54 lines
1.7 KiB
Markdown
54 lines
1.7 KiB
Markdown
---
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title: Even Fibonacci Numbers
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---
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## Problem 2: Even Fibonacci Numbers
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### Method:
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- A fibonacci sequence is a sequence where `fib(n) = fib(n-1) + fib(n-1)`.
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- In this challenge we have to sum all the even numbers upto `nth` term in the sequence.
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- Example for `fiboEvenSum(10)`:
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+ The sequence till 10th term is:
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1, 2, 3, 5, 8, 13, 21, 34, 55, 89
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+ Sum of all even number in the above sequence is:
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2 + 8 + 34 = 44
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### Solution:
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#### Basic Solution - Iterative:
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```js
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function fiboEvenSum(n) {
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let first = 1, second = 2, sum = 2, fibNum; // declaring and initializing variables
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if (n <= 1) return sum; // edge case
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for (let i = 3; i <= n; i++){ // looping till n
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fibNum = first + second; // getting the ith fibonacci number
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first = second;
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second = fibNum;
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if (fibNum%2 == 0) sum+=fibNum; // If even add to the sum variable
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}
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return sum;
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}
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```
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#### Advanced Solution - Recursive:
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```js
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// We use memoization technique to save ith fibonacci number to the fib array
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function fiboEvenSum(n){
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const fib = [1, 1, 2];
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let sumEven = fib[2];
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function fibonacci(n){
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if (n <= 1) return fib[n]; // base condition
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else if (fib[n]) return fib[n]; // if the number exists in the array we cache it and return
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else {
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fib[n] = fibonacci(n-1) + fibonacci(n-2); // otherwise calculcate and save it to the array
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if (fib[n]%2 == 0) sumEven+=fib[n]; //if the number is even, add it to the sumEven variable
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return fib[n];
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}
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}
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fibonacci(n); // run the recursive function
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return sumEven;
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}
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```
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- [Run Code](https://repl.it/@scissorsneedfoo/Project-Euler-Problem-2-Even-Fibonacci-Numbers)
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### References:
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- [Wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)
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