Skip to content
Related Articles

Related Articles

Improve Article

Find all possible ways to Split the given string into Primes

  • Difficulty Level : Hard
  • Last Updated : 17 May, 2021

Given string str that represents a number. The task is to find all possible ways to split the given string such that each segment is a prime number in the range of 1 to 106.
Examples:

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]

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

Approach:

  • The idea is to generate all possible splits of a string of size N by counting binary numbers from 0 to 2(N – 1) – 1. Where every 1 indicates that the string should split at that point.
    For example: 
 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
  • To check the prime number efficiently we will pre-process prime number in a boolean array using Sieve of Eratosthenes.

Below is the implementation of the above approach.

C++




// C++ program to Find all the
// ways to split the given string
// into Primes.
#include<bits/stdc++.h>
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<string> 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<String> 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<String> ans = new List<String>();
  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




<script>
// 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
</script>
Output: 
113,73
113,7,3
11,373
11,37,3
11,3,73
11,3,7,3



My Personal Notes arrow_drop_up
Recommended Articles
Page :