Dada la string str que representa un número. La tarea es encontrar todas las formas posibles de dividir la string dada de modo que cada segmento sea un número primo en el rango de 1 a 10 6 .
Ejemplos:
Entrada: str = “3175”
Salida:
[317, 5]
[31, 7, 5]
[3, 17, 5]
Explicación:
Puede haber 8 formas posibles de dividir:
[3175]
[317, 5] – Todos los números primos
[31, 75]
[31, 7, 5] – Todos los números primos
[3, 175]
[3, 17, 5] – Todos los números primos
[3, 1, 75]
[3, 1, 7, 5]
Entrada: str =
Salida “11373” :
[113, 73]
[113, 7, 3]
[11, 373]
[11, 37, 3]
[11, 3, 73]
[11, 3, 7, 3]
Acercarse:
- La idea es generar todas las divisiones posibles de una string de tamaño N contando números binarios del 0 al 2 (N – 1) – 1. Donde cada 1 indica que la string debe dividirse en ese punto.
Por ejemplo:
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
- Para verificar el número primo de manera eficiente, procesaremos previamente el número primo en una array booleana utilizando Sieve of Eratosthenes .
A continuación se muestra la implementación del enfoque anterior.
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>
Producción:
113,73 113,7,3 11,373 11,37,3 11,3,73 11,3,7,3
Publicación traducida automáticamente
Artículo escrito por keanu_reeves_ y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA