Count and Say Problem in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the 'Count and Say' sequence?

It is a sequence where each term is generated by describing the previous term's digits as counts of numbers. For example, starting with '1', the next term is '11' (one 1), then '21' (two 1s), then '1211' (one 2, one 1), and so on.

beginner

How do you generate the next term in the Count and Say sequence from the current term?

Read the current term from left to right, count consecutive identical digits, then say the count followed by the digit. Repeat this for the entire term to form the next term.

beginner

What is the 5th term in the Count and Say sequence starting from '1'?

The 5th term is '111221'. The sequence goes: 1, 11, 21, 1211, 111221.

intermediate

In C++, which data structure is best suited to build the next term in the Count and Say sequence efficiently?

Using a std::string to build the next term is efficient because it allows easy appending of characters and is suitable for storing sequences of digits.

advanced

What is the time complexity of generating the nth term in the Count and Say sequence?

The time complexity is approximately O(2^n) because the length of the terms roughly doubles each time, making the generation cost grow exponentially with n.

What is the next term after '21' in the Count and Say sequence?

A 1211

B 1112

C 22

D 211

The term '21' means 'one 2, one 1', so the next term is '1211'.

Which of the following best describes the process to generate the next term?

A Add 1 to each digit

B Count digits and say the count followed by the digit

C Reverse the current term

D Sort the digits in ascending order

The next term is generated by counting consecutive digits and saying the count followed by the digit.

What is the first term of the Count and Say sequence?

A 11

B 0

C 1

D 21

The sequence starts with '1' as the first term.

If the current term is '111221', what is the next term?

A 221111

B 13112221

C 111221

D 312211

'111221' is read as three 1s, two 2s, one 1, so next term is '312211'.

Which C++ standard library type is most suitable to store the Count and Say terms?

A std::string

B std::map<int,int>

C std::list<char>

D std::vector<int>

std::string is ideal for storing sequences of digits as characters and supports easy appending.

Explain how to generate the nth term of the Count and Say sequence starting from '1'.

Think about describing the previous term in words as counts of digits.

Describe the time complexity and why generating the Count and Say sequence grows exponentially.

Consider how the length of terms changes as n increases.

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