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Look-and-Say Sequence

  • Difficulty Level : Medium
  • Last Updated : 21 Jun, 2021

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

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

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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 previous term, we scan the previous term. While scanning a term, we simply keep track of count of all consecutive characters. For sequence of same characters, we append the count followed by character to generate the next term.

Below is implementation of 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 does'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
            // does'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
            // does'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
            # does'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; $j++)
        {
            // If current character
            // does't match
            if ($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
            // does'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 count of digits. Basic idea is to use a generator function which will generate 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;
}
Output
21

Thanks to Utkarsh and Neeraj for suggesting the above solution.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
 




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