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# root code

def findRoot1(x, power, epsilon):

low = 0

high = x

ans = (high+low)/2.0

while abs(ans**power - x) > epsilon:

if ans**power < x:

low = ans

else:

high = ans

ans = (high+low)/2.0

return ans

##print findRoot1(25.0, 2, .001)

##print findRoot1(27.0, 3, .001)

##print findRoot1(-27.0, 3, .001)

# so can't find cube root of negative number

def findRoot2(x, power, epsilon):

if x < 0 and power%2 == 0:

return None

# can't find even powered root of negative number

low = min(0, x)

high = max(0, x)

ans = (high+low)/2.0

while abs(ans**power - x) > epsilon:

if ans**power < x:

low = ans

else:

high = ans

ans = (high+low)/2.0

return ans

##print findRoot2(25.0, 2, .001)

##print findRoot2(27.0, 3, .001)

##print findRoot2(-27.0, 3, .001)

##

##print findRoot2(0.25, 2, .001)

##print findRoot2(-0.125, 3, .001)

def findRoot3(x, power, epsilon):

if x < 0 and power%2 == 0:

return None

# can't find even powered root of negative number

low = min(-1.0, x)

high = max(1.0, x)

ans = (high+low)/2.0

while abs(ans**power - x) > epsilon:

if ans**power < x:

low = ans

else:

high = ans

ans = (high+low)/2.0

return ans

print findRoot3(25.0, 2, .001)

print findRoot3(27.0, 3, .001)

print findRoot3(-27.0, 3, .001)

print findRoot3(0.25, 2, .001)

print findRoot3(-0.125, 3, .001)

def testFindRoot():

epsilon = 0.0001

for x in (0.25, -0.25, 2, -2, 8, -8):

for power in range(1,4):

print('Testing x = ' + str(x) +\

' and power = ' + str(power))

res = findRoot3(x, power, epsilon)

if res == None:

print(' No root')

else:

print(' ' + str(res**power) + ' ~= ' + str(x))