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In this article, we will explain in detail the 228th question of Likou, "Summarizing Intervals". By studying this article, readers will learn how to traverse and summarize intervals, and understand the related complexity analysis and simulated interview questions and answers. Each method will be accompanied by a detailed explanation for easy understanding.

Problem Description

The description of the “Summary interval” in question 228 is as follows:

Given a sorted integer array nums with no repeated elements, return a list of the smallest sorted interval ranges that exactly covers all the numbers in the array. That is, every element of nums is exactly covered by a certain interval range, and there are no two adjacent interval ranges.

Example:

输入: nums = [0,1,2,4,5,7]
输出: ["0->2","4->5","7"]
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Example:

输入: nums = [0,2,3,4,6,8,9]
输出: ["0","2->4","6","8->9"]
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Problem Solving

Method: Traverse an array

1. initial analysis：

   • Summarize the intervals by iterating over the array.
   • Maintain two variables, one to record the starting point of the interval and the other to record the current number.

2. step：

   • Traverse the array and determine whether the current number is continuous with the previous number.
   • If it is not continuous, or when traversing to the last element of the array, add the current interval to the result list and update the starting point of the interval.
   • Returns a list of results.

Code

def summaryRanges(nums):
    if not nums:
        return []
    
    ranges = []
    start = nums[0]
    
    for i in range(1, len(nums)):
        if nums[i] != nums[i - 1] + 1:
            if start == nums[i - 1]:
                ranges.append(f"{start}")
            else:
                ranges.append(f"{start}->{nums[i - 1]}")
            start = nums[i]
    
    if start == nums[-1]:
        ranges.append(f"{start}")
    else:
        ranges.append(f"{start}->{nums[-1]}")
    
    return ranges

# 测试案例
print(summaryRanges([0,1,2,4,5,7]))  # 输出: ["0->2","4->5","7"]
print(summaryRanges([0,2,3,4,6,8,9]))  # 输出: ["0","2->4","6","8->9"]
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Complexity Analysis

• time complexity: O(n), where n is the length of the array. Requires one pass through the array.
• Space complexity: O(1), no additional space is required except for returning the result.

Mock Interview Questions and Answers

Question 1: Can you describe your thinking on how to solve this problem?

answer：We can summarize the intervals by traversing the array. Maintain two variables, one to record the starting point of the interval and the other to record the current number. When traversing the array, determine whether the current number is continuous with the previous number. If not continuous or when traversing to the last element of the array, add the current interval to the result list and update the starting point of the interval.

Issue 2: Why did you choose to use array traversal to solve this problem?

answer: Traversing an array is a simple and intuitive method that can efficiently summarize continuous intervals in an array by maintaining the starting point and current number of the interval. The time complexity of this method is O(n), which is suitable for processing ordered integer arrays without repeated elements.

Issue 3: What are the time and space complexities of your algorithm?

answer: The time complexity of the algorithm is O(n), where n is the length of the array. The space complexity is O(1), and no additional space is required except for returning the result.

Question 4: How do you handle edge cases in your code?

answer: For an empty array, you can directly return an empty list. For other cases, when traversing the array, determine whether the current number is continuous with the previous number to ensure that all intervals are correctly summarized.

Question 5Q: Can you explain how iterating over an array works?

answer: Traverse the array by maintaining the starting point of the interval and the current number. When traversing the array, determine whether the current number is continuous with the previous number. If not continuous or when traversing to the last element of the array, add the current interval to the result list and update the starting point of the interval, thereby summarizing all intervals.

Question 6: How to ensure that the returned results are correct in the code?

answer：By traversing the array, gradually parsing each number, maintaining the starting point and current number of the interval, ensure that each interval is correctly summarized. The results can be verified through test cases to ensure that all intervals are correctly summarized.

Question 7Q: Can you give an example of how to answer optimization questions in an interview?

answer: In an interview, if the interviewer asks how to optimize an algorithm, I will first analyze the bottlenecks of the current algorithm, such as time complexity and space complexity, and then propose an optimization plan. For example, improve performance by reducing unnecessary operations and optimizing data structures. Explain its principles and advantages, and finally provide the optimized code implementation.

Question 8: How to verify the correctness of the code?

answer: Verify that the returned intervals are correctly aggregated by running the code and viewing the results. You can use multiple sets of test data, including normal and edge cases, to ensure that the code runs correctly in a variety of situations. For example, you can include multiple different arrays in the test data to ensure that the code results are correct.

Question 9Q: Can you explain the importance of solving the aggregation interval problem?

answer：Solving the summary interval problem is of great significance in data processing and analysis. By learning and applying the method of traversing arrays, we can improve the problem of handling continuous intervals and interval summaries. In practical applications, the summary interval problem is widely used in data visualization, time series analysis, and log processing.

Question 10: How does the algorithm perform when processing large data sets?

answer: The performance of the algorithm depends on the length of the array. When dealing with large data sets, the performance of the algorithm can be significantly improved by optimizing the method of traversing the array. For example, by reducing unnecessary operations and optimizing the data structure, the time and space complexity can be reduced, thereby improving the efficiency of the algorithm.

Summarize

This article explains in detail the 228th question of Likou, "Summarizing the interval", solves this problem efficiently by using the method of traversing the array, and provides detailed explanations and simulated interview questions and answers. I hope that readers can become more comfortable in the process of practicing Likou questions through learning this article.