Count and Say Problem in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Count and Say for n=4

What is the output of the Count and Say sequence for n=4?

DSA C#

public static string CountAndSay(int n) {
    if (n == 1) return "1";
    string prev = CountAndSay(n - 1);
    StringBuilder result = new StringBuilder();
    int count = 1;
    for (int i = 1; i < prev.Length; i++) {
        if (prev[i] == prev[i - 1]) {
            count++;
        } else {
            result.Append(count);
            result.Append(prev[i - 1]);
            count = 1;
        }
    }
    result.Append(count);
    result.Append(prev[prev.Length - 1]);
    return result.ToString();
}

Console.WriteLine(CountAndSay(4));

A "111221"

B "312211"

C "21"

D "1211"

💡 Hint

Trace the sequence from n=1 to n=4 step by step.

The sequence starts with "1" for n=1. Then n=2 is "11" (one 1), n=3 is "21" (two 1s), and n=4 is "1211" (one 2, two 1s).

❓ Predict Output

intermediate

Output of Count and Say for n=5

What is the output of the Count and Say sequence for n=5?

DSA C#

public static string CountAndSay(int n) {
    if (n == 1) return "1";
    string prev = CountAndSay(n - 1);
    StringBuilder result = new StringBuilder();
    int count = 1;
    for (int i = 1; i < prev.Length; i++) {
        if (prev[i] == prev[i - 1]) {
            count++;
        } else {
            result.Append(count);
            result.Append(prev[i - 1]);
            count = 1;
        }
    }
    result.Append(count);
    result.Append(prev[prev.Length - 1]);
    return result.ToString();
}

Console.WriteLine(CountAndSay(5));

A "111221"

B "312211"

C "1211"

D "211211"

💡 Hint

Build the sequence from n=1 to n=5 carefully.

For n=5, the sequence is "111221" which means three 1s, two 2s, and one 1.

🧠 Conceptual

advanced

Understanding the Growth of Count and Say Sequence Length

Which statement best describes the length growth of the Count and Say sequence as n increases?

A The length remains constant for all n.

B The length doubles with each increment of n.

C The length grows approximately by a factor of 1.3 to 1.4 times per step.

D The length decreases as n increases.

💡 Hint

Consider how the sequence describes the previous term.

The length of the sequence grows roughly by a factor between 1.3 and 1.4 each step, not doubling or staying constant.

🔧 Debug

advanced

Identify the Error in Count and Say Implementation

What error will this code produce when calling CountAndSay(3)? public static string CountAndSay(int n) { if (n == 1) return "1"; string prev = CountAndSay(n - 1); StringBuilder result = new StringBuilder(); int count = 1; for (int i = 0; i < prev.Length; i++) { if (prev[i] == prev[i - 1]) { count++; } else { result.Append(count); result.Append(prev[i - 1]); count = 1; } } result.Append(count); result.Append(prev[prev.Length - 1]); return result.ToString(); }

A IndexOutOfRangeException

B NullReferenceException

C No error, returns correct output

D StackOverflowException

💡 Hint

Look at the loop index and how prev[i - 1] is accessed.

The loop starts at i=0 and accesses prev[i - 1], which is prev[-1] on first iteration causing IndexOutOfRangeException.

🚀 Application

expert

Count and Say Sequence - Number of Digits at n=6

How many digits are in the Count and Say sequence output for n=6?

DSA C#

public static string CountAndSay(int n) {
    if (n == 1) return "1";
    string prev = CountAndSay(n - 1);
    StringBuilder result = new StringBuilder();
    int count = 1;
    for (int i = 1; i < prev.Length; i++) {
        if (prev[i] == prev[i - 1]) {
            count++;
        } else {
            result.Append(count);
            result.Append(prev[i - 1]);
            count = 1;
        }
    }
    result.Append(count);
    result.Append(prev[prev.Length - 1]);
    return result.ToString();
}

string output = CountAndSay(6);
int length = output.Length;

A 12

B 6

C 8

D 10

💡 Hint

Calculate the sequence step by step up to n=6 and count digits.

The sequence for n=6 is "312211" which has 6 digits. Sequence lengths: n=1: "1" (length 1) n=2: "11" (length 2) n=3: "21" (length 2) n=4: "1211" (length 4) n=5: "111221" (length 6) n=6: "312211" (length 6)

Practice

1. What does the "Count and Say" sequence start with as its first term?

easy

A. "11"

B. "1"

C. "0"

D. "21"

Solution

1. Step 1: Understand the sequence start

   The "Count and Say" sequence always begins with the string "1" as the first term.

2. Step 2: Confirm the initial term

   This initial term is the base for generating subsequent terms by counting and saying digits.

3. Final Answer:

   "1" -> Option B

4. Quick Check:

   First term = "1" [OK]

Hint: Remember: sequence always starts with "1" [OK]

Common Mistakes:

• Thinking it starts with "0"
• Confusing first term with second term
• Assuming it starts with "11" or "21"

2. Which of the following is the correct C# syntax to declare a method named CountAndSay that takes an integer n and returns a string?

easy

A. public string CountAndSay(int n)

B. string CountAndSay(int n) public

C. public CountAndSay(int n) string

D. public void CountAndSay(int n)

Solution

1. Step 1: Identify correct method declaration syntax

   In C#, method declaration starts with access modifier, then return type, method name, and parameters.

2. Step 2: Match syntax to options

   public string CountAndSay(int n) correctly declares a public method returning string with int parameter.

3. Final Answer:

   public string CountAndSay(int n) -> Option A

4. Quick Check:

   Access modifier + return type + name + parameters = public string CountAndSay(int n) [OK]

Hint: Method syntax: access modifier + return type + name + parameters [OK]

Common Mistakes:

• Placing 'public' after method name
• Using void return type when string is needed
• Incorrect order of return type and method name

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

Console.WriteLine(CountAndSay(4));

string CountAndSay(int n) {
    if (n == 1) return "1";
    string prev = CountAndSay(n - 1);
    StringBuilder result = new StringBuilder();
    int count = 1;
    for (int i = 1; i < prev.Length; i++) {
        if (prev[i] == prev[i - 1]) {
            count++;
        } else {
            result.Append(count).Append(prev[i - 1]);
            count = 1;
        }
    }
    result.Append(count).Append(prev[prev.Length - 1]);
    return result.ToString();
}

medium

A. "312211"

B. "111221"

C. "1211"

D. "21"

Solution

1. Step 1: Trace CountAndSay(4) calls

   CountAndSay(1) = "1"
   CountAndSay(2) = "11" (one 1)
   CountAndSay(3) = "21" (two 1s)
   CountAndSay(4) = "1211" (one 2, one 1)

2. Step 2: Confirm output string for n=4

   The function returns "1211" for input 4 by counting digits in previous term.

3. Final Answer:

   "1211" -> Option C

4. Quick Check:

   Count and Say term 4 = "1211" [OK]

Hint: Build sequence step-by-step from n=1 to n=4 [OK]

Common Mistakes:

• Confusing term 3 and term 4 outputs
• Miscounting repeated digits
• Appending digits in wrong order

4. Identify the bug in this C# method for the Count and Say problem:

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.Length; i++) {
        if (i < prev.Length - 1 && prev[i] == prev[i + 1]) {
            count++;
        } else {
            result += count.ToString() + prev[i];
            count = 1;
        }
    }
    return result;
}

medium

A. Using string concatenation instead of StringBuilder causes performance issues

B. The count variable is not reset correctly

C. The loop condition causes index out of range error

D. Loop index should start at 1, not 0

Solution

1. Step 1: Analyze loop and string concatenation

   The loop logic is correct for counting digits, but string concatenation with += inside loop is inefficient.

2. Step 2: Identify performance issue

   Using string concatenation repeatedly creates many string copies; StringBuilder is preferred for better performance.

3. Final Answer:

   Using string concatenation instead of StringBuilder causes performance issues -> Option A

4. Quick Check:

   String concatenation in loop = performance issue [OK]

Hint: Use StringBuilder for string building inside loops [OK]

Common Mistakes:

• Thinking loop index causes error
• Believing count reset is wrong
• Ignoring performance impact of string concatenation

5. Given the Count and Say sequence, what is the 6th term generated by the following C# method?

string CountAndSay(int n) {
    if (n == 1) return "1";
    string prev = CountAndSay(n - 1);
    StringBuilder result = new StringBuilder();
    int count = 1;
    for (int i = 1; i < prev.Length; i++) {
        if (prev[i] == prev[i - 1]) {
            count++;
        } else {
            result.Append(count).Append(prev[i - 1]);
            count = 1;
        }
    }
    result.Append(count).Append(prev[prev.Length - 1]);
    return result.ToString();
}

Console.WriteLine(CountAndSay(6));

hard

A. "21121314"

B. "13112221"

C. "1113213211"

D. "312211"

Solution

1. Step 1: Generate terms up to 6

   Term 1: "1"
   Term 2: "11" (one 1)
   Term 3: "21" (two 1s)
   Term 4: "1211" (one 2, one 1)
   Term 5: "111221" (one 1, one 2, two 1s)
   Term 6: "312211" (three 1s, two 2s, one 1)

2. Step 2: Confirm term 6 output

   The method returns "312211" for input 6, matching the sequence rules.

3. Final Answer:

   "312211" -> Option D

4. Quick Check:

   Count and Say term 6 = "312211" [OK]

Hint: Build sequence stepwise from term 1 to 6 [OK]

Common Mistakes:

• Skipping terms or miscounting digits
• Mixing up digits order in output
• Choosing longer incorrect strings