Dokonca aj Fibonacciho čísla súčet
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#practiceLinkDiv { display: none !important; } Daný limit nájdi súčet všetkých párnych členov vo Fibonacciho postupnosti pod daným limitom.
Prvých pár termínov Fibonacciho čísla sú 11 2 3 5 8 13 21 34 55 89 144 233 ... (Párne čísla sú zvýraznené).
Príklady:
Input : limit = 8 Output : 10 Explanation : 2 + 8 = 10 Input : limit = 400; Output : 188. Explanation : 2 + 8 + 34 + 144 = 188.
Jednoduchým riešením je iterovať cez všetky Fibonacciho čísla, zatiaľ čo ďalšie číslo je menšie alebo rovné danému limitu. Pre každé číslo skontrolujte, či je párne. Ak je číslo párne, pridajte ho k výsledku.
Efektívne riešenie je založené na nižšie uvedenom rekurzívny vzorec pre párne Fibonacciho čísla
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.
Odkazovať toto viac podrobností vyššie uvedeného vzorca.
Takže pri iterácii cez Fibonacciho čísla generujeme iba párne Fibonacciho čísla.
// 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>
výstup:
188
Časová zložitosť: O(n)
Pomocný priestor: O(1)
