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Minimum Groups to Cover Intervals Solution (Multiple Languages)

This README provides step-by-step explanations of the minGroups solution in five different programming languages: C++, Java, JavaScript, Python, and Go. The solution aims to determine the minimum number of groups required to cover all intervals without overlap, utilizing heaps and sorting.

C++ Code Explanation

  1. Sort Intervals:

    • The intervals are sorted by their starting time to ensure they are processed in chronological order.

  2. Min-Heap Setup:

    • A priority queue (min-heap) is used to store the end times of intervals, allowing efficient tracking of the earliest ending interval.

  3. Processing Intervals:

    • Each interval is checked to see if the earliest ending group (smallest element in the heap) can be reused. This is possible if the start time of the current interval is later than the earliest ending interval.
    • If a group can be reused, the smallest element is removed from the heap (pop operation).
    • Regardless, the current interval's end time is added to the heap (push operation).

  4. Return Group Count:

    • The size of the heap at the end represents the number of groups needed, as each group corresponds to one active interval.

Java Code Explanation

  1. Sort Intervals:

    • The intervals are sorted based on their start times using Arrays.sort().

  2. Min-Heap Setup:

    • A PriorityQueue is used to maintain the end times of the intervals that are currently grouped.

  3. Processing Intervals:

    • Each interval is processed in order. If the earliest ending group (smallest element in the heap) finishes before the current interval starts, the group is reused by removing the top element from the heap.
    • The end time of the current interval is added to the heap to reflect its presence in a group.

  4. Return Group Count:

    • The final size of the heap is returned as it represents the number of groups required.

JavaScript Code Explanation

  1. Generate Events:

    • Each interval is transformed into two events: one for the start (+1) and one for the end (-1). The end event is shifted to the next time unit by adding 1 to ensure proper overlap handling.

  2. Sort Events:

    • The events are sorted first by time and then by type (end events come before start events if they occur at the same time) to process them correctly.

  3. Process Events:

    • The events are processed one by one, adjusting the count of active groups accordingly (+1 for a start and -1 for an end). The maximum number of active groups at any time is tracked.

  4. Return Max Groups:

    • The result is the maximum number of active groups encountered during event processing.

Python Code Explanation

  1. Sort Intervals:

    • Intervals are sorted by their start time using the built-in sort() function to ensure they are processed in chronological order.

  2. Min-Heap Setup:

    • A min-heap is initialized using heapq to store the end times of intervals, enabling efficient tracking of the earliest ending group.

  3. Processing Intervals:

    • For each interval, the heap is checked to see if the earliest ending group (smallest element) can be reused. If the group can be reused (i.e., the end time is earlier than the start of the current interval), the smallest element is removed from the heap.
    • The current interval's end time is added to the heap.

  4. Return Group Count:

    • The size of the heap at the end represents the total number of groups needed.

Go Code Explanation

  1. Sort Intervals:

    • Intervals are sorted based on their start time using sort.Slice(), ensuring they are processed in chronological order.

  2. Min-Heap Setup:

    • A custom MinHeap is implemented using Go's container/heap package to store the end times of active intervals.

  3. Processing Intervals:

    • Each interval is processed, and the earliest ending group is checked for possible reuse. If a group can be reused, the heap's top element is removed.
    • The end time of the current interval is added to the heap.

  4. Return Group Count:

    • The size of the heap at the end of the process is returned as the number of groups required.

Each solution uses the same general approach of sorting intervals by their start times and leveraging a min-heap to track and reuse groups based on their end times. The key idea is to reuse groups whenever possible by checking if the current interval can fit into a previously used group based on its start and end times.