Given a Binary string, the task is to find the largest Prime Number possible by the decimal representation of a subsequence of the given binary string. If no prime number can be obtained, print -1.
Examples:
Input: S = “1001”
Output: 5
Explanation: Out of all subsequences of the string “1001”, the largest prime number that can be obtained is “101” (= 5).Input: “1011”
Output: 11
Explanation: Out of all subsequences of the string “1011”, the largest prime number that can be obtained is “1011” (= 11).
Approach: To solve the problem, the idea is to generate all possible subsequences of the string, and convert each subsequence to its equivalent decimal form. Print the largest prime number obtained from this subsequences.
Follow the steps below to solve this problem:
- Initialize a vector of pairs, say vec, for storing pairs of strings and their equivalent decimal values, in Pair.first and Pair.second respectively.
- Initialize a variable, say ans, to store the required answer.
- Iterate a loop from i = 0 to length of the string s:
- Iterate a loop from j = 0 to the length of vec:
- Store the jthpair in temp.
- If the ith character of string s is ‘1‘:
- Add the character in temp.first.
- Update the value of temp.second by left shifting the current value and adding 1 to it.
- Otherwise:
- Add the character in temp.first.
- Update the value of temp.second by left shifting the current value and adding 0 to it.
- Store this temp pair into vec.
- If the temp.second is prime:
- Store max of ans and temp.second in ans.
- If ans is equal to 0:
- No prime number can be obtained from the string s.
- Otherwise:
- Print ans.
- Iterate a loop from j = 0 to the length of vec:
Below is the implementation of the above approach:
// C++ Program to implement // the above approach #include <iostream> #include <vector> using namespace std;
// Function to check if a // number is prime or not bool isPrime( int x)
{ if (x <= 1)
return false ;
for ( int i = 2; i * i <= x; i++) {
if (x % i == 0)
// Return not prime
return false ;
}
// If prime return true
return true ;
} // Function to find the largest prime // number possible from a subsequence void largestPrime(string s)
{ // Stores pairs of subsequences and
// their respective decimal value
vector<pair<string, int > > vec{ { "" , 0 } };
// Stores the answer
int ans = 0;
// Traverse the string
for ( int i = 0; i < s.length(); i++) {
// Stores the size of the vector
int n = vec.size();
// Traverse the vector
for ( int j = 0; j < n; j++) {
// Extract the current pair
pair<string, int > temp = vec[j];
// Get the binary string from the pair
string str = temp.first;
// Stores equivalent decimal values
int val = temp.second;
// If the current character is '1'
if (s[i] == '1' ) {
// Add the character
// to the subsequence
temp.first = str + '1' ;
// Update the value by left
// shifting the current
// value and adding 1 to it
temp.second = ((val << 1) + 1);
}
// If s[i]=='0'
else {
// Add the character
// to the subsequence
temp.first = str + '0' ;
// Update the value by left
// shifting the current
// value and adding 0 to it
temp.second = ((val << 1) + 0);
}
// Store the subsequence in the vector
vec.push_back(temp);
// Check if the decimal
// representation of current
// subsequence is prime or not
int check = temp.second;
// If prime
if (isPrime(check)) {
// Update the answer
// with the largest one
ans = max(ans, check);
}
}
}
// If no prime number
// could be obtained
if (ans == 0)
cout << -1 << endl;
else
cout << ans << endl;
} // Driver Code int main()
{ // Input String
string s = "110" ;
largestPrime(s);
return 0;
} |
// Java code to implement the approach import java.util.*;
class GFG {
// Function to check if a
// number is prime or not
static boolean isPrime( int x)
{
if (x <= 1 )
return false ;
for ( int i = 2 ; i * i <= x; i++) {
if (x % i == 0 )
// Return not prime
return false ;
}
// If prime return true
return true ;
}
// Function to find the largest prime
// number possible from a subsequence
static void largestPrime(String s)
{
// Stores pairs of subsequences and
// their respective decimal value
List<StringIntPair> vec = new ArrayList<>();
vec.add( new StringIntPair( "" , 0 ));
// Stores the answer
int ans = 0 ;
// Traverse the string
for ( int i = 0 ; i < s.length(); i++) {
// Stores the size of the vector
int n = vec.size();
// Traverse the vector
for ( int j = 0 ; j < n; j++) {
// Extract the current pair
StringIntPair ele = vec.get(j);
String str = ele.str;
int val = ele.val;
// If the current character is '1'
if (s.charAt(i) == '1' ) {
// Add the character
// to the subsequence
str = str + '1' ;
// Update the value by left
// shifting the current
// value and adding 1 to it
val = ((val << 1 ) + 1 );
}
// If s[i]=='0'
else {
// Add the character
// to the subsequence
str = str + '0' ;
// Update the value by left
// shifting the current
// value and adding 0 to it
val = ((val << 1 ) + 0 );
}
// Store the subsequence in the vector
vec.add( new StringIntPair(str, val));
// Check if the decimal
// representation of current
// subsequence is prime or not
int check = val;
// If prime
if (isPrime(check)) {
// Update the answer
// with the largest one
ans = Math.max(ans, check);
}
}
}
// If no prime number
// could be obtained
if (ans == 0 )
System.out.println(- 1 );
else
System.out.println(ans);
}
// Driver Code
public static void main(String[] args)
{
// Input String
String s = "110" ;
largestPrime(s);
}
// Class to store pairs of strings and integers
static class StringIntPair {
String str;
int val;
StringIntPair(String str, int val)
{
this .str = str;
this .val = val;
}
}
} // This code is contributed by phasing17. |
# Python3 program to implement # the above approach # Function to check if a # number is prime or not def isPrime(x):
if (x < = 1 ):
return False
for i in range ( 2 , x + 1 ):
if i * i > x:
break
if (x % i = = 0 ):
# Return not prime
return False
# If prime return true
return True
# Function to find the largest prime # number possible from a subsequence def largestPrime(s):
# Stores pairs of subsequences and
# their respective decimal value
vec = [["", 0 ]]
# Stores the answer
ans = 0
# Traverse the string
for i in range ( len (s)):
# Stores the size of the vector
n = len (vec)
# Traverse the vector
for j in range (n):
# Extract the current pair
temp = vec[j]
# Get the binary string from the pair
str = temp[ 0 ]
# Stores equivalent decimal values
val = temp[ 1 ]
# If the current character is '1'
if (s[i] = = '1' ):
# Add the character
# to the subsequence
temp[ 0 ] = str + '1'
# Update the value by left
# shifting the current
# value and adding 1 to it
temp[ 1 ] = ((val << 1 ) + 1 )
# If s[i]=='0'
else :
# Add the character
# to the subsequence
temp[ 0 ] = str + '0'
# Update the value by left
# shifting the current
# value and adding 0 to it
temp[ 1 ] = ((val << 1 ) + 0 )
# Store the subsequence in the vector
vec.append(temp)
# Check if the decimal
# representation of current
# subsequence is prime or not
check = temp[ 1 ]
# If prime
if (isPrime(check)):
# Update the answer
# with the largest one
ans = max (ans, check)
break
# If no prime number
# could be obtained
if (ans = = 0 ):
print ( - 1 )
else :
print (ans)
# Driver Code if __name__ = = '__main__' :
# Input String
s = "110"
largestPrime(s)
# This code is contributed by mohit kumar 29 |
// C# code to implement the approach using System;
using System.Collections.Generic;
class GFG
{ // Function to check if a
// number is prime or not
static bool IsPrime( int x)
{
if (x <= 1)
return false ;
for ( int i = 2; i * i <= x; i++) {
if (x % i == 0)
// Return not prime
return false ;
}
// If prime return true
return true ;
}
// Function to find the largest prime
// number possible from a subsequence
static void LargestPrime( string s)
{
// Stores pairs of subsequences and
// their respective decimal value
List<Tuple< string , int > > vec
= new List<Tuple< string , int > >();
vec.Add(Tuple.Create( "" , 0));
// Stores the answer
int ans = 0;
// Traverse the string
for ( int i = 0; i < s.Length; i++) {
// Stores the size of the vector
int n = vec.Count;
// Traverse the vector
for ( int j = 0; j < n; j++) {
// Extract the current pair
var ele = vec[j];
string str = ele.Item1;
int val = ele.Item2;
// If the current character is '1'
if (s[i] == '1' ) {
// Add the character
// to the subsequence
str = str + '1' ;
// Update the value by left
// shifting the current
// value and adding 1 to it
val = ((val << 1) + 1);
}
// If s[i]=='0'
else {
// Add the character
// to the subsequence
str = str + '0' ;
// Update the value by left
// shifting the current
// value and adding 0 to it
val = ((val << 1) + 0);
}
// Store the subsequence in the vector
vec.Add(Tuple.Create(str, val));
// Check if the decimal
// representation of current
// subsequence is prime or not
int check = val;
// If prime
if (IsPrime(check)) {
// Update the answer
// with the largest one
ans = Math.Max(ans, check);
}
}
}
// If no prime number
// could be obtained
if (ans == 0)
Console.WriteLine(-1);
else
Console.WriteLine(ans);
}
// Driver Code
public static void Main( string [] args)
{
// Input String
string s = "110" ;
LargestPrime(s);
}
} // This code is contributed by phasing17 |
<script> // JavaScript Program to implement // the above approach // Function to check if a // number is prime or not function isPrime(x) {
if (x <= 1)
return false ;
for (let i = 2; i * i <= x; i++) {
if (i * i > x){
break
}
if (x % i == 0)
// Return not prime
return false ;
}
// If prime return true
return true ;
} // Function to find the largest prime // number possible from a subsequence function largestPrime(s) {
// Stores pairs of subsequences and
// their respective decimal value
let vec = [[ "" , 0]];
// Stores the answer
let ans = 0;
// Traverse the string
for (let i = 0; i < s.length; i++) {
// Stores the size of the vector
let n = vec.length;
// Traverse the vector
for (let j = 0; j < n; j++) {
// Extract the current pair
let temp = vec[j];
// Get the binary string from the pair
let str = temp[0];
// Stores equivalent decimal values
let val = temp[1];
// If the current character is '1'
if (s[i] == '1' ) {
// Add the character
// to the subsequence
temp[0] = str + '1' ;
// Update the value by left
// shifting the current
// value and adding 1 to it
temp[1] = ((val << 1) + 1);
}
// If s[i]=='0'
else {
// Add the character
// to the subsequence
temp[0] = str + '0' ;
// Update the value by left
// shifting the current
// value and adding 0 to it
temp[1] = ((val << 1) + 0);
}
// Store the subsequence in the vector
vec.push(temp);
// Check if the decimal
// representation of current
// subsequence is prime or not
let check = temp[1];
// If prime
if (isPrime(check)) {
// Update the answer
// with the largest one
ans = Math.max(ans, check);
break
}
}
}
// If no prime number
// could be obtained
if (ans == 0)
document.write(-1 + "<br>" );
else
document.write(ans + "<br>" );
} // Driver Code // Input String let s = "110" ;
largestPrime(s); </script> |
3
Time Complexity: O(2N * ?N), where N is the length of the string.
Auxiliary Space: O(2N * N)