Algorithm Practice: Understand

Summary

Here are three steps to use AI Coach to practice algorithm problem understanding:

1. Write down key points
   • Make sure you understand the problem
   • Focus on the key points
2. Identifying Constraints
   • Understanding constraints helps to classify the problem
   • Use constraints to find out test cases, particularly for handling edge cases.
3. Write down testcases
   • Validate the correctness of your solution
   • Ensure coverage of both general case and edge cases

When practicing algorithms, you can first practice understanding the problem

1. Write down key points

You can write down the key points of the problem when you are reading the problem. With this prompt, You can compare your key points with those recorded by the AI Coach to see if you have missed any important aspects.

Prompt

info

You only need to change the text inside Context

Context:
"""
Question Description:
During a city-wide festival, a ride-sharing app like Uber needs to adapt fares dynamically based on demand. The company employs an algorithm that searches for pairs of fare adjustments from different zones that sum up to a target value. This ensures the fares are attractive to riders while providing fair compensation to drivers. The input consists of an array of integers, each representing a potential fare adjustment for a specific zone, and a target integer that represents the desired total fare adjustment. Importantly, the algorithm stipulates that each adjustment can only be used once, and there is only one valid pair of indices in the array that sums to the target, guaranteeing a unique solution for each scenario. The output is the indices of the two zones whose adjustments meet the target, enabling real-time pricing adjustments in response to fluctuating demand during the event. This setup highlights the critical role of efficient algorithms in implementing effective dynamic pricing strategies in response to market conditions.
Here are the keypoints I found:

Find the index of two numbers that add up to the target.
Can't use the same element twice.
"""
Requirements:
"""

The key points you provide should not more than five, and each should not be more than 10 words long.
The key points you provide should be based solely on the textual description of the problem, without excessive speculation.
"""
Action:
"""

Ignore the key points I've provided. Instead, through reading the problem, try to list its key points, which can help you understand the problem and identify potential test cases.
Compare the differences between your key points and mine. Point out my mistakes or the key points I'm missing.
"""

Response From AI Coach

Key Points from the Question Description:

Identify two indices that sum to a target.
Each index can only be used once.
Unique solution: exactly one valid pair exists.
Input: array of integers, one target integer.
Output: indices of the two elements.
Comparison with Your Key Points:

Find the index of two numbers that add up to the target. This aligns well with my first key point, capturing the core task of identifying two indices.
Can't use the same element twice. This is also captured in my second key point, emphasizing the restriction on index usage.
Analysis:
Your key points effectively summarize the main requirements of the problem: finding two indices whose values sum to a given target, and ensuring that each number is only used once. However, your summary could benefit from explicitly mentioning:

The guarantee of a unique solution, which is crucial for understanding that there will be no ambiguity in the output.
The context of the input and output format, which clarifies what the function will receive and return.
These additions would provide a more rounded understanding of the problem constraints and expected results.

2. Identifying constraints

Based on the problem and its input/output, write down the potential constraints. For example, if the input is an array of integers, you might want to know if there are any duplicate elements in the array and the range of the numbers."

Prompt

Context:
"""
For the above problem, Here are the constraints I found:

The input array may contain duplicate elements
The input array is not sorted
The range of elements in the array could be very large
"""
Requirements:
"""

The constraints you provide should not more than five, and each should not be more than 10 words long.
"""
Action:
"""

Ignore the constraints I've provided. Instead, through reading the problem, try to list potential constraints. For example, the input array may contain duplicate elements.
Compare the differences between your constraints and mine. Point out my mistakes or where I'm missing.
"""

Response From AI Coach

Potential Constraints Derived from the Question Description

Input array may contain duplicate elements.
Input array is not necessarily sorted.
Each element can be used only once.
Exact one solution pair exists.
Elements and target may have a large range.
Comparison with Your Constraints, your constraints:

The input array may contain duplicate elements.
The input array is not sorted.
The range of elements in the array could be very large.
These constraints align very well with the constraints I derived from the problem. Here’s a detailed comparison:

"Input array may contain duplicate elements": Both your constraints and mine acknowledge this, which is important because it affects how the solution handles potential repeats in the array when searching for the pair that sums to the target.
"Input array is not sorted": We both noted this constraint, which is crucial for determining the type of algorithm that might be most efficient, as sorting the array could be an option but is not a requirement.
"The range of elements in the array could be very large": This is an important consideration for understanding potential issues with integer overflow or performance impacts due to large numbers.
Additional points I included:

"Each element can be used only once": This reiterates a part of the problem statement about not using the same element twice, which is critical for ensuring the solution respects the uniqueness of the indices.
"Exact one solution pair exists": This simplifies the solution approach because it guarantees that once a pair that meets the condition is found, no further search is necessary.
Your constraints are well-identified and cover the main issues that would affect the implementation of a solution for the problem. My additional points emphasize some operational rules and guarantees provided by the problem description, which help in streamlining the solution approach.

3. Write down testcases

Writing test cases can help you understand/analyze the problem and later test the code.

Prompt

Context:
"""
From the above problem, Here are the testcases I found:

General testcase: nums = [3, 7, 10, 4, 5], target = 14, the result is [2, 3]
Edge testcase: No edge testcase for this problem since it has exactly one solution.
"""
Requirements:
"""

the testcases should contain input, output and the reason you choose this testcase.
"""
Action:
"""

Ignore the testcases I've provided. Instead, through reading the problem, try to list one gereral testcase and one edge case.
Compare the differences between your testcases and mine. Point out my mistakes or where I'm missing.
"""

Response From AI Coach

General Test Case

Input: nums = [1, 2, 3, 4, 5], target = 9
Output: [3, 4]
Reason: This test case checks the algorithm's ability to find a pair towards the end of the list, ensuring it correctly scans through earlier elements without prematurely concluding no pair exists.
Edge Test Case

Input: nums = [5, 5, 3], target = 10
Output: [0, 1]
Reason: This test case checks the algorithm's handling of duplicate elements that are the solution, ensuring it can differentiate between indices of identical values.
Comparison with Your Test Cases

General testcase: nums = [3, 7, 10, 4, 5], target = 14, result = [2, 3]
Edge testcase: No edge testcase provided due to the assumption of exactly one solution.
Analysis

General Test Case: Your general test case is valid and effectively tests the algorithm's ability to identify correct pairs from within a list. It's a good example of a typical scenario where the elements are not adjacent.
Edge Test Case: You mentioned there's no edge case due to the guaranteed single solution. However, considering edge cases in terms of input characteristics, such as duplicates or minimal array size, is still valuable. These scenarios test the robustness of the algorithm against special but valid configurations of input data. Your assumption missed the opportunity to test how the algorithm handles duplicates or very small arrays, which are practical edge cases even in a scenario with a guaranteed solution.
In summary, while your general test case is well-chosen, introducing an edge case that tests the algorithm's handling of duplicates or minimal input sizes would provide a more comprehensive validation of the solution's robustness and correctness.