Dynamic Programming Questions
The Maximum Subarray problem is a classic algorithmic problem that involves finding the contiguous subarray within a given array of numbers that has the largest sum.
Dynamic Programming can be used to solve the Maximum Subarray problem efficiently. The approach involves breaking down the problem into smaller subproblems and using the solutions of these subproblems to build the solution for the larger problem.
To solve the Maximum Subarray problem using Dynamic Programming, we can define an auxiliary array, often called the "memoization" array, to store the maximum sum of subarrays ending at each index of the original array.
We start by initializing the first element of the memoization array with the first element of the original array. Then, for each subsequent element, we compare the sum of the current element with the sum of the current element plus the maximum sum of the subarray ending at the previous index. We update the memoization array with the maximum of these two values.
Finally, we iterate through the memoization array to find the maximum sum, which represents the maximum sum of any subarray within the original array.
This approach has a time complexity of O(n), where n is the size of the input array, making it an efficient solution for the Maximum Subarray problem.