Count Words with Given Prefix in DSA Typescript - Time & Space Complexity

Time Complexity: Count Words with Given Prefix

O(n * m)

Understanding Time Complexity

We want to understand how the time needed to count words with a given prefix changes as the number of words grows.

Specifically, how does the search for words starting with a prefix affect performance?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function countWordsWithPrefix(words: string[], prefix: string): number {
  let count = 0;
  for (const word of words) {
    if (word.startsWith(prefix)) {
      count++;
    }
  }
  return count;
}
    

This code counts how many words in the list start with the given prefix by checking each word one by one.

Identify Repeating Operations

• Primary operation: Looping through each word and checking if it starts with the prefix.
• How many times: Once for every word in the list (n times).

How Execution Grows With Input

As the number of words increases, the time to check all words grows roughly in direct proportion.

Input Size (n)	Approx. Operations
10	About 10 prefix checks
100	About 100 prefix checks
1000	About 1000 prefix checks

Pattern observation: Doubling the number of words roughly doubles the work done.

Final Time Complexity

Time Complexity: O(n * m)

This means the time grows with the number of words (n) and the length of the prefix (m) because each word is checked against the prefix.

Common Mistake

[X] Wrong: "Checking prefix is always O(1) so total time is just O(n)."

[OK] Correct: Checking if a word starts with a prefix takes time proportional to the prefix length, so it depends on both n and m.

Interview Connect

Understanding how prefix checks scale helps you explain trade-offs in searching and string matching, a common topic in interviews.

Self-Check

"What if we used a trie (prefix tree) instead of checking each word? How would the time complexity change?"

Practice

1. What does the function countWordsStartingWith(words: string[], prefix: string): number do in the context of counting words with a given prefix?

easy

A. Counts the total number of characters in all words

B. Counts how many words contain the prefix anywhere inside

C. Counts how many words in the list start with the given prefix

D. Returns the longest word starting with the prefix

Solution

1. Step 1: Understand the function purpose

   The function is designed to count words that begin with a specific prefix, not just contain it anywhere.

2. Step 2: Compare options with function goal

   Only Counts how many words in the list start with the given prefix matches the goal of counting words starting exactly with the prefix.

3. Final Answer:

   Counts how many words in the list start with the given prefix -> Option C

4. Quick Check:

   Counting words starting with prefix = Counts how many words in the list start with the given prefix [OK]

Hint: Look for words starting exactly with prefix, not containing it [OK]

Common Mistakes:

• Confusing 'start with' and 'contain' prefix
• Thinking it returns words instead of count
• Assuming it counts characters, not words

2. Which of the following TypeScript code snippets correctly counts words starting with a prefix pre in an array words?

easy

A. words.filter(word => word.startsWith(pre)).length

B. words.map(word => word.startsWith(pre)).length

C. words.reduce((count, word) => count + word.includes(pre), 0)

D. words.forEach(word => word.startsWith(pre))

Solution

1. Step 1: Identify correct method to filter words

   The filter method returns an array of words starting with the prefix, then length counts them.

2. Step 2: Check other options for correctness

   words.map(word => word.startsWith(pre)).length returns an array of booleans, so length is total words, not count of matches. words.reduce((count, word) => count + word.includes(pre), 0) uses includes incorrectly and sums booleans without conversion. words.forEach(word => word.startsWith(pre)) does not return a count.

3. Final Answer:

   words.filter(word => word.startsWith(pre)).length -> Option A

4. Quick Check:

   Filter + length counts matches = words.filter(word => word.startsWith(pre)).length [OK]

Hint: Use filter with startsWith, then get length [OK]

Common Mistakes:

• Using map instead of filter for counting
• Using includes instead of startsWith
• Using forEach without counting

3. What is the output of the following TypeScript code?

const words = ['apple', 'app', 'application', 'banana', 'apply'];
const prefix = 'app';
const count = words.filter(word => word.startsWith(prefix)).length;
console.log(count);

medium

A. 3

B. 4

C. 5

D. 2

Solution

1. Step 1: Identify words starting with 'app'

   Words starting with 'app' are 'apple', 'app', 'application', and 'apply' (4 words).

2. Step 2: Count these words

   Counting them gives 4.

3. Final Answer:

   4 -> Option B

4. Quick Check:

   Words starting with 'app' = 4 [OK]

Hint: Count words starting exactly with prefix 'app' [OK]

Common Mistakes:

• Counting 'banana' mistakenly
• Counting only exact 'app' word
• Confusing includes with startsWith

4. The following TypeScript code is intended to count words starting with prefix pre, but it returns 0. What is the error?

const words = ['prefix', 'preach', 'prevent', 'post'];
const pre = 'pre';
let count = 0;
for (let i = 0; i < words.length; i++) {
  if (words[i].startWith(pre)) {
    count++;
  }
}
console.log(count);

medium

A. Method name should be startsWith, not startWith

B. Variable pre is not defined

C. Loop should start from 1, not 0

D. count should be initialized to 1

Solution

1. Step 1: Check method name correctness

   The method to check prefix is startsWith, but code uses startWith, which is undefined.

2. Step 2: Understand effect of typo

   Because of the typo, condition is always false, so count remains 0.

3. Final Answer:

   Method name should be startsWith, not startWith -> Option A

4. Quick Check:

   Correct method name fixes count [OK]

Hint: Check method spelling: startsWith, not startWith [OK]

Common Mistakes:

• Using startWith instead of startsWith
• Incorrect loop index start
• Wrong count initialization

5. Given a large list of words, which data structure would optimize counting how many words start with a given prefix efficiently for multiple queries?

hard

A. Array sorted alphabetically

B. Stack storing words

C. Hash Map with full words as keys

D. Trie (Prefix Tree)

Solution

1. Step 1: Understand prefix query optimization

   Trie stores words by characters in a tree, allowing fast prefix searches.

2. Step 2: Compare other data structures

   Sorted arrays require binary search but less efficient for many prefix queries. Hash maps store full words, not prefixes. Stacks do not support prefix queries efficiently.

3. Final Answer:

   Trie (Prefix Tree) -> Option D

4. Quick Check:

   Trie enables fast prefix counts [OK]

Hint: Use Trie for fast prefix counting in many queries [OK]

Common Mistakes:

• Choosing array or hash map for prefix queries
• Not knowing Trie supports prefix efficiently
• Confusing stack usage for prefix search