Design Search Autocomplete System

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import heapq
from collections import defaultdict

class AutocompleteSystem:
    def __init__(self, sentences, times):
        self.data = defaultdict(int)
        self.prefix_data = defaultdict(list)
        self.prefix = ""

        for i in range(len(sentences)):
            self.data[sentences[i]] = times[i]

    def input(self, c):
        if c == "#":
            self.data[self.prefix] += 1
            self.prefix = ""
            return []

        self.prefix += c
        prefix_heap = []
        for sentence, freq in self.data.items():
            if sentence.startswith(self.prefix):
                heapq.heappush(prefix_heap, (-freq, sentence))

        self.prefix_data[self.prefix] = []
        while prefix_heap and len(self.prefix_data[self.prefix]) < 3:
            freq, sentence = heapq.heappop(prefix_heap)
            self.prefix_data[self.prefix].append(sentence)

        return self.prefix_data[self.prefix]

Identifying Problem Isomorphism

“Design Search Autocomplete System” is related to “Longest Word in Dictionary”. They share some common themes, particularly the use of Trie data structure for efficient text search.

In “Design Search Autocomplete System”, you need to design a search autocomplete system for a search engine. Users may input a sentence (at least one word and end with a special character ‘#’). The task is to provide the top 3 historical hot sentences that have the same prefix as the user’s input.

“Longest Word in Dictionary” requires you to find the longest word in a dictionary that can be built one character at a time by other words in the dictionary. Here, a Trie can be used to store the words in the dictionary and also to search for the longest word.

Both problems require understanding and implementation of Trie data structure. “Longest Word in Dictionary” is simpler as it mostly involves using Trie to store and search words. The autocomplete system in “Design Search Autocomplete System”, involves not only storing and searching, but also ranking the results, making it more complex. Understanding the basic operations of Trie in the simpler problem can provide a solid foundation for the more complex problem.

10 Prerequisite LeetCode Problems

“642. Design Search Autocomplete System” involves the design of a data structure (specifically, a Trie or Prefix Tree), string manipulation, sorting, and use of heaps.

Here are 10 problems to prepare:

“208. Implement Trie (Prefix Tree)”: This problem is the basic implementation of Trie, a must-know for solving autocomplete problems.
“677. Map Sum Pairs”: This problem asks to implement a map-sum class with a similar idea to Trie.
“79. Word Search”: Helps you practice searching in a 2D grid.
“212. Word Search II”: An enhanced version of Word Search where Trie can be applied for optimization.
“692. Top K Frequent Words”: This helps you understand the concept of getting top K elements using heap data structure, which is useful for the autocomplete system problem.
“347. Top K Frequent Elements”: Similar to above but with numbers instead of words.
“451. Sort Characters By Frequency”: It’s a sorting problem by frequency.
“49. Group Anagrams”: This problem helps you practice string manipulation and sorting.
“720. Longest Word in Dictionary”: Another problem where Trie is commonly used for efficient searching.
“140. Word Break II”: This problem involves searching for all possibilities, similar to the autocomplete system.

Build a good understanding of Trie, heap, string manipulation, and sorting which are essential for solving the “Design Search Autocomplete System” problem.

Problem Classification

Problem Statement:Design a search autocomplete system for a search engine. Users may input a sentence (at least one word and end with a special character ‘#’).

You are given a string array sentences and an integer array times both of length n where sentences[i] is a previously typed sentence and times[i] is the corresponding number of times the sentence was typed. For each input character except ‘#’, return the top 3 historical hot sentences that have the same prefix as the part of the sentence already typed.

Here are the specific rules:

The hot degree for a sentence is defined as the number of times a user typed the exactly same sentence before. The returned top 3 hot sentences should be sorted by hot degree (The first is the hottest one). If several sentences have the same hot degree, use ASCII-code order (smaller one appears first). If less than 3 hot sentences exist, return as many as you can. When the input is a special character, it means the sentence ends, and in this case, you need to return an empty list. Implement the AutocompleteSystem class:

AutocompleteSystem(String[] sentences, int[] times) Initializes the object with the sentences and times arrays. List input(char c) This indicates that the user typed the character c. Returns an empty array [] if c == ‘#’ and stores the inputted sentence in the system. Returns the top 3 historical hot sentences that have the same prefix as the part of the sentence already typed. If there are fewer than 3 matches, return them all.

Example 1:

Input [“AutocompleteSystem”, “input”, “input”, “input”, “input”] [[[“i love you”, “island”, “iroman”, “i love leetcode”], [5, 3, 2, 2]], [“i”], [" “], [“a”], [”#"]] Output [null, [“i love you”, “island”, “i love leetcode”], [“i love you”, “i love leetcode”], [], []]

Explanation AutocompleteSystem obj = new AutocompleteSystem([“i love you”, “island”, “iroman”, “i love leetcode”], [5, 3, 2, 2]); obj.input(“i”); // return [“i love you”, “island”, “i love leetcode”]. There are four sentences that have prefix “i”. Among them, “ironman” and “i love leetcode” have same hot degree. Since ’ ’ has ASCII code 32 and ‘r’ has ASCII code 114, “i love leetcode” should be in front of “ironman”. Also we only need to output top 3 hot sentences, so “ironman” will be ignored. obj.input(" “); // return [“i love you”, “i love leetcode”]. There are only two sentences that have prefix “i “. obj.input(“a”); // return []. There are no sentences that have prefix “i a”. obj.input(”#”); // return []. The user finished the input, the sentence “i a” should be saved as a historical sentence in system. And the following input will be counted as a new search.

Constraints:

n == sentences.length n == times.length 1 <= n <= 100 1 <= sentences[i].length <= 100 1 <= times[i] <= 50 c is a lowercase English letter, a hash ‘#’, or space ’ ‘. Each tested sentence will be a sequence of characters c that end with the character ‘#’. Each tested sentence will have a length in the range [1, 200]. The words in each input sentence are separated by single spaces. At most 5000 calls will be made to input.

Analyze the provided problem statement. Categorize it based on its domain, ignoring ‘How’ it might be solved. Identify and list out the ‘What’ components. Based on these, further classify the problem. Explain your categorizations.

Distilling the Problem to Its Core Elements

In order to have me distill a problem to its core, you could ask questions that prompt for a deeper analysis of the problem, understanding of the underlying concepts, and simplification of the problem’s essence. Here are some examples of such prompts:

Can you identify the fundamental concept or principle this problem is based upon? Please explain.
What is the simplest way you would describe this problem to someone unfamiliar with the subject?
What is the core problem we are trying to solve? Can we simplify the problem statement?
Can you break down the problem into its key components?
What is the minimal set of operations we need to perform to solve this problem?

These prompts guide the discussion towards simplifying the problem, stripping it down to its essential elements, and understanding the core problem to be solved.

Visual Model of the Problem

How to visualize the problem statement for this problem?

Problem Restatement

Could you start by paraphrasing the problem statement in your own words? Try to distill the problem into its essential elements and make sure to clarify the requirements and constraints. This exercise should aid in understanding the problem better and aligning our thought process before jumping into solving it.

Abstract Representation of the Problem

Could you help me formulate an abstract representation of this problem?

Given this problem, how can we describe it in an abstract way that emphasizes the structure and key elements, without the specific real-world details?

Terminology

Are there any specialized terms, jargon, or technical concepts that are crucial to understanding this problem or solution? Could you define them and explain their role within the context of this problem?

Problem Simplification and Explanation

Could you please break down this problem into simpler terms? What are the key concepts involved and how do they interact? Can you also provide a metaphor or analogy to help me understand the problem better?

Constraints

Given the problem statement and the constraints provided, identify specific characteristics or conditions that can be exploited to our advantage in finding an efficient solution. Look for patterns or specific numerical ranges that could be useful in manipulating or interpreting the data.

What are the key insights from analyzing the constraints?

Case Analysis

Could you please provide additional examples or test cases that cover a wider range of the input space, including edge and boundary conditions? In doing so, could you also analyze each example to highlight different aspects of the problem, key constraints and potential pitfalls, as well as the reasoning behind the expected output for each case? This should help in generating key insights about the problem and ensuring the solution is robust and handles all possible scenarios.

Provide names by categorizing these cases

What are the key insights from analyzing the different cases?

Identification of Applicable Theoretical Concepts

Can you identify any mathematical or algorithmic concepts or properties that can be applied to simplify the problem or make it more manageable? Think about the nature of the operations or manipulations required by the problem statement. Are there existing theories, metrics, or methodologies in mathematics, computer science, or related fields that can be applied to calculate, measure, or perform these operations more effectively or efficiently?

Problem Breakdown and Solution Methodology

Given the problem statement, can you explain in detail how you would approach solving it? Please break down the process into smaller steps, illustrating how each step contributes to the overall solution. If applicable, consider using metaphors, analogies, or visual representations to make your explanation more intuitive. After explaining the process, can you also discuss how specific operations or changes in the problem’s parameters would affect the solution? Lastly, demonstrate the workings of your approach using one or more example cases.

Inference of Problem-Solving Approach from the Problem Statement

How did you infer from the problem statement that this problem can be solved using ?

Could you please provide a stepwise refinement of our approach to solving this problem?
How can we take the high-level solution approach and distill it into more granular, actionable steps?
Could you identify any parts of the problem that can be solved independently?
Are there any repeatable patterns within our solution?

Solution Approach and Analysis

Thought Process

Explain the thought process by thinking step by step to solve this problem from the problem statement and code the final solution. Write code in Python3. What are the cues in the problem statement? What direction does it suggest in the approach to the problem? Generate insights about the problem statement.

From Brute Force to Optimal Solution

Could you please begin by illustrating a brute force solution for this problem? After detailing and discussing the inefficiencies of the brute force approach, could you then guide us through the process of optimizing this solution? Please explain each step towards optimization, discussing the reasoning behind each decision made, and how it improves upon the previous solution. Also, could you show how these optimizations impact the time and space complexity of our solution?

Code Explanation and Design Decisions

Identify the initial parameters and explain their significance in the context of the problem statement or the solution domain.
Discuss the primary loop or iteration over the input data. What does each iteration represent in terms of the problem you’re trying to solve? How does the iteration advance or contribute to the solution?
If there are conditions or branches within the loop, what do these conditions signify? Explain the logical reasoning behind the branching in the context of the problem’s constraints or requirements.
If there are updates or modifications to parameters within the loop, clarify why these changes are necessary. How do these modifications reflect changes in the state of the solution or the constraints of the problem?
Describe any invariant that’s maintained throughout the code, and explain how it helps meet the problem’s constraints or objectives.
Discuss the significance of the final output in relation to the problem statement or solution domain. What does it represent and how does it satisfy the problem’s requirements?

Remember, the focus here is not to explain what the code does on a syntactic level, but to communicate the intent and rationale behind the code in the context of the problem being solved.

Coding Constructs

Consider the following piece of complex software code.

What are the high-level problem-solving strategies or techniques being used by this code?
If you had to explain the purpose of this code to a non-programmer, what would you say?
Can you identify the logical elements or constructs used in this code, independent of any programming language?
Could you describe the algorithmic approach used by this code in plain English?
What are the key steps or operations this code is performing on the input data, and why?
Can you identify the algorithmic patterns or strategies used by this code, irrespective of the specific programming language syntax?

Language Agnostic Coding Drills

Your mission is to deconstruct this code into the smallest possible learning units, each corresponding to a separate coding concept. Consider these concepts as unique coding drills that can be individually implemented and later assembled into the final solution.

Dissect the code and identify each distinct concept it contains. Remember, this process should be language-agnostic and generally applicable to most modern programming languages.
Once you’ve identified these coding concepts or drills, list them out in order of increasing difficulty. Provide a brief description of each concept and why it is classified at its particular difficulty level.
Next, describe the problem-solving approach that would lead from the problem statement to the final solution. Think about how each of these coding drills contributes to the overall solution. Elucidate the step-by-step process involved in using these drills to solve the problem. Please refrain from writing any actual code; we’re focusing on understanding the process and strategy.

Targeted Drills in Python

Now that you’ve identified and ordered the coding concepts from a complex software code in the previous exercise, let’s focus on creating Python-based coding drills for each of those concepts.

Begin by writing a separate piece of Python code that encapsulates each identified concept. These individual drills should illustrate how to implement each concept in Python. Please ensure that these are suitable even for those with a basic understanding of Python.
In addition to the general concepts, identify and write coding drills for any problem-specific concepts that might be needed to create a solution. Describe why these drills are essential for our problem.
Once all drills have been coded, describe how these pieces can be integrated together in the right order to solve the initial problem. Each drill should contribute to building up to the final solution.

Remember, the goal is to not only to write these drills but also to ensure that they can be cohesively assembled into one comprehensive solution.