Why Longest Common Prefix in DSA C++?

The Big Idea

Discover how to find the common start of many words without checking each letter one by one!

The Scenario

Imagine you have a list of words and you want to find the longest starting part they all share. Doing this by checking each letter one by one for every word is like looking for a common thread in many tangled strings by pulling each string separately.

The Problem

Checking each word manually is slow and tiring. You might miss letters or make mistakes, especially if the list is long or words are big. It's like trying to find a common pattern in many messy ropes without a clear method.

The Solution

The Longest Common Prefix method quickly finds the shared starting letters among all words by comparing them step-by-step in a smart way. It saves time and avoids errors by stopping as soon as a difference is found.

Before vs After

✗ Before

string longestCommonPrefix(vector<string>& words) {
  if (words.empty()) return "";
  string prefix = "";
  for (int i = 0; i < words[0].size(); i++) {
    char c = words[0][i];
    for (int j = 1; j < words.size(); j++) {
      if (i >= words[j].size() || words[j][i] != c) return prefix;
    }
    prefix += c;
  }
  return prefix;
}

✓ After

string longestCommonPrefix(vector<string>& words) {
  if (words.empty()) return "";
  sort(words.begin(), words.end());
  string first = words[0];
  string last = words.back();
  int i = 0;
  while (i < first.size() && i < last.size() && first[i] == last[i]) {
    i++;
  }
  return first.substr(0, i);
}

What It Enables

This lets you quickly find the common start in many words, helping in tasks like auto-complete, search optimization, and data grouping.

Real Life Example

When you type in a search box, the system suggests words that start the same way you typed. Longest Common Prefix helps find that shared start fast.

Key Takeaways

Manual checking is slow and error-prone.

Longest Common Prefix finds shared starts efficiently.

It helps in search, auto-complete, and grouping tasks.

Practice

1. What does the Longest Common Prefix (LCP) problem ask you to find given a list of strings?

easy

A. The total count of common characters in all strings

B. The longest starting substring common to all strings

C. The longest ending substring common to all strings

D. The longest substring common to any two strings

Solution

1. Step 1: Understand the problem definition

   The Longest Common Prefix means the longest substring at the start of all strings that is the same.

2. Step 2: Compare options with the definition

   Only The longest starting substring common to all strings matches the definition exactly: longest starting substring common to all strings.

3. Final Answer:

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

4. Quick Check:

   Longest Common Prefix = longest starting substring [OK]

Hint: Focus on the start of strings, not anywhere else [OK]

Common Mistakes:

• Confusing prefix with substring anywhere
• Thinking about suffix instead of prefix
• Counting characters instead of substring

2. Which of the following C++ code snippets correctly initializes a vector of strings named strs with values "flower", "flow", "flight"?

easy

A. std::vector strs = {"flower", "flow", "flight"};

B. std::vector strs = {"flower", "flow", "flight"};

C. vector<string> strs = ("flower", "flow", "flight");

D. std::vector strs = ("flower", "flow", "flight");

Solution

1. Step 1: Check correct vector initialization syntax

   In C++, to initialize a vector of strings with values, use curly braces {} and specify type with std::vector.

2. Step 2: Validate each option

   std::vector strs = {"flower", "flow", "flight"}; uses correct syntax with std::vector and braces {}. Versions missing std:: namespace, using parentheses instead of braces, or lacking template type <std::string> are invalid.

3. Final Answer:

   std::vector strs = {"flower", "flow", "flight"}; -> Option A

4. Quick Check:

   Correct vector initialization uses braces and type [OK]

Hint: Use curly braces {} and full type for vector initialization [OK]

Common Mistakes:

• Using parentheses instead of braces
• Omitting std:: namespace
• Missing template argument

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

std::vector strs = {"interview", "internet", "internal"};
std::string prefix = strs[0];
for (int i = 1; i < strs.size(); i++) {
    int j = 0;
    while (j < prefix.size() && j < strs[i].size() && prefix[j] == strs[i][j]) {
        j++;
    }
    prefix = prefix.substr(0, j);
}
std::cout << prefix << std::endl;

medium

A. int

B. inte

C. intern

D. inter

Solution

1. Step 1: Initialize prefix and compare with each string

   Start prefix = "interview". Compare with "internet": common prefix is "inter". Update prefix = "inter".

2. Step 2: Compare updated prefix "inter" with "internal"

   Common prefix is "inter" again. So prefix remains "inter".

3. Final Answer:

   inter -> Option D

4. Quick Check:

   Common prefix of all = "inter" [OK]

Hint: Compare prefix with each string, shorten prefix on mismatch [OK]

Common Mistakes:

• Stopping after first comparison
• Not updating prefix correctly
• Confusing substring indices

4. Identify the bug in the following C++ code that tries to find the longest common prefix:

std::string longestCommonPrefix(std::vector& strs) {
    std::string prefix = strs[0];
    for (int i = 1; i < strs.size(); i++) {
        int j = 0;
        while (j < prefix.size() && j < strs[i].size() && prefix[j] == strs[i][j]) {
            j++;
        }
        prefix = prefix.substr(0, j);
        if (prefix.empty()) return "";
    }
    return prefix;
}

// Usage:
// std::vector words = {"dog", "racecar", "car"};
// std::cout << longestCommonPrefix(words) << std::endl;

medium

A. The function does not handle empty input vector

B. The function returns incorrect prefix for input {"dog", "racecar", "car"}

C. The while loop condition is incorrect and causes infinite loop

D. The function should return the longest common suffix instead

Solution

1. Step 1: Check empty input handling

   The code directly accesses strs[0] without checking if strs is empty, causing a runtime error (out-of-range access) for empty vectors.

2. Step 2: Verify other statements

   The loop logic correctly shortens the prefix, no infinite loop occurs, it returns prefix not suffix, and for {"dog", "racecar", "car"} it correctly returns "".

3. Final Answer:

   The function does not handle empty input vector -> Option A

4. Quick Check:

   Missing if(strs.empty()) return ""; [OK]

Hint: Test edge cases like empty lists first [OK]

Common Mistakes:

• Overlooking empty vector handling
• Misjudging the output for no common prefix cases
• Suspecting infinite loop in the while condition

5. Given a list of strings {"apple", "ape", "april", "apt"}, write a C++ function to find the longest common prefix using a vertical scanning approach. What will be the output of your function?

hard

A. "app"

B. "a"

C. "ap"

D. ""

Solution

1. Step 1: Understand vertical scanning approach

   Check characters column by column across all strings until mismatch or end of any string.

2. Step 2: Apply vertical scanning on given strings

   Index 0: all have 'a'. Index 1: all have 'p'. Index 2: "apple" has 'p', "ape" has 'e' (mismatch). Stop scanning.

3. Final Answer:

   "ap" -> Option C

4. Quick Check:

   Vertical scan stops at first mismatch, prefix = "ap" [OK]

Hint: Scan characters column-wise until mismatch found [OK]

Common Mistakes:

• Assuming prefix is longest word's start
• Stopping scan too early or too late
• Confusing vertical with horizontal scanning