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import math
def fac(n):
    n = round(n)
    if n == 0:
        return 1
    else:
        return n*fac(n-1)

def Fac(n):
    n = round(n)
    if n == 0:
        return 1
    else:
        sum = 1
        for i in range(1,n+1):
            sum *= i
        return sum


def runtime(s):
    import time
    time1 = time.clock()
    fac(s)
    time2 = time.clock()
    Fac(s)
    time3 = time.clock()
    math.factorial(s)
    time4 = time.clock()   

    x1 = time2 - time1
    x2 = time3 - time2
    x3 = time4 - time3
    print('The time function "fac" spent was: ', x1, 'seconds.')
    print('The time function "Fac" spent was: ', x2, 'seconds.')
    print('The time function "math.factorial" spent was: ', x3, 'seconds.')

>>> runtime(5)
The time function "fac" spent was:  1.1999999999900979e-05 seconds.
The time function "Fac" spent was:  8.000000000230045e-06 seconds.
The time function "math.factorial" spent was:  3.000000000419334e-06 seconds.
>>> runtime(10)

The time function "fac" spent was:  1.4000000000180535e-05 seconds.
The time function "Fac" spent was:  9.000000000369823e-06 seconds.
The time function "math.factorial" spent was:  2.9999999995311555e-06 seconds.
>>> runtime(20)

The time function "fac" spent was:  2.3000000000550358e-05 seconds.
The time function "Fac" spent was:  9.999999999621423e-06 seconds.
The time function "math.factorial" spent was:  3.000000000419334e-06 seconds.
>>> runtime(50)

The time function "fac" spent was:  4.2000000000541604e-05 seconds.
The time function "Fac" spent was:  1.4999999999432134e-05 seconds.
The time function "math.factorial" spent was:  5.999999999950489e-06 seconds.

def Sqrt(x):
    tol = 1e-8
    x0 = x
    diff = abs(x0**2 - x)
    while diff > tol:
        x0 = (x0**2 + x)/(2*x0)
        diff = abs(x0**2 - x)

    return(x0)

def most_frequent(S):
    S.lower()
    dic = dict()    # create an empty dictionary
    for i in S:
        dic[i] = 1 + dic.get(i, 0) # fill up the dictionary with letters and their freq
    t = []
    for i in dic:
        t.append((dic[i], i))   # create a tuple from the dictionary
    res = sorted(t, reverse = True)     # sort the tuple
    for x, y in res:
        print(y, x)

data = open("word.txt")
x = data.read()
print(most_frequent(x))

 7959
e 4958
t 3581
a 2892
o 2884
i 2810
n 2609
s 2500
r 2271
h 1944
l 1698
d 1270
c 1262
u 1105
m 927
p 829
y 764
f 711
g 674
w 635
b 602
v 457
, 404
. 356
k 273

 236
’ 154
T 97
A 94
I 92
S 90
x 87
- 74
E 62
j 54
W 53
B 46
– 44
‘ 41
q 40
: 40
C 38
0 37
L 34
1 32
? 31
R 30
P 30
O 29
M 29
H 29
D 29
N 26
; 26
' 24
F 23
2 21
) 21
( 21
G 19
9 19
Y 17
U 17
K 15
z 14
7 11
J 10
V 9
6 9
8 6
5 6
4 6
… 4
] 4
[ 4
& 4
! 4
” 3
“ 3
Z 3
é 2
3 2
— 1
Q 1
% 1