Count and Say Problem in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Count and Say for n=4

What is the output of the following JavaScript code that generates the 4th term of the Count and Say sequence?

DSA Javascript

function countAndSay(n) {
  if (n === 1) return "1";
  const prev = countAndSay(n - 1);
  let result = "";
  let count = 1;
  for (let i = 1; i <= prev.length; i++) {
    if (prev[i] === prev[i - 1]) {
      count++;
    } else {
      result += count + prev[i - 1];
      count = 1;
    }
  }
  return result;
}
console.log(countAndSay(4));

A "21"

B "1211"

C "111221"

D "312211"

💡 Hint

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

The Count and Say sequence starts with "1". The second term describes one '1' as "11". The third term describes two '1's as "21". The fourth term describes one '2' and two '1's as "111221".

❓ Predict Output

intermediate

Output of Count and Say for n=5

What is the output of the following JavaScript code that generates the 5th term of the Count and Say sequence?

DSA Javascript

function countAndSay(n) {
  if (n === 1) return "1";
  const prev = countAndSay(n - 1);
  let result = "";
  let count = 1;
  for (let i = 1; i <= prev.length; i++) {
    if (prev[i] === prev[i - 1]) {
      count++;
    } else {
      result += count + prev[i - 1];
      count = 1;
    }
  }
  return result;
}
console.log(countAndSay(5));

A "111221"

B "211"

C "1211"

D "312211"

💡 Hint

Build the sequence from previous terms.

The 5th term describes three '1's, two '2's, and one '1' from the 4th term "111221", resulting in "312211".

❓ Predict Output

advanced

Output of iterative Count and Say for n=6

What is the output of the following iterative JavaScript code that generates the 6th term of the Count and Say sequence?

DSA Javascript

function countAndSayIterative(n) {
  let result = "1";
  for (let i = 2; i <= n; i++) {
    let temp = "";
    let count = 1;
    for (let j = 1; j <= result.length; j++) {
      if (result[j] === result[j - 1]) {
        count++;
      } else {
        temp += count + result[j - 1];
        count = 1;
      }
    }
    result = temp;
  }
  return result;
}
console.log(countAndSayIterative(6));

A "13112221"

B "312211"

C "111221"

D "1211"

💡 Hint

Iterate from 1 to n, building each term from the previous.

The 6th term describes three '1's, two '2's, and one '1' from the 5th term "111221", resulting in "312211".

❓ Predict Output

advanced

Output of Count and Say for n=3 with a bug in code

What is the output of the following JavaScript code with a subtle bug when generating the 3rd term of the Count and Say sequence?

DSA Javascript

function countAndSayBug(n) {
  if (n === 1) return "1";
  const prev = countAndSayBug(n - 1);
  let result = "";
  let count = 1;
  for (let i = 1; i < prev.length; i++) {
    if (prev[i] === prev[i - 1]) {
      count++;
    } else {
      result += count + prev[i - 1];
      count = 1;
    }
  }
  return result;
}
console.log(countAndSayBug(3));

A "21"

B "1211"

C "111"

D "111221"

💡 Hint

Check the loop boundary and if the last group is counted.

The loop misses processing the last character group because it stops before the last index, so the output is incomplete "21" instead of the full correct term "21" with full count.

🧠 Conceptual

expert

Time Complexity of Count and Say Algorithm

What is the best description of the time complexity of generating the nth term in the Count and Say sequence using the standard iterative approach?

A O(2^n) because the length of the sequence roughly doubles each time

B O(n^2) because each term is generated by scanning the previous term of length proportional to n

C O(n!) because the sequence grows factorially

D O(n) because each term is generated in linear time relative to n

💡 Hint

Consider how the length of each term grows as n increases.

The length of the Count and Say sequence terms grows roughly exponentially, so generating the nth term takes exponential time O(2^n).

Practice

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

easy

A. It sorts numbers in ascending order.

B. It describes the count of digits seen in the previous term.

C. It finds the sum of digits in a number.

D. It reverses the digits of a number.

Solution

1. Step 1: Understand the sequence definition

   The Count and Say sequence describes each term by counting the number of digits appearing consecutively in the previous term.

2. Step 2: Compare options with definition

   Only It describes the count of digits seen in the previous term. matches this description exactly, others describe unrelated operations.

3. Final Answer:

   It describes the count of digits seen in the previous term. -> Option B

4. Quick Check:

   Count and Say = Counting digits [OK]

Hint: Remember: Count and Say counts digits, not sums or sorts [OK]

Common Mistakes:

• Confusing counting digits with summing digits
• Thinking it sorts or reverses digits
• Assuming it generates random sequences

2. Which of the following is the correct JavaScript syntax to start the Count and Say sequence with the first term as '1'?

easy

A. let term = 1;

B. let term = (1);

C. let term = [1];

D. let term = '1';

Solution

1. Step 1: Identify the data type for the term

   The Count and Say sequence terms are strings representing digits, so the first term should be a string '1'.

2. Step 2: Check options for correct string assignment

   let term = '1'; assigns '1' as a string, while others assign number or array types.

3. Final Answer:

   let term = '1'; -> Option D

4. Quick Check:

   Use string for digits in Count and Say [OK]

Hint: Use quotes for digits as strings in Count and Say [OK]

Common Mistakes:

• Using number type instead of string
• Using array instead of string
• Using parentheses which do nothing here

3. What will be the output of the following JavaScript code snippet?

function countAndSay(n) {
  if (n === 1) return '1';
  let prev = countAndSay(n - 1);
  let result = '';
  let count = 1;
  for (let i = 1; i < prev.length; i++) {
    if (prev[i] === prev[i - 1]) {
      count++;
    } else {
      result += count + prev[i - 1];
      count = 1;
    }
  }
  result += count + prev[prev.length - 1];
  return result;
}
console.log(countAndSay(4));

medium

A. "1211"

B. "111221"

C. "21"

D. "312211"

Solution

1. Step 1: Trace recursive calls for n=4

   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 matches '1211'

   The code builds the string by counting consecutive digits correctly, so output is '1211'.

3. Final Answer:

   "1211" -> Option A

4. Quick Check:

   4th term = "1211" [OK]

Hint: Remember sequence: 1, 11, 21, 1211, ... [OK]

Common Mistakes:

• Mixing up counts and digits order
• Off-by-one errors in loops
• Confusing recursive base case

4. Identify the bug in this Count and Say function and select the fix:

function countAndSay(n) {
  if (n === 1) return '1';
  let prev = countAndSay(n - 1);
  let result = '';
  let count = 1;
  for (let i = 1; i < prev.length; i++) {
    if (prev[i] === prev[i - 1]) {
      count++;
    } else {
      result += count + prev[i - 1];
      count = 1;
    }
  }
  return result;
}

medium

A. Add result += count + prev[prev.length - 1]; after loop

B. Initialize count = 0 instead of 1

C. Change loop to for (let i = 1; i < prev.length; i++)

D. Return prev instead of result

Solution

1. Step 1: Analyze loop and indexing

   The loop starts from i=1 and compares prev[i] with prev[i-1]. It increments count for consecutive same digits but only appends when a change is detected (else block). The last group is never appended because the loop ends without processing the trailing group.

2. Step 2: Identify missing last group addition

   The code lacks appending the final count and digit after the loop. Adding result += count + prev[prev.length - 1]; after loop ensures the last group is included.

3. Final Answer:

   Add result += count + prev[prev.length - 1]; after loop -> Option A

4. Quick Check:

   Include last group after loop [OK]

Hint: Always add last counted group after loop [OK]

Common Mistakes:

• Forgetting to add last group after loop
• Changing loop start incorrectly
• Returning wrong variable

5. Given the Count and Say sequence, what is the 6th term?
Use the sequence starting with '1' as the 1st term.

hard

A. "1113213211"

B. "13112221"

C. "312211"

D. "211213"

Solution

1. Step 1: List terms up to 6th

   1st: '1'
   2nd: '11' (one 1)
   3rd: '21' (two 1s)
   4th: '1211' (one 2, one 1)
   5th: '111221' (one 1, one 2, two 1s)
   6th: '312211' (three 1s, two 2s, one 1)

2. Step 2: Confirm 6th term matches option

   "312211" matches '312211' exactly.

3. Final Answer:

   "312211" -> Option C

4. Quick Check:

   6th term = "312211" [OK]

Hint: Build terms stepwise to find nth term [OK]

Common Mistakes:

• Skipping terms or miscounting digits
• Mixing digit counts and digits
• Choosing longer incorrect strings