SELV FIBONACCI NUMBERS SUM

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Givet en grænse, find summen af alle de lige værdier i Fibonacci-sekvensen under den givne grænse.
De første par vilkår af Fibonacci numre er 11 2 3 5 8 13 21 34 55 89 144 233 ... (Lige tal er fremhævet).
Eksempler:

Input : limit = 8 Output : 10 Explanation : 2 + 8 = 10 Input : limit = 400; Output : 188. Explanation : 2 + 8 + 34 + 144 = 188.

Anbefalet praksis Selv Fibonacci Numbers Sum Prøv det!

En simpel løsning er at iterere gennem alle Fibonacci-tal, mens det næste tal er mindre end eller lig med en given grænse. For hvert tal skal du kontrollere, om det er lige. Hvis tallet er lige, føjes det til resultatet.
En effektiv løsning er baseret på nedenstående rekursiv formel for lige Fibonacci-tal

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.

Henvis denne flere detaljer om ovenstående formel.
Så mens vi itererer over Fibonacci-tal, genererer vi kun lige Fibonacci-tal.

C++

// 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# 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>

Output:

Tidskompleksitet: På)

Hjælpeplads: O(1)

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