Solution Explanation for Faulty Sensor

This problem involves comparing two sensor readings to identify which sensor, if any, has a faulty reading. A faulty sensor drops exactly one data point, shifting subsequent points to the left and replacing the last point with a random value.

The core idea is to find the first discrepancy between the two sensor readings. Once a discrepancy is found, we can determine if the discrepancy is due to a missing data point in sensor1 or sensor2.

Approach: Two-Pointer Comparison

We iterate through both arrays simultaneously using a single pointer i.

1. Find First Discrepancy: The loop continues as long as the elements at index i in both arrays are equal. As soon as a difference is encountered, the loop breaks.

2. Check for Faulty Sensor: After finding the first discrepancy, we check if we are not at the second to last element (i < n-1). If we are not, it means that there's no way to determine the faulty sensor. This is because the last element could be the dropped element or a random replacement.

3. Determine Faulty Sensor: If we are not at the end, we have two possibilities to investigate:

   • Sensor 1 is faulty: If sensor1[i+1] != sensor2[i], this means that sensor2[i] is a valid data point, while sensor1[i+1] is the data point shifted from sensor2[i+1].
   • Sensor 2 is faulty: If sensor1[i] != sensor2[i+1], this means that sensor1[i] is a valid data point, while sensor2[i+1] is the data point shifted from sensor1[i+1]. If neither condition is met, it means there's no unique way to identify the faulty sensor.

4. No Faulty Sensor: If the loop completes without finding any discrepancies, it indicates that both sensors are likely not faulty.

5. Return Result: Based on the above checks, the function returns:

   • 1 if sensor 1 is faulty
   • 2 if sensor 2 is faulty
   • -1 if no faulty sensor is determined

Time and Space Complexity

• Time Complexity: O(n), where n is the length of the sensor arrays. We iterate through the arrays at most once.
• Space Complexity: O(1). We use a constant amount of extra space.

Code Implementations

The code implementations provided in the original response accurately reflect this approach in multiple programming languages (Python, Java, C++, Go, and TypeScript). Each implementation follows the same logic described above. The only variations are syntactic differences inherent to the programming languages.