Imagine you're a farmer named Sam who grows different types of vegetables in several continuous fields. Each field can grow a specific type of vegetable, and based on the market value of that vegetable, each field will bring a certain profit (positive integer) or loss (negative integer). The profit or loss is estimated and noted for each field. Sam can start farming from any field. but once he starts. he must continue farming the next fields in sequence without skipping any, until he decides to stop, because his tractor can only move to the next adjacent field and cannot skip fields.

Sam needs to choose which sequence of fields to farm to maximize his profits. The following array represents the estimated profits or losses for ten consecutive fields on Sam's farm, based on the types of vegetables that can be grown in each field and their respective market values.

[4, -18. 16, -14, 12, -1, 3, 1, -20, 15]

• Can you help Sam decide which sequence of fields to farm for maximum profit using an efficient algorithm? What would the profit amount be? Show a simulation of your proposed algorithm. You must show which sequence of fields he needs to select in order to achieve this maximum profit.
• Calculate the time complexity of your algorithm using proper mathematical logic. An efficient algorithm should have time complexity less than or equal to O(N * log (N)) where N is the number of fields.