How to Solve Query Kth Smallest Trimmed Number

This problem requires sorting a string array after trimming each string based on given indices. For each query, the goal is to find the Kth smallest number after trimming the specified number of digits from the end. Efficient solutions often involve sorting or utilizing quickselect methods to find the smallest element more quickly.

Problem Statement

You are given a 0-indexed array of strings nums, where each string consists of digits and all strings have the same length. You are also given a 0-indexed 2D array queries, where each query consists of two integers [ki, trimi]. For each query, trim each string in nums by removing the last trimi digits, then find the ki-th smallest number in the resulting array. The number is evaluated as an integer, and ties are broken by their indices in nums.

Return an array answer of the same length as queries, where answer[i] is the answer to the i-th query. The solution needs to handle multiple queries efficiently, considering both the trimming process and the selection of the smallest number.

Examples

Example 1

Input: nums = ["102","473","251","814"], queries = [[1,1],[2,3],[4,2],[1,2]]

Output: [2,2,1,0]

1. After trimming to the last digit, nums = ["2","3","1","4"]. The smallest number is 1 at index 2.
2. Trimmed to the last 3 digits, nums is unchanged. The 2nd smallest number is 251 at index 2.
3. Trimmed to the last 2 digits, nums = ["02","73","51","14"]. The 4th smallest number is 73.
4. Trimmed to the last 2 digits, the smallest number is 2 at index 0. Note that the trimmed number "02" is evaluated as 2.

Example 2

Input: nums = ["24","37","96","04"], queries = [[2,1],[2,2]]

Output: [3,0]

1. Trimmed to the last digit, nums = ["4","7","6","4"]. The 2nd smallest number is 4 at index 3. There are two occurrences of 4, but the one at index 0 is considered smaller than the one at index 3.
2. Trimmed to the last 2 digits, nums is unchanged. The 2nd smallest number is 24.

Constraints

• 1 <= nums.length <= 100
• 1 <= nums[i].length <= 100
• nums[i] consists of only digits.
• All nums[i].length are equal.
• 1 <= queries.length <= 100
• queries[i].length == 2
• 1 <= ki <= nums.length
• 1 <= trimi <= nums[i].length

Solution Approach

Simulate Each Query

For each query, trim the strings in nums by removing the specified number of digits from the end. After trimming, convert the strings to integers and sort the resulting list to find the ki-th smallest value. This brute-force approach directly simulates the trimming and sorting for each query.

Sorting and Quickselect

Instead of sorting the entire list for each query, you can use the Quickselect algorithm to find the ki-th smallest number efficiently. This reduces unnecessary sorting overhead and speeds up the process for large arrays and multiple queries.

Efficient Sorting with Radix Sort

Since the strings are numeric and have equal lengths, applying Radix Sort can help in sorting the trimmed strings more efficiently. By focusing on the least significant digits first, Radix Sort can achieve linear time complexity in some cases, improving the overall performance of the solution.

Complexity Analysis

The time complexity for this problem depends on the final approach used. A brute-force approach where each query is handled by sorting the entire list has a time complexity of O(N * log N) for sorting, where N is the length of the array. Quickselect can reduce this to O(N) for each query, making it more efficient when fewer elements need to be sorted. Radix Sort can achieve a time complexity of O(N * d), where d is the length of each string, which can be optimal in some cases depending on the size of nums and queries.

What Interviewers Usually Probe

• Testing the candidate's ability to optimize for multiple queries over a shared data set.
• Looking for an efficient implementation that handles trimming and sorting without unnecessary recalculations.
• Assesses familiarity with sorting algorithms like Quickselect and Radix Sort, especially in the context of numeric strings.

Common Pitfalls or Variants

Common pitfalls

• Not optimizing the trimming and sorting process, leading to excessive time complexity in handling multiple queries.
• Incorrectly handling tie-breaking in the case of equal trimmed numbers, potentially returning wrong indices.
• Forgetting to account for trimming from the end of the string and misinterpreting the query's requirement.

Follow-up variants

• Modify the problem to handle unsorted input strings that need to be sorted based on trimming and queries.
• Alter the problem to use a custom comparison function when sorting the trimmed numbers.
• Consider adding constraints where strings are not of equal length, which requires extra handling during the trimming process.

How GhostInterview Helps

• GhostInterview provides a deep dive into how array manipulation and string trimming can be optimized for large datasets.
• Through algorithmic explanations, GhostInterview helps you decide whether sorting, Quickselect, or Radix Sort should be employed for this problem.
• It guides you in making decisions around trade-offs for time and space complexity, particularly when handling multiple queries efficiently.

Topic Pages

• Array
• String
• Divide and Conquer
• Sorting
• Heap (Priority Queue)
• Radix Sort
• Quickselect

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FAQ

What is the best approach for solving Query Kth Smallest Trimmed Number?

The best approach involves either sorting the list after trimming each string or using Quickselect to find the Kth smallest element efficiently without fully sorting the array.

How do you handle tie-breaking in the Kth smallest query?

Tie-breaking is handled by considering the original index of the elements in nums after they have been trimmed and evaluated as integers.

Can Radix Sort be useful for this problem?

Yes, Radix Sort can be helpful when strings are of equal length, allowing you to sort the numbers efficiently without comparing all characters at once.

What is the time complexity of the brute force approach?

The brute force approach has a time complexity of O(N * log N) due to the sorting operation for each query, where N is the length of the array.

How can GhostInterview help me with this problem?

GhostInterview provides insights into optimizing string manipulations and helps choose the most efficient algorithm for handling trimming and sorting operations in this problem.