Asked in: Flipkart
Image of the Question
All Testcases Passed ✔
Solution
from functools import lru_cache
from sys import setrecursionlimit
setrecursionlimit(10**6)
n = int(input())
// ... rest of solution available after purchaseExplanation
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To solve this problem, start by clearly understanding the scenario and what the problem is asking for. You have two lists: one representing sender antennas and the other representing receiver antennas. The goal is to pair these antennas in such a way that the number of noiseless networks is maximized. A noiseless network implies that the signal from a sender does not overlap or cross with the signal of another network operator, which leads to noise. Essentially, you want to avoid overlaps or conflicts in pairing sender and receiver antennas.
First, think about what "noise" and "noiseless" mean in this context. Noise arises when signals overlap or cross. Overlapping signals typically occur if one antenna's range interferes with another. The problem gives an example where you have to find a maximum matching of antennas that do not cause noise. Since the problem involves two lists, the sender antennas and receiver antennas, and a need to pair them without causing noise, this hints at a matching or pairing problem.
Start by examining the values in both lists. Each antenna has a value representing its position, frequency, or some parameter relevant to matching. To maximize noiseless networks, you want to pair senders and receivers such that the pairs have minimal or no conflict. The most straightforward way to interpret this is to look for pairs where the sender and receiver antennas are close in value or meet some condition that prevents noise.
A natural direction to think about is the idea of matching pairs where the difference between the sender and receiver antenna values is minimal or bounded. This is a common approach in pairing problems—trying to match elements from two sorted lists with minimal difference, often to maximize compatible pairs.
Start by sorting both the sender antennas and receiver antennas. Sorting helps because it arranges antennas in an ordered fashion, making it easier to compare and match pairs efficiently without checking every combination, which would be computationally expensive.
Once sorted, use a two-pointer technique:
- Initialize two pointers, one for the sender list and one for the receiver list.
- Compare the antennas pointed by these two pointers.
- If the values are compatible according to a defined condition (e.g., their difference is within an acceptable range, such as zero or one), then you can consider these two antennas as a noiseless network pair. Move both pointers forward to check for the next possible pair.
- If the sender antenna value is smaller than the receiver antenna value and they cannot be paired, move the sender pointer forward to find a better match.
- If the receiver antenna value is smaller, move the receiver pointer forward instead.
This approach ensures you find the maximum number of pairs that satisfy the noiseless condition without overlaps or conflicts, as the pointers move forward only when a pair is formed or the current pair is incompatible.
Think carefully about what "compatible" means here. The problem example hints at exact or close matching between sender and receiver values. So, the condition might be that the difference between the sender antenna value and receiver antenna value is small enough to be considered noiseless—likely either zero or within a small threshold.
Continue this process until you reach the end of one of the lists. The number of successful pairs formed during this traversal represents the maximum number of noiseless networks you can establish.
Another important point is that each antenna can only be used once in the pairing, so once you use an antenna for a noiseless network, you cannot reuse it. The two-pointer method naturally enforces this because pointers move forward and never go back.
To summarize your approach:
1. Sort both lists of sender and receiver antennas to organize them.
2. Use a two-pointer approach to traverse both lists simultaneously.
3. For each pair of antennas, check if they satisfy the noiseless pairing condition (likely difference within zero or one).
4. If they match, increment the count of noiseless networks and move both pointers forward.
5. If they don't match, move the pointer of the smaller antenna value to find a better match.
6. Continue until one of the pointers reaches the end of its list.
7. The total matched pairs represent the maximum noiseless networks.
This solution works efficiently because sorting is O(N log N) or O(M log M), and the two-pointer traversal is linear O(N+M). It leverages the order of antennas to find the best pairing without overlapping signals, hence minimizing noise and maximizing noiseless networks.
By thinking in terms of sorting, pairwise comparison, and greedy pairing with two pointers, you can develop an effective algorithm to solve the problem as described.
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