Dynamic Programming Questions Medium
The time complexity of the Dynamic Programming approach for solving the Maximum Subarray Sum Circular problem is O(n), where n is the size of the input array.
In this problem, we are given an array of integers and we need to find the maximum sum of a subarray, considering that the array is circular, meaning that the subarray can wrap around to the beginning of the array.
To solve this problem using Dynamic Programming, we can make use of the Kadane's algorithm, which is a well-known approach for finding the maximum subarray sum in a linear array.
The Kadane's algorithm works by iterating through the array and keeping track of the maximum subarray sum seen so far. At each iteration, we update the maximum sum by either extending the current subarray or starting a new subarray.
To handle the circular property of the array, we can consider two cases:
1. The maximum subarray sum is within the array: In this case, we can simply apply the Kadane's algorithm to find the maximum subarray sum.
2. The maximum subarray sum wraps around to the beginning and end of the array: In this case, we can invert the sign of all elements in the array and apply the Kadane's algorithm to find the minimum subarray sum. Then, we subtract this minimum sum from the total sum of the array to get the maximum subarray sum.
By considering these two cases, we can find the maximum subarray sum circularly using Dynamic Programming in O(n) time complexity, where n is the size of the input array.