Asked in: IDFC
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Solution
def getMinCores(start, end):
arr = []
n = len(start)
for i in range(n):
// ... rest of solution available after purchaseExplanation
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To solve the problem of determining the minimum number of CPU cores needed to handle all given processes, start by carefully understanding the core concept: each CPU core can only run one process at a time, and processes have defined start and end times. Your goal is to find the smallest number of cores required so that all processes can run without overlapping on the same core.
The main challenge lies in managing overlapping intervals. If two or more processes overlap in time, they must be assigned to different cores. Therefore, the minimum number of cores needed corresponds to the maximum number of processes running simultaneously at any point in time.
To approach this problem, think about the processes as intervals on a timeline, where each interval is defined by a start and an end time. The problem then reduces to finding the maximum number of intervals overlapping at any given moment.
One natural way to tackle this is by considering the start and end times of the processes separately and then analyzing how these intervals overlap. Consider the following steps:
1. Extract and sort the start times of all processes in ascending order.
2. Similarly, extract and sort the end times of all processes in ascending order.
These sorted lists help simulate the timeline of process activity. Now, imagine traversing this timeline from the earliest start time to the latest end time, and keeping track of how many processes are active at each moment.
Use two pointers or indices: one for the start times and one for the end times. Both pointers start at the beginning of their respective arrays. Then:
- If the current start time is less than or equal to the current end time, it means a new process has started before or exactly when another process ended. So, increment the count of active processes and move the start pointer forward.
- Otherwise, if the current start time is greater than the current end time, it means a process has finished before the next process starts, so you can reduce the count of active processes by moving the end pointer forward.
During this traversal, maintain a variable to track the maximum number of active processes seen so far. This maximum represents the peak concurrency — the highest number of overlapping processes at any time, and thus, the minimum number of cores needed.
To summarize the logic:
- When a process starts, increase the count of cores in use.
- When a process ends, decrease the count of cores in use.
- The maximum count observed during this simulation is the minimal number of cores required.
This approach is efficient because sorting the start and end times takes O(n log n) time, where n is the number of processes. The two-pointer traversal through the sorted arrays takes O(n) time, resulting in an overall O(n log n) time complexity, which is optimal for this problem.
Key details to consider:
- Processes are inclusive of their start and end times. Decide whether overlapping at the end and start times of different processes counts as simultaneous or not. For example, if one process ends at time t and another starts at time t, do they overlap? Clarify this detail as it affects the comparison logic. Typically, if intervals are inclusive, processes that start exactly when another ends are considered overlapping and thus need separate cores.
- Handle edge cases such as processes with the same start and end time, which represent instantaneous tasks but still require a core.
- This problem is similar to classic interval scheduling and resource allocation problems, often solved using sweep line or interval tree approaches, but the two-pointer technique on sorted start and end arrays is simpler and efficient.
In conclusion, by thinking of the problem as finding the maximum overlap of intervals, using sorted start and end times to simulate the timeline of process execution, and tracking concurrent processes, you can determine the minimal number of CPU cores needed. This method balances clarity, efficiency, and correctness, making it a solid approach to the problem.
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