Find minimum days to deliver all orders

Q: Find minimum days to deliver all orders

This question evaluates algorithm design and combinatorial optimization skills, focusing on scheduling and load-balancing under per-center capacity constraints and frequency-based counting.

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Question

You manage N delivery centers labeled 1..N and an array orderCityList where each element is the destination city of one order (city IDs are in 1..N). Each calendar day, every center can work on at most one order. If a center’s ID equals the order’s city, that order takes 1 day of that center’s capacity; otherwise it takes 2 days of that center’s capacity (treat it as occupying two days on the assigned center). Orders cannot be split across centers. Compute the minimum number of days required to finish all orders. Example: N=3, orderCityList=[1,1,3,1,1] → 3 days, one optimal assignment by indices is Center1: {1,2,4}, Center2: {5}, Center3: {3}. Design an efficient algorithm (avoid brute force) and analyze its time and space complexity. Implement a function minDays(N, orderCityList) that returns the minimal days.

Find minimum days to deliver all orders

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