Find all possible ways to Split the given string into Primes

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]
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++
Java
Python3
C#
Javascript
// 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 Eratosthenesvoid 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 stringstring 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 codeint main(){    string str = "11373";    sieve();         PrimeSplit(str);         return 0;}
// 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 Eratosthenesstatic 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 stringstatic 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 Codepublic static void main (String[] args){    String str = "11373";    sieve();         PrimeSplit(str);}} // This code is contributed by offbeat
# Python 3 program to Find all the# ways to split the given string# into Primes.primes = [True] * 1000001maxn = 1000000 # Sieve of Eratosthenesdef 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 stringdef 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 codeif __name__ == "__main__":       st = "11373"    sieve()       PrimeSplit(st) # This code is contributed by Chitranayal
// 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 Eratosthenesstatic 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 stringstatic 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 Codepublic static void Main(String[] args){  String str = "11373";  sieve();  PrimeSplit(str);}} // This code is contributed by Rajput-Ji
<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 Eratosthenesfunction 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 stringfunction 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>
113,73
113,7,3
11,373
11,37,3
11,3,73
11,3,7,3
offbeat
Rajput-Ji
ukasp
_saurabh_jaiswal
digit-DP
number-digits
Prime Number
sieve
Bit Magic
Combinatorial
Dynamic Programming
Mathematical
Strings
Strings
Dynamic Programming
Mathematical
Bit Magic
Prime Number
sieve
Combinatorial
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