Suppose the problem is changed so that some people can be assigned to either city multiple times (reusable assignments), or the number of people sent to each city is not fixed. Which approach correctly adapts the solution?
AUse a dynamic programming approach to handle variable counts and reuse assignments
BUse the same greedy sorting by cost difference and assign exactly n people to each city
CSort by absolute cost to city A and assign all to city A to minimize cost
DAssign people greedily without sorting, picking the cheaper city for each person
Step-by-Step Solution
Solution:
Step 1: Understand problem change
Allowing reuse or variable counts breaks the fixed half assignment constraint, invalidating the greedy approach.
Step 2: Why DP is needed
Dynamic programming can explore all valid assignments with reuse or variable counts, ensuring minimal total cost under new constraints.
Final Answer:
Option A -> Option A
Quick Check:
Greedy fails when constraints are relaxed; DP handles complex state space [OK]
Quick Trick:Relaxed constraints require DP, not greedy [OK]
