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

Time Complexity: Count Words with Given Prefix

O(n * m)

Understanding Time Complexity

We want to understand how the time to count words with a certain prefix grows as the number of words or prefix length changes.

How does the work increase when we have more words or longer prefixes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public int CountWordsWithPrefix(string[] words, string prefix) {
    int count = 0;
    foreach (var word in words) {
        if (word.StartsWith(prefix)) {
            count++;
        }
    }
    return count;
}
    

This code counts how many words in the list start with the given prefix.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Checking each word to see if it starts with the prefix.
• How many times: Once for every word in the list (n times), and for each check, it compares characters up to the prefix length (m times).

How Execution Grows With Input

As the number of words (n) grows, the code checks more words. Also, longer prefixes (m) mean more character comparisons per word.

Input Size (n words, prefix length m)	Approx. Operations
10 words, prefix length 3	About 10 * 3 = 30 checks
100 words, prefix length 3	About 100 * 3 = 300 checks
1000 words, prefix length 5	About 1000 * 5 = 5000 checks

Pattern observation: The work grows linearly with the number of words and also linearly with the prefix length.

Final Time Complexity

Time Complexity: O(n * m)

This means the time grows proportionally to the number of words times the length of the prefix.

Common Mistake

[X] Wrong: "Checking the prefix is always O(1) because it's just one operation."

[OK] Correct: Actually, checking the prefix compares each character up to the prefix length, so it takes O(m) time, not constant time.

Interview Connect

Understanding how prefix checks scale helps you explain and improve search operations, a common task in coding interviews and real applications.

Self-Check

"What if we used a Trie data structure instead of checking each word? How would the time complexity change?"

Practice

1. What does the problem "Count Words with Given Prefix" ask you to do?

easy

A. Count how many words in a list start with a specific prefix

B. Find the longest word in a list

C. Sort words alphabetically

D. Replace the prefix in all words with another string

Solution

1. Step 1: Understand the problem statement

   The problem asks to count words that begin with a given prefix, not to sort or replace words.

2. Step 2: Identify the key action

   Counting words starting with the prefix is the main task.

3. Final Answer:

   Count how many words in a list start with a specific prefix -> Option A

4. Quick Check:

   Count words with prefix = Count how many words in a list start with a specific prefix [OK]

Hint: Focus on words starting with prefix, not other operations [OK]

Common Mistakes:

• Confusing counting with sorting
• Thinking the task is to replace prefixes
• Ignoring the prefix condition

2. Which of the following C# code snippets correctly checks if a string word starts with a prefix prefix?

easy

A. if (word == prefix) { /* do something */ }

B. if (word.Contains(prefix)) { /* do something */ }

C. if (word.EndsWith(prefix)) { /* do something */ }

D. if (word.StartsWith(prefix)) { /* do something */ }

Solution

1. Step 1: Recall string methods in C#

   The method StartsWith checks if a string begins with a given substring.

2. Step 2: Compare options

   Contains checks anywhere in the string, EndsWith checks the end, and == checks exact equality.

3. Final Answer:

   if (word.StartsWith(prefix)) { /* do something */ } -> Option D

4. Quick Check:

   Use StartsWith to check prefix [OK]

Hint: Use StartsWith method to check prefix in C# strings [OK]

Common Mistakes:

• Using Contains instead of StartsWith
• Checking equality instead of prefix
• Using EndsWith which checks suffix

3. What is the output of the following C# code?

string[] words = {"apple", "app", "application", "banana"};
string prefix = "app";
int count = 0;
foreach (var word in words) {
    if (word.StartsWith(prefix)) {
        count++;
    }
}
Console.WriteLine(count);

medium

A. 2

B. 1

C. 3

D. 4

Solution

1. Step 1: Check each word against prefix "app"

   Words: "apple" (yes), "app" (yes), "application" (yes), "banana" (no).

2. Step 2: Count matches

   Three words start with "app", so count = 3.

3. Final Answer:

   3 -> Option C

4. Quick Check:

   Words starting with "app" = 3 [OK]

Hint: Count words starting with prefix by checking each word [OK]

Common Mistakes:

• Counting only exact matches
• Including words that contain prefix but don't start with it
• Off-by-one counting errors

4. The following code is intended to count words starting with a prefix but gives wrong output. What is the error?

string[] words = {"cat", "car", "dog", "cart"};
string prefix = "car";
int count = 0;
for (int i = 0; i <= words.Length; i++) {
    if (words[i].StartsWith(prefix)) {
        count++;
    }
}
Console.WriteLine(count);

medium

A. The loop condition should be i < words.Length instead of <=.

B. The prefix variable is incorrect.

C. The StartsWith method is used wrongly.

D. The count variable should be initialized inside the loop.

Solution

1. Step 1: Analyze the for loop condition

   The loop runs from i = 0 to i <= words.Length, which causes an index out of range error because valid indices are 0 to words.Length - 1.

2. Step 2: Correct the loop condition

   Change condition to i < words.Length to avoid accessing invalid index.

3. Final Answer:

   The loop condition should be i < words.Length instead of <=. -> Option A

4. Quick Check:

   Loop index must be less than array length [OK]

Hint: Use i < array.Length to avoid index errors in loops [OK]

Common Mistakes:

• Using <= instead of < in loop condition
• Reinitializing count inside loop
• Misusing StartsWith method

5. Given a list of words ["tree", "trie", "trigger", "trip", "try", "matrix"] and prefix "tri", which C# code snippet correctly counts the words starting with the prefix and prints the count?

hard

A. int count = 0; foreach(var word in words) { if(word.Contains(prefix)) count++; } Console.WriteLine(count);

B. int count = words.Count(word => word.StartsWith(prefix)); Console.WriteLine(count);

C. int count = 0; for(int i=0; i<=words.Length; i++) { if(words[i].StartsWith(prefix)) count++; } Console.WriteLine(count);

D. int count = words.Length; Console.WriteLine(count);

Solution

1. Step 1: Understand the requirement

   We need to count words starting exactly with prefix "tri".

2. Step 2: Evaluate each option

   int count = words.Count(word => word.StartsWith(prefix)); Console.WriteLine(count); uses LINQ Count with StartsWith correctly.
   int count = 0; foreach(var word in words) { if(word.Contains(prefix)) count++; } Console.WriteLine(count); uses Contains which counts words containing prefix anywhere.
   int count = 0; for(int i=0; i<=words.Length; i++) { if(words[i].StartsWith(prefix)) count++; } Console.WriteLine(count); has loop with <= causing index error.
   int count = words.Length; Console.WriteLine(count); counts all words ignoring prefix.

3. Final Answer:

   int count = words.Count(word => word.StartsWith(prefix)); Console.WriteLine(count); -> Option B

4. Quick Check:

   Use LINQ Count with StartsWith for prefix count [OK]

Hint: Use LINQ Count with StartsWith for concise prefix counting [OK]

Common Mistakes:

• Using Contains instead of StartsWith
• Loop index out of range errors
• Counting all words without prefix check