-
Notifications
You must be signed in to change notification settings - Fork 263
/
061 Unique Paths.py
67 lines (52 loc) · 1.86 KB
/
061 Unique Paths.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
67
"""
A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner
of the grid (marked 'Finish' in the diagram below).
How many possible unique paths are there?
Above is a 3 x 7 grid. How many possible unique paths are there?
Note: m and n will be at most 100.
"""
import math
__author__ = 'Danyang'
class Solution(object):
def uniquePaths(self, m, n):
"""
Math solution:
if total m+n steps
(m+n) \choose m as down, the remain n as right.
mCn = n!/m!(n-m)!
:param m:
:param n:
:return:
"""
m -= 1
n -= 1
return math.factorial(m+n) / (math.factorial(n) * math.factorial(m))
def uniquePathsDP(self, m, n):
F = [[0 for _ in xrange(n+1)] for _ in xrange(m+1)]
F[1][0] = 1 # dummy entry point
for i in xrange(1, m+1):
for j in xrange(1, n+1):
F[i][j] = F[i-1][j] + F[i][j-1]
return F[m][n]
def uniquePathsNormal(self, m, n):
"""
dp
Let F be number of unique paths at position i, j
F[i][j] = F[i-1][j] + F[i][j-1]
:param m:
:param n:
:return: an integer
"""
F = [[0 for _ in xrange(n)] for _ in xrange(m)]
F[0][0] = 1 # start
# F[i][j] = F[i-1][j] + F[i][j-1]
for i in xrange(m):
for j in xrange(n):
if i == 0 and j == 0: continue
if i == 0: F[i][j] = F[i][j-1]
elif j == 0: F[i][j] = F[i-1][j]
else: F[i][j] = F[i-1][j]+F[i][j-1]
return F[m-1][n-1]
if __name__ == "__main__":
assert Solution().uniquePaths(3, 7) == 28