给定的字符串str代表一个数字。任务是找到所有可能的方法来分割给定的字符串，以使每个段都是1到10 6范围内的质数。
例子：
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]
方法：
- 这个想法是通过对从0到2 (N – 1) – 1的二进制数进行计数来生成大小为N的字符串的所有可能的拆分。其中，每1表示该点处的字符串应拆分。
例如：
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
- 为了有效地检查素数，我们将使用Eratosthenes筛子对布尔数组中的素数进行预处理。
下面是上述方法的实现。
C++
// C++ program to Find all the
// ways to split the given string
// into Primes.
#include
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 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 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 ChitranayalC#
// 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 ans = new List();
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 输出：
113,73
113,7,3
11,373
11,37,3
11,3,73
11,3,7,3