Count and Say Problem in DSA C# - Execution Trace

Concept Flow - Count and Say Problem

Start with '1'

↓

Read current string

↓

Count consecutive digits

↓

Build next string: 'count' + 'digit'

↓

Repeat until n-th term

↓

Output final string

The process starts with '1', then reads the string, counts consecutive digits, builds the next string by saying counts and digits, and repeats until the desired term.

Execution Sample

DSA C#

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 (i == prev.Length || prev[i] != prev[i - 1]) {
      result.Append(count).Append(prev[i - 1]);
      count = 1;
    } else {
      count++;
    }
  }
  return result.ToString();
}

This code recursively generates the n-th term of the count and say sequence by reading the previous term and counting consecutive digits.

Execution Table

Step	Operation	Current String	Count	Digit	Next String Built	Visual State
1	Start with base case	1	N/A	N/A	1	1
2	Read '1', count consecutive digits	1	1	1	11	1 -> 11
3	Read '11', count consecutive digits	11	2	1	21	1 -> 11 -> 21
4	Read '21', count digits	21	1	2	1211	1 -> 11 -> 21 -> 1211
5	Read '1211', count digits	1211	1	1	111221	1 -> 11 -> 21 -> 1211 -> 111221
6	Read '111221', count digits	111221	3	1	312211	1 -> 11 -> 21 -> 1211 -> 111221 -> 312211
7	Reached desired term or continue	312211	N/A	N/A	Output final string	Final output: 312211

💡 Reached the n-th term, output the final string.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
prev	N/A	1	11	21	1211	111221	312211
count	N/A	1	2	1	1	3	N/A
result (next string)	N/A	11	21	1211	111221	312211	312211

Key Moments - 3 Insights

Why do we append count and digit only when the next digit is different or at the end?

Because we need to group consecutive same digits together. The execution_table rows 2-6 show that counting continues until a different digit appears or the string ends, then we append the count and digit.

Why does the loop run until i <= prev.Length instead of i < prev.Length?

To handle the last group of digits properly. At i == prev.Length, we append the last counted group. This is shown in execution_table rows where the last group is appended at the end.

How does recursion help in building the sequence?

Each call depends on the previous term. The variable_tracker shows 'prev' changing each step, building from '1' up to the desired term.

Visual Quiz - 3 Questions

Look at the execution_table at Step 4, what is the 'Next String Built'?

A 1211

B 21

C 111221

D 312211

💡 Hint

Check the 'Next String Built' column at Step 4 in the execution_table.

At which step does the count reach 3 for digit '1'?

A Step 3

B Step 6

C Step 5

D Step 4

💡 Hint

Look at the 'Count' column in the execution_table and variable_tracker for digit '1'.

If the initial string was '2' instead of '1', how would Step 2's 'Next String Built' change?

A It would be '21'

B It would be '11'

C It would be '12'

D It would be '22'

💡 Hint

The count and say says count then digit, so count 1 of digit '2' becomes '12' or '21'?

Concept Snapshot

Count and Say Problem:
- Start with '1' as first term.
- For each term, read previous term.
- Count consecutive digits and say count + digit.
- Repeat until n-th term.
- Use recursion or iteration to build sequence.

Full Transcript

The Count and Say problem generates a sequence where each term describes the previous term's digits. Starting from '1', each next term is built by counting consecutive digits and saying the count followed by the digit. The process repeats until the desired term is reached. The code uses recursion to get the previous term, then loops through it counting digits and building the next string. Key points include appending count and digit when the next digit differs or at the end, and handling the last group properly by looping until the length of the string. The variable 'prev' holds the previous term, 'count' tracks consecutive digits, and 'result' builds the next term. The execution table shows step-by-step how the string evolves from '1' to '312211' for the 6th term.

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