寻找将给定字符串拆分为素数的所有可能方法

给定的字符串str代表一个数字。任务是找到所有可能的方法来分割给定的字符串，以使每个段都是1到10 ⁶范围内的质数。
例子：

Input: str = “3175” 
Output: 
[317, 5] 
[31, 7, 5] 
[3, 17, 5]
Explanation: 
There can be 8 possible ways to split: 
[3175] 
[317, 5] – All primes 
[31, 75] 
[31, 7, 5] – All primes 
[3, 175] 
[3, 17, 5] – All primes 
[3, 1, 75] 
[3, 1, 7, 5]
Input: str = “11373” 
Output: 
[113, 73] 
[113, 7, 3] 
[11, 373] 
[11, 37, 3] 
[11, 3, 73] 
[11, 3, 7, 3]

方法：

• 这个想法是通过对从0到2 ^{(N – 1)} – 1的二进制数进行计数来生成大小为N的字符串的所有可能的分割。其中，每1表示该点处的字符串应该分割。
  例如：

S = "3175"
 0 0 0   3175
 0 0 1   317, 5
 0 1 0   31, 75
 0 1 1   31, 7, 5
 1 0 0   3, 175
 1 0 1   3, 17, 5
 1 1 0   3, 1, 75
 1 1 1   3, 1, 7, 5

• 为了有效地检查素数，我们将使用Eratosthenes筛子对布尔数组中的素数进行预处理。

下面是上述方法的实现。

C++

// C++ program to Find all the
// ways to split the given string
// into Primes.
#include
using namespace std;
 
bool primes[1000000];
const int maxn = 1000000;
 
// Sieve of Eratosthenes
void sieve()
{
    memset(primes,true,sizeof(primes));
    primes[0] = primes[1] = 0;
     
    for(int i = 2; i * i <= maxn; i++)
    {
        if(primes[i])
        {
            for(int j = i * i ;
                   j <= maxn ; j += i)
            primes[j] = false;
        }
    }
}
 
// Function Convert integer
// to binary string
string toBinary(int n)
{
    string r = "";
    while(n != 0)
    {
        r = (n % 2 == 0 ?"0":"1") + r;
        n /= 2;
    }
    return (r == "")?"0":r;
}
 
// Function print all the all the
// ways to split the given string
// into Primes.
void PrimeSplit(string str)
{
    string temp;
    int cnt=0;
     
    // To store all possible strings
    vector ans;
    int bt = 1<<(str.size()-1);
    int n = str.size();
 
 
    // Exponetnital complexity n*(2^(n-1))
    // for bit
    for(int i = 0 ; i < bt ; i++)
    {
        temp = toBinary(i) + "0";
        int j = 0, x = n - temp.size(), y;
        while(j < x)
        {
            temp = "0" + temp;
            j++;
        }
        j = 0;
        x = 0;
        y = -1;
         
        string sp = "", tp = "";
        bool flag = 0;
         
        while(j < n)
        {
            sp += str[j];
            if(temp[j] == '1')
            {
                tp += sp + ',';
                y = stoi(sp);
                 
                // Pruning step
                if(!primes[y])
                {
                    flag = 1;
                    break;
                }
                sp = "";
            }
            j++;
        }
        tp += sp;
        if(sp != "")
        {
            y = stoi(sp);
            if(!primes[y])
            flag = 1;
        }
        if(!flag)
        ans.push_back(tp);
    }
    if(ans.size() == 0)
    {
        cout << -1 << endl;
    }
    for(auto i:ans)
    {
        cout << i << endl;
    }
}
 
// Driver code
int main()
{
    string str = "11373";
    sieve();
     
    PrimeSplit(str);
     
    return 0;
}

Java

// Java program to Find all the 
// ways to split the given string
// into Primes.
import java.util.*;
import java.lang.*;
 
class GFG{
 
static boolean[] primes = new boolean[1000001];
static int maxn = 1000000;
 
// Sieve of Eratosthenes
static void sieve()
{
    Arrays.fill(primes, true);
    primes[0] = false;
    primes[1] = false;
     
    for(int i = 2; i * i <= maxn; i++)
    {
        if (primes[i])
        {
            for(int j = i * i;
                    j <= maxn; j += i)
                primes[j] = false;
        }
    }
}
 
// Function Convert integer
// to binary string
static String toBinary(int n)
{
    String r = "";
     
    while(n != 0)
    {
        r = (n % 2 == 0 ? "0" : "1") + r;
        n /= 2;
    }
    return (r == "") ? "0" : r;
}
 
// Function print all the all the
// ways to split the given string
// into Primes.
static void PrimeSplit(String str)
{
    String temp;
    int cnt = 0;
     
    // To store all possible strings
    ArrayList ans = new ArrayList<>();
    int bt = 1 << (str.length() - 1);
    int n = str.length();
 
    // Exponetnital complexity n*(2^(n-1))
    // for bit
    for(int i = 0; i < bt; i++)
    {
        temp = toBinary(i) + "0";
        int j = 0, x = n - temp.length(), y;
         
        while(j < x)
        {
            temp = "0" + temp;
            j++;
        }
        j = 0;
        x = 0;
        y = -1;
         
        String sp = "", tp = "";
        boolean flag = false;
         
        while(j < n)
        {
            sp += str.charAt(j);
             
            if (temp.charAt(j) == '1')
            {
                tp += sp + ',';
                y = Integer.parseInt(sp);
                 
                // Pruning step
                if (!primes[y])
                {
                    flag = true;
                    break;
                }
                sp = "";
            }
            j++;
        }
        tp += sp;
         
        if (sp != "")
        {
            y = Integer.parseInt(sp);
             
            if (!primes[y])
                flag = true;
        }
        if (!flag)
        ans.add(tp);
    }
     
    if (ans.size() == 0)
    {
        System.out.println(-1);
    }
     
    for(String i : ans)
    {
        System.out.println(i);
    }
}
 
// Driver Code
public static void main (String[] args)
{
    String str = "11373";
    sieve();
     
    PrimeSplit(str);
}
}
 
// This code is contributed by offbeat

Python3

# Python 3 program to Find all the
# ways to split the given string
# into Primes.
primes = [True] * 1000001
maxn = 1000000
 
# Sieve of Eratosthenes
def sieve():
 
    primes[0] = primes[1] = 0   
    i = 2
     
    while i * i <= maxn:
        if(primes[i]):
            for j in range(i * i,
                           maxn + 1, i):
                primes[j] = False
        i += 1
 
# Function Convert integer
# to binary string
def toBinary(n):
 
    r = ""
    while(n != 0):
        if(n % 2 == 0 ):
          r = "0" + r
        else:
          r = "1" + r
        n //= 2
     
    if (r == ""):
      return "0"
    return r
 
# Function print all the all the
# ways to split the given string
# into Primes.
def PrimeSplit(st):
 
    cnt = 0
     
    # To store all
    # possible strings
    ans = []
    bt = 1 << (len(st) - 1)
    n = len(st)
 
    # Exponetnital complexity
    # n*(2^(n-1)) for bit
    for i in range(bt):   
        temp = toBinary(i) + "0"
        j = 0
        x = n - len(temp)
        while(j < x):
            temp = "0" + temp
            j += 1
         
        j = 0
        x = 0
        y = -1
         
        sp = ""
        tp = ""
        flag = 0
         
        while(j < n):
            sp += st[j]
            if(temp[j] == '1'):           
                tp += sp + ','
                y = int(sp)
                 
                # Pruning step
                if(not primes[y]):
                    flag = 1
                    break
                sp = ""
            j += 1
         
        tp += sp
         
        if(sp != ""):
            y = int(sp)
            if(not primes[y]):
               flag = 1
        
        if(not flag):
           ans.append(tp)
     
    if(len(ans) == 0):
        print (-1)
     
    for i in ans:
        print (i)
 
# Driver code
if __name__ == "__main__":
   
    st = "11373"
    sieve()   
    PrimeSplit(st)
 
# This code is contributed by Chitranayal

C#

// C# program to Find all the 
// ways to split the given string
// into Primes.
using System;
using System.Collections.Generic;
class GFG{
 
static bool[] primes =
       new bool[1000001];
static int maxn = 1000000;
 
// Sieve of Eratosthenes
static void sieve()
{
  for(int i = 0;
          i < primes.Length; i++)
  {
    primes[i] = true;
  }
  primes[0] = false;
  primes[1] = false;
 
  for(int i = 2; i * i <= maxn; i++)
  {
    if (primes[i])
    {
      for(int j = i * i;
              j <= maxn; j += i)
        primes[j] = false;
    }
  }
}
 
// Function Convert integer
// to binary string
static String toBinary(int n)
{
  String r = "";
 
  while(n != 0)
  {
    r = (n % 2 == 0 ?
         "0" : "1") + r;
    n /= 2;
  }
  return (r == "") ? "0" : r;
}
 
// Function print all the all the
// ways to split the given string
// into Primes.
static void PrimeSplit(String str)
{
  String temp;
 
  // To store all possible strings
  List ans = new List();
  int bt = 1 << (str.Length - 1);
  int n = str.Length;
 
  // Exponetnital complexity
  // n*(2^(n-1)) for bit
  for(int i = 0; i < bt; i++)
  {
    temp = toBinary(i) + "0";
    int j = 0, x = n - temp.Length, y;
 
    while(j < x)
    {
      temp = "0" + temp;
      j++;
    }
    j = 0;
    x = 0;
    y = -1;
 
    String sp = "", tp = "";
    bool flag = false;
 
    while(j < n)
    {
      sp += str[j];
 
      if (temp[j] == '1')
      {
        tp += sp + ',';
        y = Int32.Parse(sp);
 
        // Pruning step
        if (!primes[y])
        {
          flag = true;
          break;
        }
        sp = "";
      }
      j++;
    }
    tp += sp;
 
    if (sp != "")
    {
      y = Int32.Parse(sp);
 
      if (!primes[y])
        flag = true;
    }
     
    if (!flag)
      ans.Add(tp);
  }
 
  if (ans.Count == 0)
  {
    Console.WriteLine(-1);
  }
 
  foreach(String i in ans)
  {
    Console.WriteLine(i);
  }
}
 
// Driver Code
public static void Main(String[] args)
{
  String str = "11373";
  sieve();
  PrimeSplit(str);
}
}
 
// This code is contributed by Rajput-Ji

Javascript

// Javascript program to Find all the
// ways to split the given string
// into Primes.
 
let primes = new Array(1000000);
const maxn = 1000000;
 
// Sieve of Eratosthenes
function sieve()
{
    primes.fill(true)
    primes[0] = primes[1] = 0;
     
    for(let i = 2; i * i <= maxn; i++)
    {
        if(primes[i])
        {
            for(let j = i * i ;
                j <= maxn ; j += i)
            primes[j] = false;
        }
    }
}
 
// Function Convert integer
// to binary string
function toBinary(n)
{
    let r = "";
    while(n != 0)
    {
        r = (n % 2 == 0 ?"0":"1") + r;
        n = Math.floor(n / 2);
    }
    return (r == "")?"0":r;
}
 
// Function print all the all the
// ways to split the given string
// into Primes.
function PrimeSplit(str)
{
    let temp;
    let cnt=0;
     
    // To store all possible strings
    let ans = new Array();
    let bt = 1 << (str.length-1);
    let n = str.length;
 
 
    // Exponetnital complexity n*(2^(n-1))
    // for bit
    for(let i = 0 ; i < bt ; i++)
    {
        temp = toBinary(i) + "0";
        let j = 0, x = n - temp.length, y;
        while(j < x)
        {
            temp = "0" + temp;
            j++;
        }
        j = 0;
        x = 0;
        y = -1;
         
        let sp = "", tp = "";
        let flag = 0;
         
        while(j < n)
        {
            sp += str[j];
            if(temp[j] == '1')
            {
                tp += sp + ',';
                y = parseInt(sp);
                 
                // Pruning step
                if(!primes[y])
                {
                    flag = 1;
                    break;
                }
                sp = "";
            }
            j++;
        }
        tp += sp;
        if(sp != "")
        {
            y = parseInt(sp);
            if(!primes[y])
            flag = 1;
        }
        if(!flag)
        ans.push(tp);
    }
    if(ans.length == 0)
    {
        document.write(-1 + "<br>");
    }
    for(let i of ans)
    {
        document.write(i + "<br>");
    }
}
 
// Driver code
 
let str = "11373";
sieve();
     
PrimeSplit(str);
 
// This code is contributed by _saurabh_jaiswal

输出：

113,73
113,7,3
11,373
11,37,3
11,3,73
11,3,7,3