-
Notifications
You must be signed in to change notification settings - Fork 0
/
p113.py
66 lines (54 loc) · 1.22 KB
/
p113.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
LIMIT = 100
# x represents the increasing values
x = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] for i in range(LIMIT)]
for i in range(len(x[0])):
x[0][i] = 1
x[0][0] = 0
for i in range(1, len(x)):
for j in range(len(x[i])):
for k in range(j + 1):
x[i][j] += x[i-1][k]
# y represents the decreasing values
y = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0] for i in range(LIMIT)]
for i in range(len(y[0])):
y[0][i] = 1
y[0][0] = 0
for i in range(1, len(y)):
for j in range(len(y[i])):
for k in range(j, len(y[i])):
y[i][j] += y[i-1][k]
if LIMIT <= 6:
print(x)
print(y)
"""
Increasing numbers of 2 digit having 0 as the last digit:
"""
total = 0
for i in range(len(x)):
total += sum(x[i])
total += sum(y[i])
print(total - LIMIT*9) # TODO: Substract values which are at the same time increasing and decreasing, that is, numbers with all equal digits.
"""
If len was 3, we should take out:
1, 11, 111
2, 22, 222
3, 33, 333
4, 44, 444
5, 55, 555
6, 66, 666
7, 77, 777
8, 88, 888
9, 99, 999
Number of increasing numbers of 2 digits ending with
0 - 0
1 - 1 (11)
2 - 2 (12, 22)
3 - 3 (13, 23, 33)
4 - 4 (14, 24, 34, 44)
...
Number of increasing numbers of 3 digits ending with
0 - 0
1 - 1 (111)
2 - 3 (112, 122, 222)
3 - 6 (113, 123, 133, 223, 233, 333)
"""