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Leetcode 2960. Count Tested Devices After Test Operations

Problem Statement

You are given an integer n, which represents the number of devices in a lab from 1 to n. You are also given a 2D integer array operations where operations[i] = [left, right, testId] means that all devices in the inclusive range [left, right] are assigned to test with the test operation identifier testId.

Find out how many devices were assigned at least one test operation from the list of operations provided.

Example:

Input: n = 5, operations = [[1, 2, 1], [2, 4, 2], [3, 5, 3]]
Output: 5
Explanation: The devices and their test assignments are:
Device 1 -> Test 1,
Device 2 -> Test 1, Test 2,
Device 3 -> Test 2, Test 3,
Device 4 -> Test 2, Test 3,
Device 5 -> Test 3
Out of the 5 devices, all devices are assigned at least one test operation.

Clarifying Questions

1. Are the ranges in operations always valid and within the bounds of 1 to n?
   • Yes, the ranges are guaranteed to be valid within the given bounds.
2. Can there be overlapping ranges in the operations array?
   • Yes, there can be overlapping ranges.
3. Do we need to consider the unique test IDs for different devices, or is the number of devices assigned to any test sufficient?
   • We only need to consider whether a device is assigned at least one test, irrespective of the test ID.

Strategy

To solve this problem, we need to keep track of the devices assigned to any of the test operations. Here’s a potential plan:

1. Initialization:
   • Create a boolean array assigned of size n+1 (considering 1-based indexing) to track whether each device from 1 to n has been assigned any test. Initialize all values to false.
2. Process Operations:
   • Iterate over the operations array. For each operation [left, right, testId], mark all devices in the range [left, right] as true in the assigned array.
3. Count Assigned Devices:
   • Count the number of true values in the assigned array (ignoring the zeroth index).
4. Return the Count:
   • Return the count of devices that have been assigned at least one test.

Code

Here’s how you can implement this strategy in C++:

#include <vector>

int countTestedDevices(int n, std::vector<std::vector<int>>& operations) {
    // Step 1: Initialize the 'assigned' array to false for each device.
    std::vector<bool> assigned(n + 1, false);

    // Step 2: Process each operation
    for (const auto& op : operations) {
        int left = op[0];
        int right = op[1];
        for (int i = left; i <= right; ++i) {
            assigned[i] = true;
        }
    }

    // Step 3: Count the number of devices that have been assigned at least one test.
    int count = 0;
    for (int i = 1; i <= n; ++i) {
        if (assigned[i]) {
            ++count;
        }
    }

    return count;
}

Time Complexity

• Initialization: Initializing the assigned array takes O(n).
• Processing Operations: Each operation can potentially update up to n devices. In the worst case, this step takes O(m*n), where m is the number of operations.
• Counting Assigned Devices: This involves a simple loop over n elements, which is O(n).

Overall Time Complexity: O(m*n) in the worst case, because each operation might iterate through all n devices.

Optimization Consideration:

• If operations contain a large number of elements, we might consider using a more efficient data structure or algorithm (e.g., sweep line algorithm or segment tree) to handle overlapping ranges more effectively.

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