algorithm, where we keep track of the minimum sum found so far and update it whenever a new minimum sum is found.
6. Finally, we compare the maximum subarray sum from step 4 with the maximum subarray sum from step 5, and return the maximum of the two as the result.
By using this dynamic programming approach, we can efficiently solve the Maximum Subarray Sum Circular problem in linear time complexity, O(n), where n is the size of the circular array.