Longest Common Prefix in DSA Typescript - Time & Space Complexity

Time Complexity: Longest Common Prefix

O(n * m)

Understanding Time Complexity

We want to understand how the time needed to find the longest common prefix grows as we add more words or longer words.

How does the work increase when the input list or word length grows?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function longestCommonPrefix(strs: string[]): string {
  if (strs.length === 0) return "";
  let prefix = strs[0];
  for (let i = 1; i < strs.length; i++) {
    while (strs[i].indexOf(prefix) !== 0) {
      prefix = prefix.substring(0, prefix.length - 1);
      if (prefix === "") return "";
    }
  }
  return prefix;
}
    

This code finds the longest common prefix string among an array of strings by comparing and shortening the prefix as needed.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The outer loop goes through each string in the array after the first.
• How many times: The outer loop runs (n - 1) times where n is the number of strings.
• The inner while loop compares the current prefix with the start of each string and shortens it until it matches.
• The inner loop can run up to the length of the prefix (m) times in the worst case.

How Execution Grows With Input

As we add more strings or longer strings, the number of comparisons grows.

Input Size (n strings, max length m)	Approx. Operations
10 strings, length 5	About 45 comparisons
100 strings, length 10	About 900 comparisons
1000 strings, length 20	About 20,000 comparisons

Pattern observation: The work grows roughly with the product of the number of strings and the length of the prefix.

Final Time Complexity

Time Complexity: O(n * m)

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

Common Mistake

[X] Wrong: "The time depends only on the number of strings, not their length."

[OK] Correct: The length of the prefix matters because we compare characters one by one, so longer prefixes mean more work.

Interview Connect

Understanding this complexity helps you explain how your solution scales and shows you can analyze string operations clearly.

Self-Check

"What if we sorted the strings first and only compared the first and last strings? How would the time complexity change?"

Practice

1. What does the Longest Common Prefix (LCP) of a list of strings represent?

easy

A. The longest starting substring common to all strings

B. The longest ending substring common to all strings

C. The longest substring found anywhere in all strings

D. The shortest string in the list

Solution

1. Step 1: Understand the prefix concept

   A prefix is a substring at the start of a string.

2. Step 2: Define longest common prefix

   The LCP is the longest substring starting from the beginning that all strings share.

3. Final Answer:

   The longest starting substring common to all strings -> Option A

4. Quick Check:

   Prefix means start of string = B [OK]

Hint: Focus on the start of strings to find common parts [OK]

Common Mistakes:

• Confusing prefix with suffix
• Looking for substring anywhere, not just start
• Choosing shortest string as prefix

2. Which of the following TypeScript function signatures correctly represents a function to find the longest common prefix of an array of strings?

easy

A. function longestCommonPrefix(strs: string[]): string

B. function longestCommonPrefix(strs: number[]): string

C. function longestCommonPrefix(strs: string): string[]

D. function longestCommonPrefix(strs: string[]): number

Solution

1. Step 1: Identify input type

   The input should be an array of strings, so type is string[].

2. Step 2: Identify output type

   The output is the longest common prefix, a string.

3. Final Answer:

   function longestCommonPrefix(strs: string[]): string -> Option A

4. Quick Check:

   Input array of strings, output string = D [OK]

Hint: Input is string array, output is string prefix [OK]

Common Mistakes:

• Using number[] instead of string[]
• Returning array instead of string
• Passing single string instead of array

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

function longestCommonPrefix(strs: string[]): string {
  if (strs.length === 0) return "";
  let prefix = strs[0];
  for (let i = 1; i < strs.length; i++) {
    while (strs[i].indexOf(prefix) !== 0) {
      prefix = prefix.substring(0, prefix.length - 1);
      if (prefix === "") return "";
    }
  }
  return prefix;
}

console.log(longestCommonPrefix(["flower", "flow", "flight"]));

medium

A. "flow"

B. "fl"

C. "f"

D. "flight"

Solution

1. Step 1: Initialize prefix and loop through strings

   Start with prefix = "flower". Check "flow": prefix "flower" not prefix of "flow", shorten to "flowe", then "flow", which is prefix of "flow".

2. Step 2: Check next string "flight"

   "flow" not prefix of "flight", shorten to "flo", then "fl", which is prefix of "flight".

3. Final Answer:

   "fl" -> Option B

4. Quick Check:

   Common start is "fl" = A [OK]

Hint: Shorten prefix until it matches start of all strings [OK]

Common Mistakes:

• Returning first string without checking others
• Not shortening prefix correctly
• Confusing substring indices

4. Identify the bug in this TypeScript function for longest common prefix:

function longestCommonPrefix(strs: string[]): string {
  if (strs.length === 0) return "";
  let prefix = strs[0];
  for (let i = 1; i <= strs.length; i++) {
    while (strs[i].indexOf(prefix) !== 0) {
      prefix = prefix.substring(0, prefix.length - 1);
      if (prefix === "") return "";
    }
  }
  return prefix;
}

medium

A. Use prefix.includes() instead of indexOf()

B. Prefix should be initialized as empty string

C. Loop condition should be i < strs.length, not i <= strs.length

D. Return type should be string[] instead of string

Solution

1. Step 1: Check loop boundary

   The loop uses i <= strs.length, which causes out-of-bounds access at i = strs.length.

2. Step 2: Correct loop condition

   Change to i < strs.length to avoid accessing undefined element.

3. Final Answer:

   Loop condition should be i < strs.length, not i <= strs.length -> Option C

4. Quick Check:

   Array index out of bounds = C [OK]

Hint: Use < not <= for zero-based array loops [OK]

Common Mistakes:

• Off-by-one error in loop condition
• Initializing prefix incorrectly
• Misusing string methods

5. Given the array ["interview", "interval", "internal", "internet"], what is the longest common prefix? Also, explain why the prefix stops where it does.

hard

A. "inte" because all strings start with these four letters

B. "in" because only first two letters are common

C. "int" because the sixth letter differs in some strings

D. "inter" because all strings start with these five letters

Solution

1. Step 1: Compare characters one by one

   Check each character index across all strings: 'i', 'n', 't', 'e', 'r' are common in all.

2. Step 2: Identify where mismatch occurs

   At index 5, 'v' in "interview" and "interval", but 'n' in "internal" and "internet", so prefix stops at "inter".

3. Final Answer:

   "inter" because all strings start with these five letters -> Option D

4. Quick Check:

   Common start "inter" = B [OK]

Hint: Check each character position until mismatch found [OK]

Common Mistakes:

• Assuming prefix is longer than actual common part
• Ignoring character positions carefully
• Confusing similar but different letters