Suma parzystych liczb Fibonacciego
Wypróbuj w praktyce GfG 
#practiceLinkDiv { display: none !important; }
#practiceLinkDiv { display: none !important; } Mając dany limit, znajdź sumę wszystkich wyrazów o parzystych wartościach w ciągu Fibonacciego poniżej podanego limitu.
Kilka pierwszych terminów Liczby Fibonacciego są 1 1 2 3 5 8 13 21 34 55 89 144 233 ... (Liczby parzyste są podświetlone).
Przykłady:
Input : limit = 8 Output : 10 Explanation : 2 + 8 = 10 Input : limit = 400; Output : 188. Explanation : 2 + 8 + 34 + 144 = 188.
Prostym rozwiązaniem jest iteracja po wszystkich liczbach Fibonacciego, podczas gdy następna liczba jest mniejsza lub równa podanemu limitowi. Dla każdej liczby sprawdź, czy jest parzysta. Jeśli liczba jest parzysta, dodaj ją do wyniku.
Skuteczne rozwiązanie opiera się na poniższym rekursywna formuła na parzyste liczby Fibonacciego
Recurrence for Even Fibonacci sequence is: EFn = 4EFn-1 + EFn-2 with seed values EF0 = 0 and EF1 = 2. EFn represents n'th term in Even Fibonacci sequence.
Wspominać Ten więcej szczegółów powyższego wzoru.
Zatem podczas iteracji po liczbach Fibonacciego generujemy tylko parzyste liczby Fibonacciego.
// Find the sum of all the even-valued terms in // the Fibonacci sequence which do not exceed // given limit. #include using namespace std ; // Returns sum of even Fibonacci numbers which are // less than or equal to given limit. int evenFibSum ( int limit ) { if ( limit < 2 ) return 0 ; // Initialize first two even Fibonacci numbers // and their sum long long int ef1 = 0 ef2 = 2 ; long long int sum = ef1 + ef2 ; // calculating sum of even Fibonacci value while ( ef2 <= limit ) { // get next even value of Fibonacci sequence long long int ef3 = 4 * ef2 + ef1 ; // If we go beyond limit we break loop if ( ef3 > limit ) break ; // Move to next even number and update sum ef1 = ef2 ; ef2 = ef3 ; sum += ef2 ; } return sum ; } // Driver code int main () { int limit = 400 ; cout < < evenFibSum ( limit ); return 0 ; }
Java // Find the sum of all the even-valued terms in // the Fibonacci sequence which do not exceed // given limit. import java.io.* ; class GFG { // Returns sum of even Fibonacci numbers which are // less than or equal to given limit. static int evenFibSum ( int limit ) { if ( limit < 2 ) return 0 ; // Initialize first two even Fibonacci numbers // and their sum long ef1 = 0 ef2 = 2 ; long sum = ef1 + ef2 ; // calculating sum of even Fibonacci value while ( ef2 <= limit ) { // get next even value of Fibonacci sequence long ef3 = 4 * ef2 + ef1 ; // If we go beyond limit we break loop if ( ef3 > limit ) break ; // Move to next even number and update sum ef1 = ef2 ; ef2 = ef3 ; sum += ef2 ; } return ( int ) sum ; } // Driver code public static void main ( String [] args ) { int limit = 400 ; System . out . println ( evenFibSum ( limit )); } } // This code is contributed by vt_m.
Python3 # Find the sum of all the even-valued # terms in the Fibonacci sequence which # do not exceed given limit. # Returns sum of even Fibonacci numbers which # are less than or equal to given limit. def evenFibSum ( limit ) : if ( limit < 2 ) : return 0 # Initialize first two even Fibonacci numbers # and their sum ef1 = 0 ef2 = 2 sm = ef1 + ef2 # calculating sum of even Fibonacci value while ( ef2 <= limit ) : # get next even value of Fibonacci # sequence ef3 = 4 * ef2 + ef1 # If we go beyond limit we break loop if ( ef3 > limit ) : break # Move to next even number and update # sum ef1 = ef2 ef2 = ef3 sm = sm + ef2 return sm # Driver code limit = 400 print ( evenFibSum ( limit )) # This code is contributed by Nikita Tiwari.
C# // C# program to Find the sum of all // the even-valued terms in the // Fibonacci sequence which do not // exceed given limit.given limit. using System ; class GFG { // Returns sum of even Fibonacci // numbers which are less than or // equal to given limit. static int evenFibSum ( int limit ) { if ( limit < 2 ) return 0 ; // Initialize first two even // Fibonacci numbers and their sum long ef1 = 0 ef2 = 2 ; long sum = ef1 + ef2 ; // calculating sum of even // Fibonacci value while ( ef2 <= limit ) { // get next even value of // Fibonacci sequence long ef3 = 4 * ef2 + ef1 ; // If we go beyond limit // we break loop if ( ef3 > limit ) break ; // Move to next even number // and update sum ef1 = ef2 ; ef2 = ef3 ; sum += ef2 ; } return ( int ) sum ; } // Driver code public static void Main () { int limit = 400 ; Console . Write ( evenFibSum ( limit )); } } // This code is contributed by Nitin Mittal.
PHP // Find the sum of all the // even-valued terms in the // Fibonacci sequence which // do not exceed given limit. // Returns sum of even Fibonacci // numbers which are less than or // equal to given limit. function evenFibSum ( $limit ) { if ( $limit < 2 ) return 0 ; // Initialize first two even // Fibonacci numbers and their sum $ef1 = 0 ; $ef2 = 2 ; $sum = $ef1 + $ef2 ; // calculating sum of // even Fibonacci value while ( $ef2 <= $limit ) { // get next even value of // Fibonacci sequence $ef3 = 4 * $ef2 + $ef1 ; // If we go beyond limit // we break loop if ( $ef3 > $limit ) break ; // Move to next even number // and update sum $ef1 = $ef2 ; $ef2 = $ef3 ; $sum += $ef2 ; } return $sum ; } // Driver code $limit = 400 ; echo ( evenFibSum ( $limit )); // This code is contributed by Ajit. ?>
JavaScript < script > // Javascript program to find the sum of all the even-valued terms in // the Fibonacci sequence which do not exceed // given limit. // Returns sum of even Fibonacci numbers which are // less than or equal to given limit. function evenFibSum ( limit ) { if ( limit < 2 ) return 0 ; // Initialize first two even Fibonacci numbers // and their sum let ef1 = 0 ef2 = 2 ; let sum = ef1 + ef2 ; // calculating sum of even Fibonacci value while ( ef2 <= limit ) { // get next even value of Fibonacci sequence let ef3 = 4 * ef2 + ef1 ; // If we go beyond limit we break loop if ( ef3 > limit ) break ; // Move to next even number and update sum ef1 = ef2 ; ef2 = ef3 ; sum += ef2 ; } return sum ; } // Function call let limit = 400 ; document . write ( evenFibSum ( limit )); < /script>
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