Count and Say Problem in DSA Typescript

Mental Model

We describe a number by counting how many times each digit appears in order and then saying that count and digit out loud.

Analogy: Imagine reading a list of colored beads aloud by saying how many beads of each color you see in a row, like 'two red, one blue'.

1 -> 11 -> 21 -> 1211 -> 111221 -> null

Dry Run Walkthrough

Input: Generate the 5th term starting from '1'

Goal: Find the 5th number in the count and say sequence

Step 1: Start with '1' as the first term

'1'

Why: This is the base term to describe

Step 2: Read '1' as 'one 1', so second term is '11'

'11'

Why: We count one '1' and say it

Step 3: Read '11' as 'two 1s', so third term is '21'

'21'

Why: We count two '1's and say it

Step 4: Read '21' as 'one 2, one 1', so fourth term is '1211'

'1211'

Why: We count one '2' then one '1'

Step 5: Read '1211' as 'one 1, one 2, two 1s', so fifth term is '111221'

'111221'

Why: We count one '1', one '2', then two '1's

Result:

'111221' is the 5th term in the sequence

Annotated Code

DSA Typescript

class CountAndSay {
  static countAndSay(n: number): string {
    if (n === 1) return '1';
    const prev = this.countAndSay(n - 1);
    let result = '';
    let count = 1;
    for (let i = 1; i <= prev.length; i++) {
      if (i < prev.length && prev[i] === prev[i - 1]) {
        count++;
      } else {
        result += `${count}${prev[i - 1]}`;
        count = 1;
      }
    }
    return result;
  }
}

// Driver code
const n = 5;
console.log(CountAndSay.countAndSay(n));

if (n === 1) return '1';

Base case: first term is '1'

const prev = this.countAndSay(n - 1);

Recursively get previous term

for (let i = 1; i <= prev.length; i++) {

Traverse previous term to count digits

if (i < prev.length && prev[i] === prev[i - 1]) { count++; }

Count consecutive same digits

else { result += `${count}${prev[i - 1]}`; count = 1; }

Append count and digit, reset count

Output

111221

Complexity Analysis

Time: O(2^n) because each term can roughly double in length compared to the previous term

Space: O(2^n) because the output string grows exponentially with n

vs Alternative: No simpler approach exists since each term depends on fully processing the previous term

Edge Cases

n = 1 (smallest input)

Returns '1' immediately as base case

DSA Typescript

if (n === 1) return '1';

n = 0 or negative (invalid input)

No explicit handling; function may recurse infinitely or error

DSA Typescript

No guard; user should input n >= 1

When to Use This Pattern

When asked to generate a sequence where each term describes the previous term's digits, use the Count and Say pattern to build terms step-by-step.

Common Mistakes

Mistake: Not resetting the count after appending a group to the result
Fix: Reset count to 1 after appending count and digit

Mistake: Off-by-one error in loop causing index out of bounds
Fix: Loop up to i <= prev.length and handle last group in else block

Summary

Generates the nth term of the count and say sequence by describing digits of the previous term.

Use when you need to build a sequence where each term narrates the count of digits in the previous term.

The key insight is to group consecutive digits and say their count followed by the digit.

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