Brute Force approach

Time complexity: O(n²). Space complexity: O(1).

The brute-force approach compares each day's temperature with the previous day's temperature. This is straightforward but inefficient, as it checks every record against every other record.

This complexity arises because for each record, we might need to check all previous records, leading to a quadratic number of comparisons.

1. Step 1: Iterate through each record in the Weather table.
2. Step 2: For each record, check if there is a previous day's record.
3. Step 3: If the current day's temperature is higher than the previous day's temperature, store the current record's id.

1. Record: (1, 2015-01-01, 10) - No previous day. 2. Record: (2, 2015-01-02, 25) - Compare with (1, 2015-01-01, 10) -> 25 > 10, store id 2. 3. Record: (3, 2015-01-03, 20) - Compare with (2, 2015-01-02, 25) -> 20 < 25, do not store. 4. Record: (4, 2015-01-04, 30) - Compare with (3, 2015-01-03, 20) -> 30 > 20, store id 4. 5. Result: ids 2 and 4.

Optimal Solution approach

Time complexity: O(n). Space complexity: O(n).

The optimal solution uses a self-join to efficiently compare each day's temperature with the previous day's temperature, reducing the number of comparisons needed.

This complexity is linear because each record is processed a constant number of times, and we only store results for qualifying records.

1. Step 1: Use a self-join on the Weather table to connect each record with its previous day's record.
2. Step 2: Filter the results where the current day's temperature is greater than the previous day's temperature.
3. Step 3: Select the id of the records that meet the criteria.

1. Join (1, 2015-01-01, 10) with (2, 2015-01-02, 25) -> 25 > 10, store id 2. 2. Join (2, 2015-01-02, 25) with (3, 2015-01-03, 20) -> 20 < 25, do not store. 3. Join (3, 2015-01-03, 20) with (4, 2015-01-04, 30) -> 30 > 20, store id 4. 4. Result: ids 2 and 4.

Key Insights

• Understanding how to use self-joins can significantly optimize queries involving comparisons.
• Recognizing patterns in data (like daily temperatures) can help in structuring queries effectively.

Common Mistakes

• Not considering edge cases, such as the first record which has no previous day to compare.
• Overcomplicating the query structure when a simple join suffices.

Interview Tips

• Always clarify the requirements and constraints of the problem before jumping into coding.
• Think about the time and space complexity of your solution and be prepared to explain it.
• Practice writing SQL queries on paper or in a simple editor to get comfortable with syntax and logic.