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++
// 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 // 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
// 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 // 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 |
Python3
# 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 # 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#
// 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 // 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 |
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 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// 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 codelet 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
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