Let us rewrite the Newton’s approximation of square with while loop.
def newton(x, y, tolerance=1e-6):
while abs(x**2 - y) > tolerance:
x = 0.5 * (x + y * 1.0 / x)
return x
def sqrt(y, tolerance=1e-6):
return newton(1, y, tolerance)
print sqrt(2)
print sqrt(3)
print sqrt(5)
Here’s the Euclidean algorithm rewritten using he while loop.
def gcd(a, b):
while b != 0:
temp = a
a = b
b = temp % b
return a
print gcd(50, 42)
print gcd(53, 11)
print gcd(304, 493)
Finally, we rewrite the definite integral.
def integral(f, a, b, k=500):
d = (b-a)*1.0/k
i = 0
sum = 0.0
while i < k:
sum += f(a + d/2 + i*d)
i += 1
return sum * d
print integral(lambda x: x**2, 0, 1)
print integral(lambda x: x**3, 0, 1, 10000)