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UniquePaths.py
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UniquePaths.py
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# Brute force
class Solution1:
def uniquePaths(self, m: int, n: int) -> int:
if m == 0 or n == 0:
return 0
if m == 1 or n == 1:
return 1
return self.uniquePaths(m - 1, n) + self.uniquePaths(m, n - 1)
# Reserve memorization:
class Solution2:
def uniquePaths(self, m: int, n: int) -> int:
# m is column, n is row
memo = [[0 for i in range(m)] for i in range(n)]
return self.findPaths(m, n, 0, 0, memo)
def findPaths(self, m: int, n: int, r: int, c: int, memo: [[int]]):
if r == n or c == m:
return 0
if r == n - 1 and c == m - 1:
return 1
if memo[r][c] == 0:
memo[r][c] = self.findPaths(m, n, r + 1, c, memo) + self.findPaths(m, n, r, c + 1, memo)
return memo[r][c]
# Dynamic programming:
class Solution3:
def uniquePaths(self, m: int, n: int) -> int:
# m is column, n is row
memo = [[0 for i in range(m)] for i in range(n)]
for i in range(m):
memo[0][i] = 1
for i in range(n):
memo[i][0] = 1
for i in range(1, n):
for j in range(1, m):
memo[i][j] = memo[i - 1][j] + memo[i][j - 1]
return memo[n - 1][m - 1]
print(Solution1().uniquePaths(3, 2))
# # expected: 3
print(Solution2().uniquePaths(7, 3))
# expected: 28
print(Solution3().uniquePaths(23, 12))
# # expected: 193536720