38. Count and Say - Detailed Explanation

Problem Statement

Description:
The count-and-say sequence is a sequence of strings where each term is generated by "reading" the previous term and describing the count of consecutive identical digits.

• The sequence starts with "1".
• Each subsequent term is generated by reading the previous term, counting the number of digits in groups of the same digit, and then concatenating the counts and the digits.

For example:

• Term 1: "1"
• Term 2: Read Term 1 as "one 1" → "11"
• Term 3: Read Term 2 as "two 1s" → "21"
• Term 4: Read Term 3 as "one 2, then one 1" → "1211"
• Term 5: Read Term 4 as "one 1, one 2, two 1s" → "111221"

Input:
An integer n (1 ≤ n ≤ 30).

Output:
The nth term of the count-and-say sequence as a string.

Example 1:

• Input: n = 1
• Output: "1"
• Explanation:
  The first term of the sequence is "1".

Example 2:

• Input: n = 4
• Output: "1211"
• Explanation:
  • Term 1: "1"
  • Term 2: "11" (one 1)
  • Term 3: "21" (two 1s)
  • Term 4: "1211" (one 2 followed by one 1)

Hints

• Hint 1:
  The key idea is to generate each term by "reading" the previous term. For each group of consecutive identical digits, record the count followed by the digit.

• Hint 2:
  Use an iterative process (or recursion) where you start with the initial term "1" and build the next term by scanning the current string, counting repeated characters.

• Hint 3:
  Make sure to handle the last group of digits in the string after the loop ends.

Approaches

Iterative Approach (Preferred)

Idea:
Start with the string "1". For each term from 2 up to n, build the next term by iterating over the current term:

1. Initialize a new string builder (or result string).
2. Use a pointer to traverse the current term.
3. Count how many times the same digit appears consecutively.
4. Append the count and the digit to the new string.
5. Replace the current term with the new string and repeat.

Steps:

• Set current = "1".
• For i from 2 to n:
  • Initialize an empty string next = "".
  • For each group of consecutive characters in current:
    • Count the number of characters in that group.
    • Append the count and the character to next.
  • Set current = next.
• Return current as the nth term.

3.2. Recursive Approach

Idea:
Define a recursive function where:

• The base case is n == 1, which returns "1".
• For n > 1, first recursively compute the (n-1)th term, then build the nth term by "reading" that term.

Note:
The iterative approach is typically more straightforward and efficient for this problem.

Detailed Walkthrough (Iterative Approach)

Consider n = 4:

1. Term 1:
   current = "1"

2. Term 2:

   • Read "1" as "one 1" → append "11"
   • Now, current = "11"

3. Term 3:

   • Read "11":
     • There are two 1's → append "21"
   • Now, current = "21"

4. Term 4:

   • Read "21":
     • One 2 → append "12"
     • One 1 → append "11"
   • Concatenate: "12" + "11" = "1211"
   • Now, current = "1211"

Return "1211" as the 4th term.

Code Implementation

Python Code