Largest number with prime digits

Given a huge integer value n, find the largest integer value x such that x <= n and all the digits of x are prime.

Examples:

Input : n = 45
Output : 37
37 is the largest number smaller than
or equal to with all prime digits.

Input : n = 1000
Output : 777

Input : n = 7721
Output : 7577

Input : n = 7221
Output : 5777



We know that the prime digits are 2, 3, 5 and 7. Also since we have to manipulate each digit of a very large number it will be easier if we do it as a string. The main idea is to find the first non-prime digit and then
find the first digit greater than 2 in its left. Now we can replace the found digit with the prime digit that is just less than it. If the digit is 2, we have to erase it and replace the next digit with 7. After this we can replace the remaining digits to its right by 7.

Following is the implementation of the above algorithm:

C++

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// CPP program to find largest number smaller than
// equal to n with all prime digits.
#include <bits/stdc++.h>
using namespace std;
  
// check if character is prime
bool isPrime(char c)
{
    return (c == '2' || c == '3' || c == '5' || c == '7');
}
  
// replace with previous prime character
void decrease(string& s, int i)
{
    // if 2 erase s[i] and replace next with 7
    if (s[i] <= '2') {
        s.erase(i, 1);
        s[i] = '7';
    }
  
    else if (s[i] == '3')
        s[i] = '2';
    else if (s[i] <= '5')
        s[i] = '3';
    else if (s[i] <= '7')
        s[i] = '5';
    else
        s[i] = '7';
  
    return;
}
  
string primeDigits(string s)
{
    for (int i = 0; i < s.length(); i++) {
  
        // find first non prime char
        if (!isPrime(s[i])) {
  
            // find first char greater than 2
            while (s[i] <= '2' && i >= 0)
                i--;
  
            // like 20
            if (i < 0) {
                i = 0;
                decrease(s, i);
            }
  
            // like 7721
            else
                decrease(s, i);
  
            // replace remaining with 7
            for (int j = i + 1; j < s.length(); j++) 
                s[j] = '7';            
  
            break;
        }
    }
  
    return s;
}
  
// Driver code
int main()
{
    string s = "45";
    cout << primeDigits(s) << endl;
  
    s = "1000";
    cout << primeDigits(s) << endl;
  
    s = "7721";
    cout << primeDigits(s) << endl;
  
    s = "7221";
    cout << primeDigits(s) << endl;
  
    s = "74545678912345689748593275897894708927680";
    cout << primeDigits(s) << endl;
  
    return 0;
}

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<?php 


// PHP program to find largest  


// number smaller than equal  


// to n with all prime digits. 


  


// check if character is prime 


function isPrime($c) 


{ 


    return ($c == '2' || $c == '3' ||  


            $c == '5' || $c == '7') ?  


                                  1 : 0; 


} 


  


// replace with previous 


// prime character 


function decrease($s, $i) 


{ 


    // if 2 erase s[i] and 


    // replace next with 7 


    if ($s[$i] <= '2')  


    { 


          


        $s[$i] = '*'; 


        $a = str_split($s); 


        $s = ""; 


        for($h = 0; $h < count($a); $h++) 


            if($a[$h] != '*') 


                $s = $s.$a[$h]; 


          


        $s[$i] = '7'; 


    } 


  


    else if ($s[$i] == '3') 


        $s[$i] = '2'; 


    else if ($s[$i] <= '5') 


        $s[$i] = '3'; 


    else if ($s[$i] <= '7') 


        $s[$i] = '5'; 


    else


        $s[$i] = '7'; 


  


    return $s; 


} 


  


function primeDigits($s) 


{ 


    for ($i = 0; $i < strlen($s); $i++) 


    { 


  


        // find first non prime char 


        if (isPrime($s[$i]) == 0)  


        { 


  


            // find first char  


            // greater than 2 


            while ($i >= 0 &&  


                   $s[$i] <= '2') 


                --$i; 


  


            // like 20 


            if ($i < 0)  


            { 


                $i = 0; 


                $s = decrease($s, $i); 


            } 


  


            // like 7721 


            else


                $s = decrease($s, $i); 


  


            // replace remaining with 7 


            for ($j = $i + 1;  


                 $j < strlen($s); $j++)  


                $s[$j] = '7';      


  


            break; 


        } 


    } 


  


    return $s; 


} 


  


// Driver code 


$s = "45"; 


echo primeDigits($s) . "\n"; 


  


$s = "1000"; 


echo primeDigits($s) . "\n"; 


  


$s = "7721"; 


echo primeDigits($s) . "\n"; 


  


$s = "7221"; 


echo primeDigits($s) . "\n"; 


  


$s = "74545678912345689748593275897894708927680"; 


echo primeDigits($s); 


  


// This code is contributed by mits. 


?> 



















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Output:


37
777
7577
5777
73777777777777777777777777777777777777777



The time complexity of the above program is O(N) where N is the length of the string.



          
          
          
          

            

    

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