unique_path
unique_path.py 源码
# 不同路径
# 使用分治的思想，递归解决
def unique_path_1(m: int, n: int) -> int:
def helper(a, b, i, j) -> int:
if i == a and j == b:
return 1
x, y = 0, 0
if i < a:
x = helper(a, b, i + 1, j)
if j < b:
y = helper(a, b, i, j + 1)
return x + y
return helper(m, n, 1, 1)
# 动态规划的思路解决
def unique_path_2(m: int, n: int) -> int:
# dp = [[1 for _ in range(n)] for _ in range(m)]
dp = [[1] * n] * m
for i in range(1, m):
for j in range(1, n):
dp[i][j] = dp[i - 1][j] + dp[i][j - 1]
return dp[-1][-1]
# 简化一维的写法
def unique_path_3(m: int, n: int) -> int:
dp = [1] * n
for i in range(1, m):
for j in range(1, n):
dp[j] += dp[j - 1]
return dp[-1]
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