Count and Say Problem in DSA C++ - Build from Scratch

Count and Say Problem

📖 Scenario: Imagine you are working with a special sequence of numbers called the "Count and Say" sequence. Each term describes the previous term by counting the number of digits in groups. For example, starting with "1", the next term says "one 1" which is "11", then "two 1s" which is "21", and so on.

🎯 Goal: You will build a program that generates the n-th term of the Count and Say sequence using simple loops and string operations.

📋 What You'll Learn

Create a string variable to hold the starting term "1"

Create an integer variable n to represent which term to generate

Use a loop to generate terms from 2 up to n

Inside the loop, read the previous term and build the next term by counting consecutive digits

Print the final generated term

💡 Why This Matters

🌍 Real World

The Count and Say sequence is a classic example of run-length encoding, which is used in data compression and pattern recognition.

💼 Career

Understanding string manipulation and sequence generation is useful in software development, especially in areas like data processing, compression algorithms, and coding interviews.

1

Setup the starting term and target term number

Create a string variable called term and set it to "1". Also create an integer variable called n and set it to 5.

DSA C++

# Your code here

Hint

Start by storing the first term "1" in a string variable named term. Then set n to 5 to find the 5th term.

2

Prepare a loop to generate terms up to n

Write a for loop with an integer variable i starting from 2 up to and including n.

DSA C++

std::string term = "1";
int n = 5;

// Your code here

Hint

Use a for loop starting at 2 because the first term is already set. Loop until i equals n.

3

Build the next term by counting digits

Inside the loop, create a new empty string called next_term. Use a while loop with an index j to read term. Count consecutive identical digits and append the count and digit to next_term. After processing, assign next_term to term.

DSA C++

std::string term = "1";
int n = 5;

for (int i = 2; i <= n; i++) {
    // Your code here
}

Hint

Use two nested loops: the outer while to scan the string, and the inner while to count repeated digits. Append count and digit to next_term.

4

Print the final term

Write a std::cout statement to print the variable term followed by a newline.

DSA C++

Hint

Use std::cout << term << std::endl; to print the final term.

Practice

1. What does the "Count and Say" sequence represent in simple terms?

easy

A. A sequence where each term describes the count of digits in the previous term

B. A sequence of random numbers generated by counting

C. A sequence where each term is the sum of previous two terms

D. A sequence of prime numbers only

Solution

1. Step 1: Understand the sequence definition

   The Count and Say sequence generates each term by describing the digits of the previous term.

2. Step 2: Example of the sequence

   Starting with "1", the next term is "11" (one 1), then "21" (two 1s), and so on.

3. Final Answer:

   A sequence where each term describes the count of digits in the previous term -> Option A

4. Quick Check:

   Count and Say = describe previous term counts [OK]

Hint: Remember: each term says counts of digits in previous term [OK]

Common Mistakes:

• Thinking it's a sum sequence
• Confusing with random or prime sequences
• Ignoring the description aspect

2. Which of the following is the correct way to start the Count and Say sequence in C++?

easy

A. int s = 1;

B. vector<int> s = {1};

C. char s = '1';

D. string s = "1";

Solution

1. Step 1: Identify the data type for sequence terms

   Each term is a string representing digits, so string type is appropriate.

2. Step 2: Check initialization

   Initializing with string "1" correctly starts the sequence.

3. Final Answer:

   string s = "1"; -> Option D

4. Quick Check:

   Sequence terms are strings, so string initialization [OK]

Hint: Use string type to hold digit sequences [OK]

Common Mistakes:

• Using int instead of string
• Using char which holds only one character
• Using vector<int> unnecessarily

3. What is the output of the following C++ code snippet for n = 4?

string countAndSay(int n) {
    if (n == 1) return "1";
    string prev = countAndSay(n - 1);
    string result = "";
    int count = 1;
    for (int i = 1; i <= prev.size(); i++) {
        if (i < prev.size() && prev[i] == prev[i - 1]) {
            count++;
        } else {
            result += to_string(count) + prev[i - 1];
            count = 1;
        }
    }
    return result;
}

cout << countAndSay(4);

medium

A. 21

B. 111221

C. 1211

D. 312211

Solution

1. Step 1: Trace the sequence up to n=4

   n=1: "1"; n=2: "11" (one 1); n=3: "21" (two 1s); n=4: "1211" (one 2, one 1)

2. Step 2: Confirm code logic matches sequence

   The code counts consecutive digits and appends count + digit, matching the sequence.

3. Final Answer:

   1211 -> Option C

4. Quick Check:

   Count and Say term 4 = 1211 [OK]

Hint: Write terms stepwise to avoid confusion [OK]

Common Mistakes:

• Confusing term 3 and 4
• Miscounting consecutive digits
• Off-by-one errors in loop

4. Identify the bug in this C++ code snippet for Count and Say:

string countAndSay(int n) {
    if (n == 1) return "1";
    string prev = countAndSay(n - 1);
    string result = "";
    int count = 1;
    for (int i = 0; i < prev.size(); i++) {
        if (i + 1 < prev.size() && prev[i] == prev[i + 1]) {
            count++;
        } else {
            result += to_string(count) + prev[i];
            count = 1;
        }
    }
    return result;
}

medium

A. No bug, code is correct

B. Count variable is not reset properly

C. Loop index should start from 1, not 0

D. The condition in if statement should compare prev[i] and prev[i-1]

Solution

1. Step 1: Analyze loop and conditions

   The loop starts at 0 and compares current and next characters correctly.

2. Step 2: Check count reset and result building

   Count increments on matching digits and resets after appending count and digit to result.

3. Final Answer:

   No bug, code is correct -> Option A

4. Quick Check:

   Loop and count logic correct [OK]

Hint: Check loop indices and comparisons carefully [OK]

Common Mistakes:

• Starting loop at 1 causing index errors
• Incorrect comparison direction
• Forgetting to reset count

5. Given the Count and Say sequence starting with "1", what is the 6th term in the sequence?

hard

A. 1211

B. 312211

C. 1113213211

D. 13112221

Solution

1. Step 1: List terms up to 6

   Term 1: "1"; Term 2: "11"; Term 3: "21"; Term 4: "1211"; Term 5: "111221"; Term 6: "312211"

2. Step 2: Confirm term 6 matches option

   Term 6 describes term 5: three 1s, two 2s, one 1 -> "312211"

3. Final Answer:

   312211 -> Option B

4. Quick Check:

   Term 6 = 312211 by counting term 5 digits [OK]

Hint: Write terms stepwise to avoid confusion [OK]

Common Mistakes:

• Mixing term 5 and 6
• Miscounting digits in term 5
• Skipping terms or misreading digits