看和说序列

在 Look-and-say（或 Count and Say）序列中找到第 n 项。 Look-and-say 序列是以下整数的序列：
1、11、21、1211、111221、312211、13112221、1113213211、……

上面的序列是如何产生的？
通过读取第 (n-1) 项生成的第 n 项。

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

如何找到第n个术语？

例子：

Input: n = 3
Output: 21

Input: n = 5
Output: 111221

这个想法很简单，我们生成从 1 到 n 的所有项。前两个术语被初始化为“1”和“11”，所有其他术语都是使用前面的术语生成的。为了使用前一个词生成一个词，我们扫描前一个词。在扫描一个词时，我们只需跟踪所有连续字符的计数。对于相同字符的序列，我们在字符后面附加计数以生成下一个术语。

下面是上述想法的实现。

C++

// C++ program to find n'th term in look and say
// sequence
#include 
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

Javascript

 
// 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
 

输出

21

另一种方法（使用 STL）：还有一个想法，我们可以使用 c++ stl 中的 unordered_map 来跟踪位数。基本思想是使用生成器函数，该函数将从前一个字符串。在 count 和 say函数中，我们将遍历从 1 到 n-1 的整数并不断更新我们的结果。

C++

#include 
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
        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;
}

Javascript

// 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
 

输出

21