On recursion and Fibonacci sequence

python in , Frequently used fibonacci Sequence to explain recursion , But there will always be a period of confusion when you understand it . Actually, take it apart , Don't complicated .

def fibonacci(n):
    if n==1 or n==2:
        return 1
    else:
        return fibonacci(n-1)+fibonacci(n-2)

print(fibonacci(5))

analysis ：

1. Put parameters “5” Plug in fibonacci(n) function , Because of inequality 1 or 2, So run else, return ： perform fibonacci（4）+fibonacci（3）, That is, it is required to execute two functions ..

2.1 perform fibonacci(4) function ：

2.1.1 Because the parameter is 4, Still not waiting 1 or 2, So keep running else, return ： perform fibonacci（3）+fibonacci（2）. among fibonacci（2） The result is 1.

2.1.1.1 perform fibonacci（3）, Continuing is not equal to 1 or 2, So run else, return ： perform fibonacci（2）+fibonacci（1）——>fibonacci（3） The result is 2

thus ,fibonacci(4) The result is 3（1+2）

2.2 perform fibonacci（3） function ：

Thus we can see that , The result is 2..

3. go back to fibonacci（5）, Get the results ：fibonacci（4）+fibonacci（3）=3+2=5

  Recursion can calculate the sequence , But because “ In the middle ” Too much ,n A little higher （ such as 50）, The calculation time is very long . therefore , If you simply want to calculate the data , It's better to be direct —— As long as the number is not too exaggerated , It's all in seconds

import time

t1=time.time()
a,b,i=0,1,1
for n in range(10000):
    print("N Items for ：",i,"Fi The value is ：",b)
    a, b ,i = b, a+b, i+1
t2=time.time()
t=t2-t1
print(" when ：",t)


N Items for ： 10000 Fi The value is ： 33644764876431783266621612005107543310302148460680063906564769974680081442166662368155595513633734025582065332680836159373734790483865268263040892463056431887354544369559827491606602099884183933864652731300088830269235673613135117579297437854413752130520504347701602264758318906527890855154366159582987279682987510631200575428783453215515103870818298969791613127856265033195487140214287532698187962046936097879900350962302291026368131493195275630227837628441540360584402572114334961180023091208287046088923962328835461505776583271252546093591128203925285393434620904245248929403901706233888991085841065183173360437470737908552631764325733993712871937587746897479926305837065742830161637408969178426378624212835258112820516370298089332099905707920064367426202389783111470054074998459250360633560933883831923386783056136435351892133279732908133732642652633989763922723407882928177953580570993691049175470808931841056146322338217465637321248226383092103297701648054726243842374862411453093812206564914032751086643394517512161526545361333111314042436854805106765843493523836959653428071768775328348234345557366719731392746273629108210679280784718035329131176778924659089938635459327894523777674406192240337638674004021330343297496902028328145933418826817683893072003634795623117103101291953169794607632737589253530772552375943788434504067715555779056450443016640119462580972216729758615026968443146952034614932291105970676243268515992834709891284706740862008587135016260312071903172086094081298321581077282076353186624611278245537208532365305775956430072517744315051539600905168603220349163222640885248852433158051534849622434848299380905070483482449327453732624567755879089187190803662058009594743150052402532709746995318770724376825907419939632265984147498193609285223945039707165443156421328157688908058783183404917434556270520223564846495196112460268313970975069382648706613264507665074611512677522748621598642530711298441182622661057163515069260029861704945425047491378115154139941550671256271197133252763631939606902895650288268608362241082050562430701794976171121233066073310059947366875
 when ： 12.951853275299072

 Process ended , Exit code 0