1.) ARGUMENT OF CORRECTNESS FOR CODE 2.) RUNTIME ANALYSIS FOR CODE CODE: \'\'\'r

Question

1.) ARGUMENT OF CORRECTNESS FOR CODE

2.) RUNTIME ANALYSIS FOR CODE

CODE:

'''returns the largest integer x such that x^k does not exceed n,

assuming k and n are both positive integers'''

def iroot(k, n):

    num=1

    #looping until num^k is greater than n

    while True:

        #checking if current number ^ k is greater than n

        if pow(num,k)>n:

            #returning previous number

            return num-1

        #moving to next number

        num+=1

#testing various cases

print(iroot(3,125)) #5

print(iroot(3,126)) #5

print(iroot(3,124)) #4

Explanation / Answer

in first function passing the value 3,125

initialize the num value to 1

and while will looping until false so the there is no statement of returning false, when the is conditon is true it will return.

in if condition it will check 1^3>n and 1^3=1 is grater than n value means condition will return false 1>125 the condition will false and if condition will not execute till the the num vaue will increase num=2

in second time the same process will execute and the num vaue will increase to num=3

in third time the same process will execute and the num vaue will increase to num=4

in fourth time the same process will execute and the num vaue will increase to num=5

in fifth time the same process will execute and the num vaue will increase to num=6

in sixth time in if conditon the 6^3=216 it will check 216>n means 216>125 yes then the if conditon will execute and the decrement the num value to 1 num=5 so it will return the 5

the same process will continue to second print statement and it will print 5

the same process will continue to third print statement and it will print 4

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