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++
// 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 eras[i] and replace next with 7 if (s[i] < = '2' ): # s.erase(i, 1); 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. ?> |
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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