Welcome back to our course on algorithmic problem-solving with TypeScript data structures. Today, we will sharpen our focus on maps — a powerful data structure you've been introduced to in previous lessons. This session will demonstrate how TypeScript's maps, with their type safety and robust functionalities, can be leveraged to efficiently solve common algorithmic problems often encountered in coding interviews.

Let's explore a familiar scenario: at a party, one person stands out as the "celebrity" because everyone seems to know them. Similarly, in an array, we want to identify an element that appears more than half the time — our task is to identify this celebrity element among a group of numbers.

The naive approach to identify this celebrity is to count the occurrences of each number by iterating over the array for each element, checking if it repeats enough to meet our criteria. This method results in significant computational time ($O(n^2)$) on larger arrays, presenting obvious inefficiencies.

To approach this more efficiently, we use a map, which acts as a sophisticated voting tally system. This allows us to track each element's occurrences as we traverse the array a single time, avoiding the need to review the entire list for each integer repeatedly.

Let's break down this process using our celebrity analogy step by step with TypeScript:

TypeScript
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1function findCelebrityElement(arr: number[]): number {
2    let countMap = new Map<number, number>();
3    let majorityThreshold = Math.floor(arr.length / 2);
4
5    for (let num of arr) {
6        countMap.set(num, (countMap.get(num) || 0) + 1);
7        if (countMap.get(num)! > majorityThreshold) {
8            return num;
9        }
10    }
11    return -1;
12}

Here, we define a map that counts each number's appearances, utilizing type annotations to enforce the type safety TypeScript provides. The majorityThreshold dictates the count needed for an element to be considered the 'celebrity'. As we proceed, we update and check each element's frequency and can efficiently determine when an element meets the threshold with type assurance.

Imagine transitioning to a digital library setting, where finding all articles containing a specific word, such as "sustainability," is essential. We need an efficient system for indexing words to the documents in which they appear — crucial functionality for modern search engines.

The naive method involves manually scanning each document to check word occurrences, akin to flipping through all the pages of each book. While feasible for small, short documents, this approach fails to scale and is prone to errors and redundancies.

Utilizing maps and sets in TypeScript creates an efficient indexing system, akin to a digital catalog. This allows for quick, accurate searches and effectively manages a large volume of data.

TypeScript
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1function createKeywordIndex(documents: string[]): Map<string, Set<number>> {
2  const index: Map<string, Set<number>> = new Map();
3
4  documents.forEach((doc, docIndex) => {
5    let words = doc.split(/\s+/);
6    words.forEach(word => {
7      if (index.has(word)) {
8        index.get(word)!.add(docIndex);
9      } else {
10        index.set(word, new Set([docIndex]));
11      }
12    });
13  });
14
15  return index;
16}

By defining a Map<string, Set<number>>, we're able to index words and associate them with documents by their numeric indexes in a type-safe manner. Each word found is cataloged within the map, ensuring accurate and efficient retrieval.

Through the algorithmic challenges in this lesson, we've demonstrated how TypeScript's maps can be strategically employed to solve complex problems with enhanced computational efficiency and type safety. The findCelebrityElement function illustrates optimizing search algorithms, while the createKeywordIndex showcases structuring data for rapid access. By using TypeScript, you benefit from stringent type assurance, delivering not only reliable but also robust solutions, thereby equipping you to tackle coding challenges with confidence and precision.