You are developing software for a logistics company that optimizes delivery routes for a fleet of vehicles. The company wants to employ a divide and conquer approach to efficiently compute the shortest route for each vehicle.

Algorithm A: This algorithm divides the map of delivery points into three regions, each roughly half the size of the original map. It then recursively finds the shortest route for each region and combines them in linear time.

Algorithm B: This algorithm divides the map into four quadrants, each approximately half the size of the original map. It recursively calculates the shortest route for each quadrant and combines them in constant time.

Algorithm C: This algorithm divides the map into twenty$-$seven sectors$,$ each approximately onethird the size of the original map. It recursively calculates the shortest route for each sector and combines them in $O(1)$ time.

Algorithm D: This algorithm divides the map into two sectors$,$ each approximately half the size of the original map. It recursively calculates the shortest route for each sector and combines them in $O(nlog(n))$ time.

Define the recurrence relation for each algorithm and then solve it by using iterative method, in the end select one with better time complexity.

Note: You are required to use iterative method to solve the above problems.