Enésimo número inteligente
Dado um número n, encontre o enésimo número inteligente (1 <=n <=1000). Smart number is a number which has at least three distinct prime factors. We are given an upper limit on value of result as MAX For example 30 is 1st smart number because it has 2 3 5 as it's distinct prime factors. 42 is 2nd smart number because it has 2 3 7 as it's distinct prime factors. Exemplos:
Input : n = 1 Output: 30 // three distinct prime factors 2 3 5 Input : n = 50 Output: 273 // three distinct prime factors 3 7 13 Input : n = 1000 Output: 2664 // three distinct prime factors 2 3 37Recomendado: resolva em PRÁTICA primeiro antes de passar para a solução.
A ideia é baseada Peneira de Eratóstenes . Usamos um array para usar um array prime[] para controlar os números primos. Também usamos a mesma matriz para acompanhar a contagem de fatores primos vistos até agora. Sempre que a contagem chega a 3, adicionamos o número ao resultado.
- Pegue um array primes[] e inicialize-o com 0.
- Agora sabemos que o primeiro número primo é i = 2, então marque primos[2] = 1, ou seja; primos[i] = 1 indica que 'i' é um número primo.
- Agora percorra o array primos[] e marque todos os múltiplos de 'i' pela condição primes[j] -= 1 onde 'j' é múltiplo de 'i' e verifique a condição primes[j]+3 = 0 porque sempre que primos[j] se torna -3 indica que anteriormente tinha sido múltiplo de três fatores primos distintos. Se condição primos[j]+3=0 torna-se verdade, o que significa que 'j' é um número inteligente, então armazene-o em um array result[].
- Agora classifique o resultado da matriz [] e retorne o resultado [n-1].
Abaixo está a implementação da ideia acima.
C++ // C++ implementation to find n'th smart number #include using namespace std ; // Limit on result const int MAX = 3000 ; // Function to calculate n'th smart number int smartNumber ( int n ) { // Initialize all numbers as not prime int primes [ MAX ] = { 0 }; // iterate to mark all primes and smart number vector < int > result ; // Traverse all numbers till maximum limit for ( int i = 2 ; i < MAX ; i ++ ) { // 'i' is maked as prime number because // it is not multiple of any other prime if ( primes [ i ] == 0 ) { primes [ i ] = 1 ; // mark all multiples of 'i' as non prime for ( int j = i * 2 ; j < MAX ; j = j + i ) { primes [ j ] -= 1 ; // If i is the third prime factor of j // then add it to result as it has at // least three prime factors. if ( ( primes [ j ] + 3 ) == 0 ) result . push_back ( j ); } } } // Sort all smart numbers sort ( result . begin () result . end ()); // return n'th smart number return result [ n -1 ]; } // Driver program to run the case int main () { int n = 50 ; cout < < smartNumber ( n ); return 0 ; }
Java // Java implementation to find n'th smart number import java.util.* ; import java.lang.* ; class GFG { // Limit on result static int MAX = 3000 ; // Function to calculate n'th smart number public static int smartNumber ( int n ) { // Initialize all numbers as not prime Integer [] primes = new Integer [ MAX ] ; Arrays . fill ( primes new Integer ( 0 )); // iterate to mark all primes and smart // number Vector < Integer > result = new Vector <> (); // Traverse all numbers till maximum // limit for ( int i = 2 ; i < MAX ; i ++ ) { // 'i' is maked as prime number // because it is not multiple of // any other prime if ( primes [ i ] == 0 ) { primes [ i ] = 1 ; // mark all multiples of 'i' // as non prime for ( int j = i * 2 ; j < MAX ; j = j + i ) { primes [ j ] -= 1 ; // If i is the third prime // factor of j then add it // to result as it has at // least three prime factors. if ( ( primes [ j ] + 3 ) == 0 ) result . add ( j ); } } } // Sort all smart numbers Collections . sort ( result ); // return n'th smart number return result . get ( n - 1 ); } // Driver program to run the case public static void main ( String [] args ) { int n = 50 ; System . out . println ( smartNumber ( n )); } } // This code is contributed by Prasad Kshirsagar
Python3 # Python3 implementation to find # n'th smart number # Limit on result MAX = 3000 ; # Function to calculate n'th # smart number def smartNumber ( n ): # Initialize all numbers as not prime primes = [ 0 ] * MAX ; # iterate to mark all primes # and smart number result = []; # Traverse all numbers till maximum limit for i in range ( 2 MAX ): # 'i' is maked as prime number because # it is not multiple of any other prime if ( primes [ i ] == 0 ): primes [ i ] = 1 ; # mark all multiples of 'i' as non prime j = i * 2 ; while ( j < MAX ): primes [ j ] -= 1 ; # If i is the third prime factor of j # then add it to result as it has at # least three prime factors. if ( ( primes [ j ] + 3 ) == 0 ): result . append ( j ); j = j + i ; # Sort all smart numbers result . sort (); # return n'th smart number return result [ n - 1 ]; # Driver Code n = 50 ; print ( smartNumber ( n )); # This code is contributed by mits
C# // C# implementation to find n'th smart number using System.Collections.Generic ; class GFG { // Limit on result static int MAX = 3000 ; // Function to calculate n'th smart number public static int smartNumber ( int n ) { // Initialize all numbers as not prime int [] primes = new int [ MAX ]; // iterate to mark all primes and smart // number List < int > result = new List < int > (); // Traverse all numbers till maximum // limit for ( int i = 2 ; i < MAX ; i ++ ) { // 'i' is maked as prime number // because it is not multiple of // any other prime if ( primes [ i ] == 0 ) { primes [ i ] = 1 ; // mark all multiples of 'i' // as non prime for ( int j = i * 2 ; j < MAX ; j = j + i ) { primes [ j ] -= 1 ; // If i is the third prime // factor of j then add it // to result as it has at // least three prime factors. if ( ( primes [ j ] + 3 ) == 0 ) result . Add ( j ); } } } // Sort all smart numbers result . Sort (); // return n'th smart number return result [ n - 1 ]; } // Driver program to run the case public static void Main () { int n = 50 ; System . Console . WriteLine ( smartNumber ( n )); } } // This code is contributed by mits
PHP // PHP implementation to find n'th smart number // Limit on result $MAX = 3000 ; // Function to calculate n'th smart number function smartNumber ( $n ) { global $MAX ; // Initialize all numbers as not prime $primes = array_fill ( 0 $MAX 0 ); // iterate to mark all primes and smart number $result = array (); // Traverse all numbers till maximum limit for ( $i = 2 ; $i < $MAX ; $i ++ ) { // 'i' is maked as prime number because // it is not multiple of any other prime if ( $primes [ $i ] == 0 ) { $primes [ $i ] = 1 ; // mark all multiples of 'i' as non prime for ( $j = $i * 2 ; $j < $MAX ; $j = $j + $i ) { $primes [ $j ] -= 1 ; // If i is the third prime factor of j // then add it to result as it has at // least three prime factors. if ( ( $primes [ $j ] + 3 ) == 0 ) array_push ( $result $j ); } } } // Sort all smart numbers sort ( $result ); // return n'th smart number return $result [ $n - 1 ]; } // Driver program to run the case $n = 50 ; echo smartNumber ( $n ); // This code is contributed by mits ?>
JavaScript < script > // JavaScript implementation to find n'th smart number // Limit on result const MAX = 3000 ; // Function to calculate n'th smart number function smartNumber ( n ) { // Initialize all numbers as not prime let primes = new Array ( MAX ). fill ( 0 ); // iterate to mark all primes and smart number let result = []; // Traverse all numbers till maximum limit for ( let i = 2 ; i < MAX ; i ++ ) { // 'i' is maked as prime number because // it is not multiple of any other prime if ( primes [ i ] == 0 ) { primes [ i ] = 1 ; // mark all multiples of 'i' as non prime for ( let j = i * 2 ; j < MAX ; j = j + i ) { primes [ j ] -= 1 ; // If i is the third prime factor of j // then add it to result as it has at // least three prime factors. if ( ( primes [ j ] + 3 ) == 0 ) result . push ( j ); } } } // Sort all smart numbers result . sort (( a b )=> a - b ); // return n'th smart number return result [ n - 1 ]; } // Driver program to run the case let n = 50 ; document . write ( smartNumber ( n )); // This code is contributed by shinjanpatra < /script>
Saída:
273
Complexidade de tempo: O(MAX)
Espaço Auxiliar: O(MAX)
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