# Find all possible ways to Split the given string into Primes

Given a 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:

[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:

1. The idea is to generate all possible splits of a string of size N by counting binary number 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
```
2. 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 ` `using` `namespace` `std; ` ` `  `bool` `primes; ` `const` `int` `maxn = 1000000; ` ` `  `// Sieve of Eratosthenes ` `void` `sieve() ` `{ ` `    ``memset``(primes,``true``,``sizeof``(primes)); ` `    ``primes = primes = 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; ` `} `

Output:

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

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