Dato un numero n trova l'n-esimo numero intelligente (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. Esempi:
tutorial sulla scintilla
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 37Consigliato: risolverlo PRATICA prima di passare alla soluzione.
L'idea è basata su Setaccio di Eratostene . Usiamo un array per utilizzare un array prime[] per tenere traccia dei numeri primi. Utilizziamo lo stesso array anche per tenere traccia del conteggio dei fattori primi visto finora. Ogni volta che il conteggio raggiunge 3 aggiungiamo il numero al risultato.
- Prendi un array primes[] e inizializzalo con 0.
- Ora sappiamo che il primo numero primo è i = 2 quindi segna primes[2] = 1 i.e; primi[i] = 1 indica che 'i' è un numero primo.
- Ora attraversa l'array primes[] e contrassegna tutti i multipli di 'i' con la condizione primes[j] -= 1 dove 'j' è multiplo di 'i' e controlla la condizione primes[j]+3 = 0 perché ogni volta che primes[j] diventa -3 indica che in precedenza era multiplo di tre distinti fattori primi. Se condizione primi[j]+3=0 diventa vero, significa che 'j' è uno Smart Number, quindi memorizzalo in un array result[].
- Ora ordina il risultato dell'array[] e restituisce il risultato[n-1].
Di seguito è riportata l'implementazione dell'idea di cui sopra.
C++// C++ implementation to find n'th smart number #include
// 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 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# 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 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 $primes=array_fill(0$MAX0); // 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 ?> <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((ab)=>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>
Produzione:
273
Complessità temporale: O(MAX)
Spazio ausiliario: O(MAX)