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Classesofalgorithms

Itera0vealgorithmsallowustodomorecomplexthingsthansimplearithme0c

Wecanrepeatasequenceofstepsmul0ple0mesbasedonsomedecision;leadstonewclassesofalgorithms

Oneusefulexampleareguessandcheckmethods

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Guessandcheck

Rememberourdeclara0vedefini0onofsquarerootofx!

Ifwecouldguesspossiblevaluesforsquareroot(callitg),thencanusedefini0ontocheckifg*g = x!

Wejustneedagoodwaytogenerateguesses

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Findingacuberootofaninteger

Onewaytousethisideaofgenera0ngguessesinordertofindacuberootofx isto

firsttry0**3,then1**3,then2**3,andsoon

Canstopwhenreachk suchthatk**3 > x! Onlyafinitenumberofcasestotry

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Somecode

x = int(raw_input('Enter an integer: '))!ans = 0!

while ans**3 < x:!ans = ans + 1!

if ans**3 != x:! print(str(x) + ' is not a perfect cube')!else:! print('Cube root of ' + str(x) + ' is '+ str(ans))!

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Extendingscope

Onlyworksforposi0veintegers Easytofixbykeepingtrackofsign,lookingfor

solu0ontoposi0vecase

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Somecode

x = int(raw_input('Enter an integer: '))!ans = 0!

while ans**3 < abs(x):!ans = ans + 1!if ans**3 != abs(x):!

print(str(x) + ' is not a perfect cube')!else:!

if x < 0:!ans = - ans!

print('Cube root of ' + str(x) + ' is '+ str(ans))!

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Loopcharacteris0cs

Needaloopvariable Ini0alizedoutsideloopChangeswithinloopTestfortermina0ondependsonvariable

Usefultothinkaboutadecremen'ngfunc'onMapssetofprogramvariablesintoanintegerWhenloopisentered,valueisnon-nega0veWhenvalueis

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Whathappensifwemissacondi0on?

Supposewedontini0alizethevariable? Supposewedontchangethevariableinside

theloop?

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Exhaus0veenumera0on

Guessandcheckmethodscanworkonproblemswithafinitenumberofpossibili0es

Exhaus0veenumera0onisagoodwaytogenerateguessesinanorganizedmanner