HO3 Bisection

x = 25
low = 0
high = x
epsilon = .01
increment = 0.001
ans = (low + high)/2.0
guesses = 0

while abs(ans*ans - x) >= epsilon:
    if ans*ans > x:
        high = ans
    else:
        low = ans
    guesses += 1
    ans = (high + low)/2.0
print guesses
if abs(ans*ans - x) < epsilon:
    print "The square root of ", x, "within a margin of ", epsilon, " is ", ans
else:
    print "no square root"

# 1. 12.25*12.25 > x. Low = 0, High = 25, ans =(0+25)/2 = 12.25
# 2. 6.25*6.25 > x. Low = 0, High = 12.25, (0 + 12.5)/2= 6.25
# 3. 3.125*3.125 < x. low =0, High = 6.25, ans = (0, 6.25)/2 = 3.125
# 4. low = ans 3.125, High = 6.25