{"id":26536,"date":"2017-12-20T21:41:14","date_gmt":"2017-12-20T16:11:14","guid":{"rendered":"https:\/\/www.wikitechy.com\/technology\/?p=26536"},"modified":"2017-12-20T21:41:14","modified_gmt":"2017-12-20T16:11:14","slug":"python-programming-program-fibonacci-numbers","status":"publish","type":"post","link":"https:\/\/www.wikitechy.com\/technology\/python-programming-program-fibonacci-numbers\/","title":{"rendered":"Python Programming – Program for Fibonacci numbers"},"content":{"rendered":"

The Fibonacci numbers are the numbers in the following integer sequence.<\/span><\/p>\n

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, \u2026\u2026..<\/p>\n

In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation<\/p>\n

    Fn<\/sub> = Fn-1<\/sub> + Fn-2<\/sub><\/pre>\n
with seed values<\/p>\n
F0<\/sub> = 0 and F1<\/sub> = 1.<\/pre>\n
Write a function int fib(int n)<\/em> that returns Fn<\/sub>. For example, if n<\/em> = 0, then fib()<\/em> should return 0. If n = 1, then it should return 1. For n > 1, it should return Fn-1<\/sub> + Fn-2<\/sub><\/p>\n
For n = 9\r\nOutput:34<\/pre>\n
Following are different methods to get the nth Fibonacci number.<\/p>\n[ad type=”banner”]\n
Method 1 ( Use recursion ) <\/strong>
\nA simple method that is a direct recursive implementation mathematical recurrence relation given above.<\/p>\n
 
 Python<\/span> <\/div> 
# Function for nth Fibonacci number def Fibonacci(n):    if n<0:        print("Incorrect input")    # First Fibonacci number is 0    elif n==1:        return 0    # Second Fibonacci number is 1    elif n==2:        return 1    else:        return Fibonacci(n-1)+Fibonacci(n-2) # Driver Program print(Fibonacci(9))<\/code><\/pre> <\/div>\n
Output<\/p>\n
34<\/pre>\n
Time Complexity:<\/em> T(n) = T(n-1) + T(n-2) which is exponential.
\nWe can observe that this implementation does a lot of repeated work (see the following recursion tree). So this is a bad implementation for nth Fibonacci number.<\/p>\n
                         fib(5)   \r\n                     \/             \\     \r\n               fib(4)                fib(3)   \r\n             \/      \\                \/     \\\r\n         fib(3)      fib(2)         fib(2)    fib(1)\r\n        \/     \\        \/    \\       \/    \\  \r\n  fib(2)   fib(1)  fib(1) fib(0) fib(1) fib(0)\r\n  \/    \\\r\nfib(1) fib(0)\r\n<\/pre>\n
Extra Space:<\/em> O(n) if we consider the function call stack size, otherwise O(1).<\/p>\n[ad type=”banner”]\n
Method 2 ( Use Dynamic Programming )<\/strong>
\nWe can avoid the repeated work done is the method 1 by storing the Fibonacci numbers calculated so far.<\/p>\n
 
 Python<\/span> <\/div> 
# Function for nth fibonacci number - Dynamic Programing# Taking 1st two fibonacci nubers as 0 and 1 FibArray = [0,1] def fibonacci(n):    if n<0:        print("Incorrect input")    elif n<=len(FibArray):        return FibArray[n-1]    else:        temp_fib = fibonacci(n-1)+fibonacci(n-2)        FibArray.append(temp_fib)        return temp_fib # Driver Program print(fibonacci(9))<\/code><\/pre> <\/div>\n
Output:<\/p>\n
34<\/pre>\n
Time Complexity:<\/em> O(n)
\nExtra Space: <\/em>O(n)<\/p>\n
Method 3 ( Space Optimized Method 2 )<\/strong>
\nWe can optimize the space used in method 2 by storing the previous two numbers only because that is all we need to get the next Fibonacci number in series.<\/p>\n
 
 Python<\/span> <\/div> 
# Function for nth fibonacci number - Space Optimisataion# Taking 1st two fibonacci numbers as 0 and 1 def fibonacci(n):    a = 0    b = 1    if n < 0:        print("Incorrect input")    elif n == 0:        return a    elif n == 1:        return b    else:        for i in range(2,n):            c = a + b            a = b            b = c        return b # Driver Program print(fibonacci(9))<\/code><\/pre> <\/div>\n
Output:<\/p>\n
Time Complexity:<\/em> O(n)
\nExtra Space: <\/em>O(1)<\/p>\n[ad type=”banner”]\n
 <\/p>\n","protected":false},"excerpt":{"rendered":"
Python Programming – Program for Fibonacci numbers – Dynamic Programming The Fibonacci numbers are the numbers in the following integer sequence.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,70145,4148],"tags":[72847,72842,72845,70483,72848,72840,72852,79066,79077,74977,79103,79115,79113,72855,72853,79111,74961,79114,74934,79116,79106,72851],"class_list":["post-26536","post","type-post","status-publish","format-standard","hentry","category-coding","category-dynamic-programming","category-python","tag-concept-of-dynamic-programming","tag-define-dynamic-programming","tag-definition-of-dynamic-programming","tag-dynamic-programming","tag-dynamic-programming-code-generation-algorithm","tag-dynamic-programming-definition","tag-problems-on-dynamic-programming","tag-program-for-fibonacci-numbers","tag-program-for-fibonacci-series","tag-python-program-for-fibonacci-series","tag-python-program-to-find-fibonacci-numbers-using-dynamic-programming","tag-python-program-to-find-fibonacci-series","tag-python-program-to-print-fibonacci-series","tag-simple-dynamic-programming-example","tag-types-of-dynamic-programming","tag-write-a-program-in-python-for-fibonacci-series","tag-write-a-program-to-generate-the-fibonacci-series","tag-write-a-program-to-generate-the-fibonacci-series-in-python","tag-write-a-program-to-print-fibonacci-series","tag-write-a-python-program-for-fibonacci-series","tag-write-a-python-program-to-print-nth-fibonacci-number","tag-youtube-dynamic-programming"],"_links":{"self":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26536","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/comments?post=26536"}],"version-history":[{"count":0,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/posts\/26536\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/media?parent=26536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/categories?post=26536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wikitechy.com\/technology\/wp-json\/wp\/v2\/tags?post=26536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}