Look-and-Say Sequence

Find the n’th term in Look-and-say (Or Count and Say) Sequence. The look-and-say sequence is the sequence of the below integers: 
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, … 

How is the above sequence generated?
n’th term is generated by reading (n-1)’th term.

The first term is "1"

Second term is "11", generated by reading first term as "One 1" 
(There is one 1 in previous term)

Third term is "21", generated by reading second term as "Two 1"

Fourth term is "1211", generated by reading third term as "One 2 One 1" 

and so on

How to find n’th term? 

Example:

Input: n = 3
Output: 21

Input: n = 5
Output: 111221

The idea is simple, we generate all terms from 1 to n. First, two terms are initialized as “1” and “11”, and all other terms are generated using previous terms. To generate a term using the previous term, we scan the previous term. While scanning a term, we simply keep track of the count of all consecutive characters. For a sequence of the same characters, we append the count followed by the character to generate the next term.

Below is an implementation of the above idea.  

C++

// C++ program to find n'th term in look and say
// sequence
#include <bits/stdc++.h>
using namespace std;

// Returns n'th term in look-and-say sequence
string countnndSay(int n)
{
    // Base cases
    if (n == 1)      return "1";
    if (n == 2)      return "11";

    // Find n'th term by generating all terms from 3 to
    // n-1.  Every term is generated using previous term
    string str = "11"; // Initialize previous term
    for (int i = 3; i<=n; i++)
    {
        // In below for loop, previous character
        // is processed in current iteration. That
        // is why a dummy character is added to make
        // sure that loop runs one extra iteration.
        str += '$';
        int len = str.length();

        int cnt = 1; // Initialize count of matching chars
        string  tmp = ""; // Initialize i'th term in series

        // Process previous term to find the next term
        for (int j = 1; j < len; j++)
        {
            // If current character doesn't match
            if (str[j] != str[j-1])
            {
                // Append count of str[j-1] to temp
                tmp += cnt + '0';

                // Append str[j-1]
                tmp += str[j-1];

                // Reset count
                cnt = 1;
            }

            //  If matches, then increment count of matching
            // characters
            else cnt++;
        }

        // Update str
        str = tmp;
    }

    return str;
}

// Driver program
int main()
{
    int N = 3;
    cout << countnndSay(N) << endl;
    return 0;
}

Java

// Java program to find n'th
// term in look and say sequence

class GFG
{

    // Returns n'th term in
    // look-and-say sequence
    static String countnndSay(int n)
    {
    // Base cases
    if (n == 1)     return "1";
    if (n == 2)     return "11";

    // Find n'th term by generating
    // all terms from 3 to n-1.
    // Every term is generated
    // using previous term

    // Initialize previous term
    String str = "11";
    for (int i = 3; i <= n; i++)
    {
        // In below for loop, previous
        // character is processed in
        // current iteration. That is
        // why a dummy character is
        // added to make sure that loop
        // runs one extra iteration.
        str += '$';
        int len = str.length();

        int cnt = 1; // Initialize count
                     // of matching chars
        String tmp = ""; // Initialize i'th
                         // term in series
        char []arr = str.toCharArray();

        // Process previous term
        // to find the next term
        for (int j = 1; j < len; j++)
        {
            // If current character
            // doesn't match
            if (arr[j] != arr[j - 1])
            {
                // Append count of
                // str[j-1] to temp
                tmp += cnt + 0;

                // Append str[j-1]
                tmp += arr[j - 1];

                // Reset count
                cnt = 1;
            }

            // If matches, then increment
            // count of matching characters
            else cnt++;
        }

        // Update str
        str = tmp;
    }

    return str;
    }

    // Driver Code
    public static void main(String[] args)
    {
        int N = 3;
        System.out.println(countnndSay(N));
    }
}

// This code is contributed
// by ChitraNayal

C#

// C# program to find n'th
// term in look and say sequence
using System;

class GFG
{

    // Returns n'th term in
    // look-and-say sequence
    static string countnndSay(int n)
    {
    // Base cases
    if (n == 1)     return "1";
    if (n == 2)     return "11";

    // Find n'th term by generating
    // all terms from 3 to n-1.
    // Every term is generated using
    // previous term

    // Initialize previous term
    string str = "11";
    for (int i = 3; i <= n; i++)
    {
        // In below for loop, previous
        // character is processed in
        // current iteration. That is
        // why a dummy character is
        // added to make sure that loop
        // runs one extra iteration.
        str += '$';
        int len = str.Length;

        int cnt = 1; // Initialize count of
                     // matching chars
        string tmp = ""; // Initialize i'th
                         // term in series
        char []arr = str.ToCharArray();

        // Process previous term
        // to find the next term
        for (int j = 1; j < len; j++)
        {
            // If current character
            // doesn't match
            if (arr[j] != arr[j - 1])
            {
                 // Append count of
                // str[j-1] to temp
                tmp += cnt + 0;

                // Append str[j-1]
                tmp += arr[j - 1];

                // Reset count
                cnt = 1;
            }

            // If matches, then increment
            // count of matching characters
            else cnt++;
        }

        // Update str
        str = tmp;
    }

    return str;
    }

    // Driver Code
    public static void Main()
    {
        int N = 3;
        Console.Write(countnndSay(N));
    }
}

// This code is contributed
// by ChitraNayal

Python3

# Python 3 program to find
# n'th term in look and
# say sequence

# Returns n'th term in
# look-and-say sequence
def countnndSay(n):

    # Base cases
    if (n == 1):
        return "1"
    if (n == 2):
        return "11"

    # Find n'th term by generating
    # all terms from 3 to n-1.
    # Every term is generated using
    # previous term

    # Initialize previous term
    s = "11"
    for i in range(3, n + 1):

        # In below for loop,
        # previous character is
        # processed in current
        # iteration. That is why
        # a dummy character is
        # added to make sure that
        # loop runs one extra iteration.
        s += '$'
        l = len(s)

        cnt = 1 # Initialize count
                # of matching chars
        tmp = "" # Initialize i'th
                 # term in series

        # Process previous term to
        # find the next term
        for j in range(1 , l):

            # If current character
            # doesn't match
            if (s[j] != s[j - 1]):

                # Append count of
                # str[j-1] to temp
                tmp += str(cnt + 0)

                # Append str[j-1]
                tmp += s[j - 1]

                # Reset count
                cnt = 1

            # If matches, then increment
            # count of matching characters
            else:
                cnt += 1

        # Update str
        s = tmp
    return s;

# Driver Code
N = 3
print(countnndSay(N))

# This code is contributed
# by ChitraNayal

PHP

<?php
// PHP program to find
// n'th term in look
// and say sequence

// Returns n'th term in
// look-and-say sequence
function countnndSay($n)
{
    // Base cases
    if ($n == 1)
        return "1";
    if ($n == 2)
        return "11";

    // Find n'th term by generating
    // all terms from 3 to n-1.
    // Every term is generated
    // using previous term

    // Initialize previous term
    $str = "11";
    for ($i = 3;
         $i <= $n; $i++)
    {
        // In below for loop,
        // previous character is
        // processed in current
        // iteration. That is why
        // a dummy character is
        // added to make sure that
        // loop runs one extra iteration.
        $str = $str.'$';
        $len = strlen($str);

        $cnt = 1; // Initialize count of
                  // matching chars
        $tmp = ""; // Initialize i'th
                   // term in series

        // Process previous term
        // to find the next term
        for ($j = 1; $j < $len; $j++)
        {
            // If current character
            // doesn't match
            if ($str[$j] != $str[$j - 1])
            {
                // Append count of
                // str[j-1] to temp
                $tmp = $tmp.$cnt + 0;

                // Append str[j-1]
                $tmp = $tmp. $str[$j - 1];

                // Reset count
                $cnt = 1;
            }

            // If matches, then increment
            // count of matching characters
            else $cnt++;
        }

        // Update str
        $str = $tmp;
    }

    return $str;
}

// Driver Code
$N = 3;
echo countnndSay($N);
return 0;

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>

// Javascript program to find n'th
// term in look and say sequence

// Returns n'th term in
// look-and-say sequence
function countnndSay(n)
{

    // Base cases
    if (n == 1)
        return "1";
    if (n == 2)
        return "11";

    // Find n'th term by generating
    // all terms from 3 to n-1.
    // Every term is generated
    // using previous term

    // Initialize previous term
    let str = "11";

    for(let i = 3; i <= n; i++)
    {

        // In below for loop, previous
        // character is processed in
        // current iteration. That is
        // why a dummy character is
        // added to make sure that loop
        // runs one extra iteration.
        str += '$';
        let len = str.length;

        // Initialize count
        // of matching chars
        let cnt = 1;

        // Initialize i'th
        // term in series
        let tmp = "";
        let arr = str.split("");

        // Process previous term
        // to find the next term
        for(let j = 1; j < len; j++)
        {

            // If current character
            // doesn't match
            if (arr[j] != arr[j - 1])
            {

                // Append count of
                // str[j-1] to temp
                tmp += cnt + 0;

                // Append str[j-1]
                tmp += arr[j - 1];

                // Reset count
                cnt = 1;
            }

            // If matches, then increment
            // count of matching characters
            else cnt++;
        }

        // Update str
        str = tmp;
    }
    return str;
}

// Driver Code
let N = 3;

document.write(countnndSay(N));

// This code is contributed by avanitrachhadiya2155

</script>

Output

21

Another Approach(Using STL): There is one more idea where we can use unordered_map from c++ stl to track the count of digits. Basic idea is to use a generator function that will generate a string from the previous string. In the count and say function we will iterate over integers from 1 to n-1 and keep updating our result.

C++

#include <bits/stdc++.h>
using namespace std;

// generator function returns int string from prev int
// string e.g. -> it will return '1211' for '21' ( One 2's
// and One 1)
string generator(string str)
{
    string ans = "";

    unordered_map<char, int>
        tempCount; // It is used to count integer sequence

    for (int i = 0; i < str.length() + 1; i++) {
        // when current char is different from prev one we
        // clear the map and update the ans
        if (tempCount.find(str[i]) == tempCount.end()
            && i > 0) {
            auto prev = tempCount.find(str[i - 1]);
            ans += to_string(prev->second) + prev->first;
            tempCount.clear();
        }
        // when current char is same as prev one we increase
        // it's count value
        tempCount[str[i]]++;
    }

    return ans;
}

string countnndSay(int n)
{
    string res = "1"; // res variable keep tracks of string
                      // from 1 to n-1

    // For loop iterates for n-1 time and generate strings
    // in sequence "1" -> "11" -> "21" -> "1211"
    for (int i = 1; i < n; i++) {
        res = generator(res);
    }

    return res;
}

int main()
{

    int N = 3;
    cout << countnndSay(N) << endl;
    return 0;
}

Java

import java.io.*;
import java.util.*;

class GFG {
  // generator function returns int string from prev int
  // string e.g. -> it will return '1211' for '21' ( One 2's
  // and One 1)
  static String generator(String str)
  {
    String ans = "";

    HashMap<Character, Integer>tempCount = new HashMap<>(); // It is used to count integer sequence

    for (int i = 0; i < str.length() + 1; i++) {
      // when current char is different from prev one we
      // clear the map and update the ans
      if (i == str.length()  || tempCount.containsKey(str.charAt(i)) == false && i > 0) {
        ans += String.valueOf(tempCount.get(str.charAt(i-1))) + str.charAt(i-1);
        tempCount.clear();
      }
      // when current char is same as prev one we increase
      // it's count value

      if(i == str.length()){
        tempCount.put(null, 1);
      }
      else{
        if(tempCount.containsKey(str.charAt(i))){
          tempCount.put(str.charAt(i), tempCount.get(str.charAt(i))+1);
        }
        else{
          if(i != str.length())tempCount.put(str.charAt(i), 1);
        }
      }
    }
    return ans;
  }

  static String countnndSay(int n)
  {
    String res = "1"; // res variable keep tracks of string
    // from 1 to n-1

    // For loop iterates for n-1 time and generate strings
    // in sequence "1" -> "11" -> "21" -> "1211"
    for (int i = 1; i < n; i++) {
      res = generator(res);
    }

    return res;
  }

  // Driver Code
  public static void main(String args[])
  {
    int N = 3;
    System.out.println(countnndSay(N));
  }
}

// This code is contributed by shinjanpatra

Javascript

<script>
// generator function returns int string from prev int
// string e.g. -> it will return '1211' for '21' ( One 2's
// and One 1)
function generator(str)
{
    let ans = "";

    let tempCount = new Map(); // It is used to count integer sequence

    for ( i = 0; i < str.length + 1; i++)
    {

        // when current char is different from prev one we
        // clear the map and update the ans
        if (tempCount.has(str[i]) == false && i > 0) {
            let prev = tempCount.get(str[i - 1]);
            ans += prev.toString() + str[i - 1];
            tempCount.clear();
        }

        // when current char is same as prev one we increase
        // it's count value
        if(tempCount.has(str[i]) == false)
           tempCount.set(str[i],1);
        else
        tempCount.set(str[i],tempCount.get(str[i])+1);

    }

    return ans;
}

function countnndSay(n)
{
    let res = "1"; // res variable keep tracks of string
                      // from 1 to n-1

    // For loop iterates for n-1 time and generate strings
    // in sequence "1" -> "11" -> "21" -> "1211"
    for (let i = 1; i < n; i++) {
        res = generator(res);
    }

    return res;
}

// driver code
let N = 5;
document.write(countnndSay(N),"</br>");

// This code is contributed by shinjanpatra

</script>

Output

21

Thanks to Utkarsh and Neeraj for suggesting the above solution.

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