Asked in: Amazon
Image of the Question
All Testcases Passed ✔
Solution
def minOperations(locations):
h = {}
for i in locations:
h[i] = 1+h.get(i,0)
// ... rest of solution available after purchaseExplanation
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To solve this problem, start by carefully analyzing the rules of the operations allowed and the structure of the input. You are given a list of products, each associated with a location identifier. The goal is to ship all products using the minimum number of operations. There are two types of operations: shipping one product, or shipping two products at once, but only if those two products come from different locations.
At first glance, it might seem intuitive to always try and use the operation that ships two products, as that removes more items per operation and could reduce the total number of operations. However, this is only possible when you have two products from different locations available to pair up. Therefore, the key challenge here is to group and pair products in a way that maximizes the use of the "two-product" shipping operation, while minimizing the need to fall back on the "single-product" operation.
Begin your thought process by examining the frequency of each location in the array. This is important because if most products come from a single location, you will be forced to ship many of them one by one due to the restriction that two products can only be shipped together if they come from different locations.
For example, consider a scenario where all products are from the same location. In this case, no two-product operation is possible, and each product will have to be shipped individually, resulting in n operations. On the other hand, if all products are from unique locations, you can pair them up almost entirely, performing roughly n/2 operations (plus one more if n is odd).
This observation suggests that the distribution of products across locations plays a crucial role in determining the minimum number of operations. The imbalance caused by any location that appears too frequently can limit your pairing options and force you to use more single-product operations.
So the natural strategy is to count how many products come from each unique location. Once you have these counts, identify the location with the highest frequency—let’s call it the dominant location. If the number of products from this location exceeds the total number of products from all other locations combined, then the excess products must be shipped one at a time, since there won’t be enough products from different locations to pair with them.
With that in mind, you can formulate a conceptual approach:
1. Count the frequency of each location to know how many products come from each.
2. Find the location with the maximum count, as this will dictate how many unmatched products might remain.
3. Compare the maximum frequency to the sum of the rest. If the rest can balance out the dominant location through pairing, then you can form enough two-product shipments to cover most of the inventory, and you'll need at most (n + 1) // 2 operations.
4. If the dominant location is too frequent, you will be forced to ship the extra products from it one by one. In that case, the minimum number of operations equals the number of products from the dominant location, as you can only pair as many times as you have products from other locations.
This leads to the insight that the worst case is governed by the maximum between the dominant frequency and (n + 1) // 2. This is because the dominant frequency sets a lower bound on operations when there are not enough different-location products to pair with, and (n + 1) // 2 represents the ideal number of operations if pairing is maximized (i.e., two products per operation, rounding up if n is odd).
Another aspect to think about is how pairing affects the inventory size. Each two-product operation reduces the inventory by 2, while each one-product operation reduces it by 1. Since the goal is to minimize the number of operations, pairing is always preferred when possible.
In essence, the central idea is to maximize pairing across different locations while accounting for any imbalance caused by overrepresented locations. By identifying how many products from the dominant location can be paired with others, and how many must be shipped individually, you can compute the minimum number of operations needed.
In conclusion, approach this problem by:
- Grouping products by location
- Determining the maximum number of pairings possible
- Recognizing when pairing is limited due to frequency imbalance
- Using these insights to calculate the fewest operations required to ship everything
This structured, frequency-driven approach will lead you to the correct and efficient solution.
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