Count and Say Problem in DSA Typescript - 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 followed by the digit. 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 from the current term in the Count and Say sequence?

You read the current term from left to right, count how many times a digit repeats consecutively, 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 with "1"?

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

intermediate

Why is the Count and Say problem useful for learning algorithms?

It helps practice string manipulation, loops, and understanding how to process sequences step-by-step. It also teaches how to convert one form of data into another by counting and describing.

advanced

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

The time complexity is roughly O(2^n) because the length of the terms can grow exponentially with n, making each generation longer to process.

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

A 211

B 1211

C 22

D 1112

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

What does the term "111221" represent in the Count and Say sequence?

A One 3, two 2s, one 1

B One 1, one 2, two 1s

C One 1, one 1, two 2s, one 1

D Three 1s, two 2s, one 1

"111221" means three 1s, two 2s, and one 1.

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

A 1

B 11

C 0

D 10

The sequence starts with "1".

Which of these best describes the process to get the next term?

A Sort digits and count

B Reverse the digits

C Count consecutive digits and say count then digit

D Add 1 to each digit

You count consecutive digits and say the count followed by the digit.

If the current term is "111", what is the next term?

A 31

B 13

C 1111

D 21

"111" means three 1s, so the next term is "31".

Explain how to generate the nth term in the Count and Say sequence starting from "1".

Think about describing the previous term step-by-step.

Describe why the length of terms in the Count and Say sequence grows quickly.

Consider how each term describes groups of digits from the previous term.

Practice

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

easy

A. It describes each term by counting and saying the digits of the previous term.

B. It sorts the digits of the previous term in ascending order.

C. It adds the digits of the previous term to get the next term.

D. It reverses the digits of the previous term to form the next term.

Solution

1. Step 1: Understand the sequence definition

   The "Count and Say" sequence generates each term by describing the count of digits seen in the previous term.

2. Step 2: Compare options with definition

   Only It describes each term by counting and saying the digits of the previous term. correctly states this process; others describe unrelated operations.

3. Final Answer:

   It describes each term by counting and saying the digits of the previous term. -> Option A

4. Quick Check:

   Count and Say = Describe digits count [OK]

Hint: Remember: count digits, then say them aloud [OK]

Common Mistakes:

• Thinking it sorts digits instead of counting
• Assuming it sums digits for next term
• Confusing with reversing digits

2. Which of the following TypeScript function signatures correctly represents a function that takes a number n and returns the nth term of the Count and Say sequence as a string?

easy

A. function countAndSay(n: number): string

B. function countAndSay(n: string): number

C. function countAndSay(): number

D. function countAndSay(n: number): number[]

Solution

1. Step 1: Identify input and output types

   The function should take a number n (term index) and return a string representing that term.

2. Step 2: Match signature with requirements

   function countAndSay(n: number): string matches input as number and output as string; others mismatch types or parameters.

3. Final Answer:

   function countAndSay(n: number): string -> Option A

4. Quick Check:

   Input number, output string [OK]

Hint: Input is term number, output is sequence string [OK]

Common Mistakes:

• Using wrong input type (string instead of number)
• Returning number or array instead of string
• Missing input parameter

3. What is the output of the following TypeScript code snippet?

function countAndSay(n: number): string {
  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));

medium

A. "21"

B. "111221"

C. "312211"

D. "1211"

Solution

1. Step 1: Trace recursive calls and terms

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

2. Step 2: Confirm output for n=4

   The code returns "1211" for n=4, matching "1211".

3. Final Answer:

   "1211" -> Option D

4. Quick Check:

   Term 4 = "1211" [OK]

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

Common Mistakes:

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

4. Identify the bug in this TypeScript implementation of the Count and Say sequence:

function countAndSay(n: number): string {
  if (n === 1) return "1";
  const prev = countAndSay(n - 1);
  let result = "";
  let count = 1;
  for (let i = 0; i < prev.length; i++) {
    if (prev[i] === prev[i + 1]) {
      count++;
    } else {
      result += count + prev[i];
      count = 1;
    }
  }
  return result;
}

medium

A. The count variable is not reset correctly inside the loop.

B. The loop should start from i = 1, not 0.

C. Accessing prev[i + 1] causes out-of-bounds error on last iteration.

D. The base case should return "0" instead of "1".

Solution

1. Step 1: Analyze loop boundary and indexing

   The loop runs from i=0 to prev.length-1, but accesses prev[i+1], which is undefined at last index.

2. Step 2: Identify error cause

   Accessing prev[i+1] at last iteration causes out-of-bounds access, leading to incorrect behavior or runtime error.

3. Final Answer:

   Accessing prev[i + 1] causes out-of-bounds error on last iteration. -> Option C

4. Quick Check:

   Check array bounds when accessing i+1 [OK]

Hint: Check array access at last index carefully [OK]

Common Mistakes:

• Ignoring last element boundary
• Starting loop at wrong index
• Incorrect base case value

5. Given the Count and Say sequence, what is the 6th term generated by the following TypeScript function?

function countAndSay(n: number): string {
  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(6));

hard

A. "13112221"

B. "312211"

C. "1113213211"

D. "21121314"

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 output matches term 6

   The function returns "312211" for n=6, matching "312211".

3. Final Answer:

   "312211" -> Option B

4. Quick Check:

   Term 6 = "312211" [OK]

Hint: Memorize first 6 terms or trace stepwise [OK]

Common Mistakes:

• Mixing up term 5 and 6
• Miscounting repeated digits
• Skipping recursive calls