# Prime in a binary string PINBS Solution

## Codechef Prime in a binary string PINBS Solution

You are given a binary string S of length N. Your task is to check if there exists a substring of S which is the binary representation of a prime number.

Formally, check if there exist integers L and R such that 1≤L≤R≤N, and the substring SLSL+1SL+2…SR, when treated as a binary integer, is prime.

Print `"Yes"` if such a substring exists, and `"No"` if it doesn’t.

Input Format

• The first line of input contains a single integer T, denoting the number of test cases. The description of T test cases follows.
• Each testcase consists of a single line of input, containing a binary string S.

Output Format

For each test case, output a single line containing one string — `"Yes"` or `"No"`, the answer to the problem.

You may print each character of the answer in uppercase or lowercase (for example, the strings “yEs”, “yes”, “Yes” and “YES” will all be treated as identical).

Constraints

• 1≤T≤2.5⋅104
• |S|≤105
• The sum of |S| over all tests does not exceed 3⋅105

• 1≤T≤103
• |S|≤10

• Original constraints

Sample Input 1

``````3
1
111
101101``````

Sample Output 1

``````No
Yes
Yes``````

Explanation

Test case 1: There is only one substring, namely `"1"`, and it isn’t prime.

Test case 2: The substrings of the given string are {{`"1"``"11"``"111"``"1"``"11"``"1"`}}. Of these, `"111"` which represents 7 in binary, and `"11"` which represents 3 in binary, are primes.

Test case 3: One of the substrings of the string is `"1101"`, which is the binary representation of 13 a prime.

### SOLUTION

Program: Prime in a binary string PINBS Solution in C++

``````#include <bits/stdc++.h>
using namespace std;
#define int long long
signed main()
{int t;cin>>t;while(t--){
string s;cin>>s;
int c = 0;
for(int i=0;i<s.length()-1;i++){
if(s[i]=='1'){
cout<<"YES"<<endl;
c++;
break;
}
}
if(c==0) cout<<"NO"<<endl;
}
return 0;
}``````

Program: Prime in a binary string PINBS Solution in Java

``````import java.util.*;
import java.lang.*;
import java.io.*;
public class Main
{
public static void main (String[] args) throws java.lang.Exception
{
Scanner sc=new Scanner(System.in);

int t=sc.nextInt();
while(t-->0)
{
String s=sc.next();
String p=s;
int n=s.length();
s=s.replace("10","");
p=p.replace("11","");
if(s.length()!=n || p.length()!=n)
System.out.println("Yes");
else
System.out.println("No");
}

}
}``````

Program: Prime in a binary string PINBS Solution in Python

``````for _ in range(int(input())):
s = input()
if '10' in s:
print("YES")
elif '11' in s:
print("YES")
else:
print("NO")``````