forked from kamyu104/LeetCode-Solutions
-
Notifications
You must be signed in to change notification settings - Fork 0
/
letter-tile-possibilities.py
64 lines (55 loc) · 1.98 KB
/
letter-tile-possibilities.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
# Time: O(n^2)
# Space: O(n)
import collections
class Solution(object):
def numTilePossibilities(self, tiles):
"""
:type tiles: str
:rtype: int
"""
fact = [0.0]*(len(tiles)+1)
fact[0] = 1.0;
for i in xrange(1, len(tiles)+1):
fact[i] = fact[i-1]*i
count = collections.Counter(tiles)
# 1. we can represent each alphabet 1..26 as generating functions:
# G1(x) = 1 + x^1/1! + x^2/2! + x^3/3! + ... + x^count1/count1!
# G2(x) = 1 + x^1/1! + x^2/2! + x^3/3! + ... + x^count2/count2!
# ...
# G26(x) = 1 + x^1/1! + x^2/2! + x^3/3! + ... + x^count26/count26!
#
# 2. let G1(x)*G2(x)*...*G26(x) = c0 + c1*x1 + ... + ck*x^k, k is the max number s.t. ck != 0
# => ci (1 <= i <= k) is the number we need to divide when permuting i letters
# => the answer will be : c1*1! + c2*2! + ... + ck*k!
coeff = [0.0]*(len(tiles)+1)
coeff[0] = 1.0
for i in count.itervalues():
new_coeff = [0.0]*(len(tiles)+1)
for j in xrange(len(coeff)):
for k in xrange(i+1):
if k+j >= len(new_coeff):
break
new_coeff[j+k] += coeff[j]*1.0/fact[k]
coeff = new_coeff
result = 0
for i in xrange(1, len(coeff)):
result += int(round(coeff[i]*fact[i]))
return result
# Time: O(r), r is the value of result
# Space: O(n)
class Solution2(object):
def numTilePossibilities(self, tiles):
"""
:type tiles: str
:rtype: int
"""
def backtracking(counter):
total = 0
for k, v in counter.iteritems():
if not v:
continue
counter[k] -= 1
total += 1+backtracking(counter)
counter[k] += 1
return total
return backtracking(collections.Counter(tiles))