Count and Say

class Solution {
public:
    string countAndSay(int n) {
        regex pattern("(.)\\1*");
        string result = "1";
        for (int i = 2; i <= n; i++) {
            string temp;
            for (sregex_iterator it = sregex_iterator(result.begin(), result.end(), pattern);
                 it != sregex_iterator(); it++) {
                temp += to_string(it->str().length()) + it->str(1);
            }
            result = temp;
        }
        return result;
    }
};

The solution for the "Count and Say" problem in C++ involves generating a sequence where each term is a verbal description of the previous term's digits, starting with "1". The provided code achieves this using a regex pattern to group consecutive similar digits in the string.

• The countAndSay function takes an integer n as its parameter and returns the n-th term of the count-and-say sequence.
• To create the sequence, start with the string "1".
• Use a loop to iteratively build each term from the second to the n-th term.
• Utilize the regex library with the pattern "(.)\\1*" which matches any digit followed by zero or more occurrences of the same digit.
• Iterate over matches using sregex_iterator, construct the next sequence term by concatenating the count of digits and the digit itself.
• Update result with this sequence for each iteration until reaching term n.
• Finally, the function returns the n-th term of the sequence.

This approach efficiently builds each term based on the description of the previous term, leveraging regular expressions for pattern matching to count and describe consecutive digits. This C++ solution is an elegant implementation leveraging string manipulation and regular expressions to solve the problem without auxiliary functions or complex logic.

import java.util.regex.Matcher;
import java.util.regex.Pattern;

class Solution {
    public String sequenceGenerator(int count) {
        String output = "1";
        Pattern regex = Pattern.compile("(.)\\1*");
        for (int index = 1; index < count; ++index) {
            Matcher match = regex.matcher(output);
            StringBuffer newString = new StringBuffer();
            while (match.find()) {
                newString.append(match.group().length() + match.group().charAt(0));
            }
            output = newString.toString();
        }
        return output;
    }
}

The "Count and Say" problem involves generating the n-th term of a sequence where each term is a read-off of the count of each group of similar digits in the previous term. The Java solution provided implements a method called sequenceGenerator in a class Solution. This method takes an integer count as an argument and generates the count-th sequence string following these steps:

1. Initialize the output string with the starting sequence "1".
2. Define a regex pattern to match consecutive identical characters using Pattern.compile("(.)\\1*").
3. Iterate from 1 to count - 1. For each iteration:
   1. Use a Matcher to find and process each sequence of identical characters in the current output.
   2. For each match found, append to a new StringBuffer the length of the match and the character of the match (essentially "saying" how many of a particular character there are).
4. Update output with the newly constructed string from StringBuffer.
5. After completing all iterations, return the final output.

The approach efficiently creates each sequence in the series by using regex to group and count consecutive identical characters, and then constructing the next sequence based on these counts. This solution harnesses Java's Pattern and Matcher classes for regex operations and string manipulation capabilities to build the sequence iteratively.

char *sequenceGenerate(int length) {
    char *result = (char *)malloc(5000 * sizeof(char));
    strcpy(result, "1");
    for (int step = 2; step <= length; step++) {
        char *next = (char *)malloc(5000 * sizeof(char));
        int index = 0;
        for (int pos = 0; pos < strlen(result);) {
            int freq = 0;
            while (result[pos] == result[pos + freq]) freq++;
            next[index++] = (char)(freq + '0');
            next[index++] = result[pos];
            pos += freq;
        }
        next[index] = '\0';
        free(result);
        result = next;
    }
    return result;
}

The provided C code implements a solution to the "Count and Say" problem, generating the sequence up to a given length. Follow these steps to understand how the sequence is constructed and how the function operates:

1. Memory Allocation for Result: Initially, memory is allocated for the result string which can hold up to 5000 characters. This string stores the current sequence.

2. Initial Sequence Setup: Starts with the "1" sequence.

3. Loop Through Each Step: Iterations begin from 2 up to the desired sequence length.

4. Generate Next Sequence:

   • Allocate memory for the next string which will store the new sequence generated in the current iteration.
   • Initialize an index to keep track of the position in the next sequence string.

5. Count Frequencies:

   • For each character in result, count how many times it consecutively appears using a nested loop.
   • Convert the count (frequency) to a character and store it followed by the character itself into the next string.

6. Update and Clean Up:

   • Null-terminate the next string.
   • Free the memory allocated for the result of the previous sequence.
   • Update result to point to next.

7. Final Output:

   • After completing all iterations, return the final result string, which represents the sequence for the given length.

This efficient procedure leverages dynamic memory allocation, careful counting of character frequencies, and iterative building of the sequence string. Each step carefully builds upon the last, ensuring that the sequence is correctly formed for each integer increment up to the desired length. Memory management is crucial as each iteration involves freeing and reallocating memory to avoid leaks.

var countSaySequence = function (sequenceNumber) {
    let current = "1";
    for (let index = 2; index <= sequenceNumber; index++) {
        let nextSeq = "";
        const sequencePattern = /(.)\1*/g;
        let patternMatch;
        while ((patternMatch = sequencePattern.exec(current)) !== null) {
            nextSeq += patternMatch[0].length.toString() + patternMatch[1];
        }
        current = nextSeq;
    }
    return current;
};

The "Count and Say" problem involves generating a sequence where each term describes the count of each group of consecutive digits in the previous term. The solution provided is a JavaScript function that computes the sequence up to the desired term number. Follow these steps within the code to understand how it achieves this:

• Initialize current as the starting sequence string "1".
• Use a loop starting from 2 up to the given sequenceNumber. This loop iterates through each sequence number counting and saying based on current.
• Inside the loop, create an empty string nextSeq that builds the next sequence.
• Define a regular expression sequencePattern = /(.)\1*/g to match groups of consecutive identical digits.
• Utilize a while loop to process matches found by executing the regex pattern on current. This loop continues until no more matches exist.
• For each match found, append to nextSeq the length of the consecutive digits (number of repeats) followed by the digit itself.
• Assign nextSeq to current after processing all groups of digits for the current sequence.

At the end of the function, return current which contains the desired count and say sequence for the specified term number.

Remember to:

• Ensure the input sequenceNumber is a positive integer greater than 0 to avoid errors or unexpected behaviors.
• Observe how the regular expression effectively identifies and groups the recurring digits, which is pivotal for constructing the sequence.
• Keep in mind that the output sequence’s length grows exponentially as sequenceNumber increases, thus managing larger values might impact performance.

class Solution:
    def compute_sequence(self, num: int) -> str:
        current = "1"
        for _ in range(num - 1):
            current = re.sub(
                r"(.)\1*", lambda match: str(len(match.group(0))) + match.group(1), current
            )
        return current

The provided Python solution addresses the "Count and Say" problem by utilizing regular expressions to generate sequential terms. The solution class, named Solution, contains the method compute_sequence, which takes an integer num as the input and returns the num-th term of the Count and Say sequence as a string.

Follow these steps to understand the solution:

1. Initialize a variable current with the string "1", which is the base case of the sequence.
2. Iterate num - 1 times to generate the sequence up to the desired term.
3. In each iteration, use a regular expression to group consecutive identical characters in the current string.
4. Replace each group with the count of characters in the group followed by the character itself, using re.sub() function.
5. The lambda function in re.sub() computes the replacement string for each match, concatenating the length of the match and the matched character.
6. After completing all iterations, the function returns the final value of current representing the num-th term of the sequence.

This solution efficiently constructs each term by building upon the previous term, iterating through the sequence only as many times as required, making it scalable for larger inputs.