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Largest number with prime digits

  • Difficulty Level : Medium
  • Last Updated : 21 May, 2021

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++




// 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;
}

Java




// Java program to find largest number smaller than
// equal to n with all prime digits.
class GFG
{
 
    // check if character is prime
    public static boolean isPrime(char c)
    {
        return (c == '2' || c == '3' || c == '5' || c == '7');
    }
 
    // replace with previous prime character
    public static void decrease(StringBuilder s, int i)
    {
        if (s.charAt(i) <= '2')
        {
 
            // if 2 erase s[i] and replace next with 7
            s.deleteCharAt(i);
            s.setCharAt(i, '7');
        }
        else if (s.charAt(i) == '3')
            s.setCharAt(i, '2');
        else if (s.charAt(i) <= '5')
            s.setCharAt(i, '3');
        else if (s.charAt(i) <= '7')
            s.setCharAt(i, '5');
        else
            s.setCharAt(i, '7');
 
        return;
    }
 
    public static String primeDigits(StringBuilder s)
    {
        for (int i = 0; i < s.length(); i++)
        {
 
            // find first non prime char
            if (!isPrime(s.charAt(i)))
            {
 
                // find first char greater than 2
                while (i >= 0 && s.charAt(i) <= '2')
                    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.setCharAt(j, '7');
                break;
            }
        }
 
        return s.toString();
    }
 
    // Driver code
    public static void main(String[] args)
    {
        StringBuilder s = new StringBuilder("45");
        System.out.println(primeDigits(s));
 
        s = new StringBuilder("1000");
        System.out.println(primeDigits(s));
 
        s = new StringBuilder("7721");
        System.out.println(primeDigits(s));
 
        s = new StringBuilder("7221");
        System.out.println(primeDigits(s));
 
        s = new StringBuilder("74545678912345689748593275897894708927680");
        System.out.println(primeDigits(s));
    }
}
 
// This code is contributed by
// sanjeev2552

Python3




# Python3 program to find largest number
# smaller than equal to n with all prime digits.
 
# check if character is prime
def isPrime(c):
    return (c == '2' or c == '3' or
            c == '5' or c == '7')
 
# replace with previous prime character
def decrease(s, i):
     
    # if 2 erase s[i] and replace next with 7
    if (s[i] <= '2'):
        s.pop(i)
        s[i] = '7'
    elif (s[i] == '3'):
        s[i] = '2'
    elif (s[i] <= '5'):
        s[i] = '3'
    elif (s[i] <= '7'):
        s[i] = '5'
    else:
        s[i] = '7'
 
def primeDigits(s):
    s = [i for i in s]
    i = 0
 
    while i < len(s):
 
        # find first non prime char
        if (isPrime(s[i]) == False):
 
            # find first char greater than 2
            while (s[i] <= '2' and i >= 0):
                i -= 1
 
            # like 20
            if (i < 0):
                i = 0
                decrease(s, i)
         
            # like 7721
            else:
                decrease(s, i)
 
            # replace remaining with 7
            for j in range(i + 1,len(s)):
                s[j] = '7'
 
            break
        i += 1
 
    return "".join(s)
 
# Driver code
s = "45"
print(primeDigits(s))
 
s = "1000"
print(primeDigits(s))
 
s = "7721"
print(primeDigits(s))
 
s = "7221"
print(primeDigits(s))
 
s = "74545678912345689748593275897894708927680"
print(primeDigits(s))
 
# This code is contributed by Mohit Kumar

PHP




<?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.
?>

Javascript




<script>
// Javascript 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');
    }
     
    // replace with previous prime character
    function decrease(s,i)
    {
         
        
        if (s[i] <= '2')
        {
  
            // if 2 erase s[i] and replace next with 7
            s.splice(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 s;
         
    }
     
    function primeDigits(s)
    {
        for (let i = 0; i < s.length; i++)
        {
  
            // find first non prime char
            if (!isPrime(s[i]))
            {
  
                // find first char greater than 2
                while (i >= 0 && s[i].charCodeAt(0) <= '2'.charCodeAt(0))
                    i--;
                  
                // like 20
                if (i < 0)
                {
                    i = 0;
                    s=decrease(s.split(""), i);
                }
                  
                // like 7721
                else
                    s=decrease(s.split(""), i);
  
                // replace remaining with 7
                for (let j = i + 1; j < s.length; j++)
                    s[j] = '7';
                break;
            }
        }
  
        return s.join("");
    }
     
    // Driver code
    let s = "45";
    document.write(primeDigits(s)+"<br>");
  
    s = "1000";
    document.write(primeDigits(s)+"<br>");
  
    s = "7721";
    document.write(primeDigits(s)+"<br>");
  
    s = "7221";
    document.write(primeDigits(s)+"<br>");
  
    s = "74545678912345689748593275897894708927680";
    document.write(primeDigits(s)+"<br>");
     
     
     
 
// This code is contributed by unknown2108
</script>

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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